# Berry-curvature-induced linear magnetotransport in magnetic Weyl semimetals

Zetao Zhang  State Key Laboratory of Low Dimensional Quantum Physics and
Department of Physics, Tsinghua University, Beijing 100084, China  Yizhou Liu
<EMAIL_ADDRESS>Department of Condensed Matter Physics, Weizmann
Institute of Science, Rehovot 76100, Israel  Wenhui Duan  State Key Laboratory
of Low Dimensional Quantum Physics and Department of Physics, Tsinghua
University, Beijing 100084, China  Institute for Advanced Study, Tsinghua
University, Beijing 100084, China  Frontier Science Center for Quantum
Information, Beijing 100084, China

###### Abstract

Magnetotransport such as the giant magnetoresistance and Hall effect lies at
the heart of fundamental physics and technologies. Recently, some experiments
have clearly demonstrated linear magnetotransport (LMT) proportional to
magnetic field but the underlying physical mechanism is still unclear. In this
work, we show that Berry curvature effect is a new mechanism dominating the
LMT. The Berry-curvature-induced LMT widely exists in 66 out of 122 magnetic
point groups. For typical magnetic Weyl semimetals Co3Sn2S2 and ferromagnetic
MnBi2Te4, Berry curvature induces LMT conductivities reaching orders of
$10^{4}$ and $10^{2}$ ${\rm\Omega^{-1}m^{-1}}$ per tesla, respectively, which
are tunable through magnetization canting induced by moderate magnetic fields.
We further reveal that Berry-curvature-induced LMT can be detected by Hall
effect and especially intrinsic magnetoresistance exceeding $100\%$ per tesla
insensitive to the sample quality. Our results agree with recent experiments
and uncover the important role of Berry curvature in LMT.

Introduction.—Concepts of Berry phase and curvature have revolutionized modern
condensed matter physics Xiao  _et al._ (2010); Vanderbilt (2018), and are
essential for the description of various topological materials Hasan and Kane
(2010); Qi and Zhang (2011); Yan and Felser (2017); Armitage  _et al._ (2018);
Sato and Ando (2017). In Weyl semimetals (WSMs), Berry curvature is especially
prominent, due to the existence of two-fold degenerate points acting as
monopoles of Berry curvature Yan and Felser (2017); Armitage  _et al._ (2018).
As a consequence, Berry curvature introduces strong modifications to the
electron motion Sundaram and Niu (1999); Xiao  _et al._ (2010) and is closely
related to various exotic magnetotransport phenomena Nandy  _et al._ (2017);
Gao (2019); Liu  _et al._ (2021) such as the negative magnetoresistance (MR)
Son and Spivak (2013); Burkov (2014), a chiral magnetic effect Fukushima  _et
al._ (2008); Zyuzin and Burkov (2012); Armitage  _et al._ (2018) which
originates from chiral anomaly as inspired from the studies in particle
physics Adler (1969); Bell and Jackiw (1969); Nielsen and Ninomiya (1983) and
has been confirmed experimentally Huang  _et al._ (2015).

Lying at the heart of physics and technologies, magnetotransport is
characterized by the Hall effect and MR corresponding to the antisymmetric and
symmetric parts of resistivity tensor $\rho_{\alpha\beta}$, respectively.
According to Onsager’s relation:
$\rho_{\alpha\beta}(\bm{m},\bm{B})=\rho_{\beta\alpha}(-\bm{m},-\bm{B})$ with
$\bm{m}$ and $\bm{B}$ being the magnetization and magnetic field, respectively
Onsager (1931); Tokura and Nagaosa (2018), for nonmagnetic materials the
lowest order dependence of MR on magnetic field is $B^{2}$, which is the case
of ordinary MR effect (Fig. 1(a)). However, for magnetic materials linear MR
proportional to $B$ could exist (Fig. 1(b)). In linear magnetotransport (LMT)
proportional to $B$, except for the ordinary Hall effect originating from
Lorenz force, linear MR has also been observed in various topological
materials, such as quantum anomalous Hall insulators Chang  _et al._ (2013);
Deng  _et al._ (2020), Dirac semimetals Feng  _et al._ (2015); Liang  _et al._
(2015); Novak  _et al._ (2015); Narayanan  _et al._ (2015); Zhao  _et al._
(2015) and topological insulators Tang  _et al._ (2011); Wang  _et al._
(2012); Wang and Lei (2012), where the underlying mechanisms are attributed to
topological edge states Checkelsky  _et al._ (2012); Chang  _et al._ (2013),
Zeeman splitting Feng  _et al._ (2015); Liang  _et al._ (2015); Wang and Lei
(2012), disorders Parish and Littlewood (2003, 2005); Novak  _et al._ (2015);
Narayanan  _et al._ (2015) or Landau levels Abrikosov (1998, 2000); Zhao  _et
al._ (2015); Wang  _et al._ (2012). Although LMT is extensively studied, the
role of Berry curvature in LMT is still unclear in realistic materials.

Figure 1: Schematics of (a) quardratic magnetoresistance (MR) in nonmagnetic
materials and (b) linear MR in magnetic materials at small magnetic field $B$,
respectively. The upper (lower) panel shows the electrical conductivity
$\sigma$ (magnetization $m$) as a function of external magnetic field $B$.

In this work we clarify the role of Berry curvature in LMT and reveal its
dominance in recent LMT experiments on magnetic WSMs. We find Berry-curvature-
induced LMT is widely supported by 66 out of all 122 magnetic point groups
(MPGs). Based on first-principles calculations, we predict Berry curvature
induces LMT conductivities up to $10^{4}$ and $10^{2}$
${\rm\Omega^{-1}m^{-1}}$ per tesla in representative magnetic WSMs Co3Sn2S2
and ferromagnetic (FM) MnBi2Te4, respectively, which can be tuned through
magnetization canting induced by moderate magnetic fields. Experimentally,
Berry-curvature-induced LMT can be characterized by signatures including
linear Hall resistance and especially intrinsic linear MR up to $100\%$ per
tesla. Our analyses are well consistent with recent LMT experiments on
Co3Sn2S2 and FM MnBi2Te4 Jiang  _et al._ (2021a); Li  _et al._ (2021); Lei
_et al._ (2020); Zhu  _et al._ (2020); Huan  _et al._ (2021), supporting that
LMT in these two materials is mostly contributed by Berry curvature through
modifying density of states (DOS) exp . These results deepen understandings of
Berry-curvature-induced LMT and reveal the importance of Berry curvature in
LMT.

Theory of Berry-curvature-induced LMT.—Based on semiclassical theory Sundaram
and Niu (1999); Xiao  _et al._ (2010), the electric current is
$j_{\alpha}=\sigma^{0}_{\alpha\beta}E_{\beta}+\sigma^{\text{LMT}}_{\alpha\beta\gamma}E_{\beta}B_{\gamma}$
up to linear responses of both electric and magnetic fields $\bm{E}$ and
$\bm{B}$ (see details in section S1 of Supplemental Material (SM) SM ), where
$\sigma^{0}_{\alpha\beta}$ includes magnetic-field-independent Drude and
anomalous Hall conductivities and
$\sigma^{\text{LMT}}_{\alpha\beta\gamma}B_{\gamma}$ gives Berry-curvature-
induced LMT conductivity. $\sigma^{\text{LMT}}_{\alpha\beta\gamma}$ includes
three parts SM ; Das and Agarwal (2019):

$\sigma^{\text{LMT}}_{\alpha\beta\gamma}=-\chi_{\alpha\beta\gamma}+\chi_{\alpha}\delta_{\beta\gamma}+\chi_{\beta}\delta_{\alpha\gamma},$
(1)

where the rank-3 tensor $\chi_{\alpha\beta\gamma}$ is given by

$\chi_{\alpha\beta\gamma}=\frac{e^{3}\tau}{\hbar}\sum_{n}\int\frac{d^{3}k}{(2\pi)^{3}}~{}v^{\alpha}_{n\bm{k}}v^{\beta}_{n\bm{k}}\Omega^{\gamma}_{n\bm{k}}\left(-\frac{\partial
f^{0}_{n\bm{k}}}{\partial\varepsilon_{n\bm{k}}}\right),$ (2)

and the rank-1 tensors are given by $\chi_{\alpha}=\chi_{\alpha\gamma\gamma}$
and $\chi_{\beta}=\chi_{\beta\gamma\gamma}$. Einstein’s convention of
summation over repeated indices is assumed. In Eq. (2), $f^{0}_{n\bm{k}}$ is
the Fermi-Dirac distribution, $\tau$ is the relaxation time,
$\bm{v}_{n\bm{k}}$ is the group velocity, and $\bm{\Omega}_{n\bm{k}}$ is the
Berry curvature of the $n$-th band. The first term on the right-hand side of
Eq. (1) (the rank-3 tensor $\chi_{\alpha\beta\gamma}$) originates from
modified DOS while the following two (the rank-1 tensors
$\chi_{\alpha,\beta}$) originate from chiral anomaly and $\bm{B}$-induced
anomalous velocity as detailedly discussed in section S1 of SM SM . Because
$-\partial
f^{0}_{n\bm{k}}/\partial\varepsilon_{n\bm{k}}\approx\delta(\mu-\varepsilon_{n\bm{k}})$
at low temperature with $\mu$ the chemical potential, the LMT is mainly
determined by the electronic states near the Fermi surface. Due to the
invariance of $\chi_{\alpha\beta\gamma}$ by exchanging $\alpha$ and $\beta$,
LMT conductivity $\sigma^{\text{LMT}}_{\alpha\beta\gamma}B_{\gamma}$ is a
symmetric tensor, distinguishing itself from the antisymmetric linear Hall
conductivity $\sigma^{\text{H}}_{\alpha\beta\gamma}B_{\gamma}$ Tan  _et al._
(2021).

Table 1: List of all 122 magnetic point groups classified by the existence of rank-3 and rank-1 tensors $\chi_{\alpha\beta\gamma}$ and $\chi_{\alpha,\beta}$. $\checkmark$ means at least one tensor component is nonzero while $\times$ means the tensor is completely forbidden. In Berry-curvature-induced LMT, $\chi_{\alpha\beta\gamma}$ corresponds to the mechanism of modified density of states, and $\chi_{\alpha,\beta}$ correspond to mechanisms of chiral anomaly and $\bm{B}$-induced anomalous velocity. Magnetic point groups | $\chi_{\alpha\beta\gamma}$ | $\chi_{\alpha,\beta}$
---|---|---
11′, $\overline{1}1^{\prime}$, $\overline{1}^{\prime}$, 21′, m1′, 2/m1′, 2′/m, 2/m′, 2221′, mm21′, mmm1′, m′mm, m′m′m′, 41′, $\overline{4}1^{\prime}$, 4/m1′, 4/m′, 4′/m′, 4221′, 4mm1′, $\overline{4}2m1^{\prime}$, 4/mmm1′, 4/m′mm, 4′/m′m′m, 4/m′m′m′, 31′, $\overline{3}1^{\prime}$, $\overline{3}^{\prime}$, 321′, 3m1′, $\overline{3}m1^{\prime}$, $\overline{3}^{\prime}$m, $\overline{3}^{\prime}$m′, 61′, $\overline{6}1^{\prime}$, 6/m1′, 6′/m, 6/m′, 6221′, 6mm1′, $\overline{6}$m$21^{\prime}$, 6/mmm1′, 6/m′mm, 6′/mmm′, 6/m′m′m′, 231′, m$\overline{3}1^{\prime}$, m${}^{\prime}\overline{3}^{\prime}$, 432, 4321′, $\overline{4}3$m, $\overline{4}3$m1′, m$\overline{3}$m, m$\overline{3}$m1′, m${}^{\prime}\overline{3}^{\prime}$m, m${}^{\prime}\overline{3}^{\prime}$m′ | $\times$ | $\times$
222, mm2, mmm, 4′, $\overline{4}^{\prime}$, 4′/m, 422, 4′22′, 4mm, 4′m′m, $\overline{4}2$m, $\overline{4}^{\prime}$2′m, $\overline{4}^{\prime}$2m′, 4/mmm, 4′/mm′m, 32, 3m, $\overline{3}$m, 6′, $\overline{6}^{\prime}$, 6′/m′, 622, 6′22′, 6mm, 6′mm′, $\overline{6}$m2, $\overline{6}^{\prime}$m′2, $\overline{6}^{\prime}$m2′, 6/mmm, 6′/m′mm′, 23, m$\overline{3}$, 4′32′, $\overline{4}^{\prime}$3m′, m$\overline{3}$m′ | $\checkmark$ | $\times$
1, $\overline{1}$, 2, 2′, m, m′, 2/m, 2′/m′, 2′2′2, m′m2′, m′m′2, m′m′m, 4, $\overline{4}$, 4/m, 42′2′, 4m′m′, $\overline{4}2^{\prime}$m′, 4/mm′m′, 3, $\overline{3}$, 32′, 3m′, $\overline{3}$m′, 6, $\overline{6}$, 6/m, 62′2′, 6m′m′, $\overline{6}$m′2′, 6/mm′m′ | $\checkmark$ | $\checkmark$

General symmetry properties of LMT.—Because both $\bm{v}_{n\bm{k}}$ and
$\bm{\Omega}_{n\bm{k}}$ are odd under time reversal symmetry (TRS,
$\mathcal{T}$), tensors $\chi_{\alpha\beta\gamma}$ and $\chi_{\alpha,\beta}$
are forbidden by TRS. Besides, crystalline symmetries also place strong
constraints on LMT (see details in section S2 of SM SM ). We further find that
both $\chi_{\alpha\beta\gamma}$ and $\chi_{\alpha,\beta}$ must also vanish in
those crystals with combined inversion-time-reversal symmetry $\mathcal{PT}$,
and cubic point groups $O$, $T_{d}$, and $O_{h}$ including four-fold rotation
symmetries $\\{C_{4x},C_{4y},C_{4z}\\}$ or improper rotation symmetries
$\\{\mathcal{P}C_{4x},\mathcal{P}C_{4y},\mathcal{P}C_{4z}\\}$ even if TRS is
broken. Moreover, $\chi_{\alpha,\beta}$ must vanish while
$\chi_{\alpha\beta\gamma}$ survives in those crystals having $C_{nv}$
symmetry, combined rotation-time-reversal symmetry $C_{n}\mathcal{T}$ ($n\neq
2$), or two perpendicular rotation symmetries $C_{n}$ and $C^{\prime}_{n}$.
Then all the MPGs supporting Berry-curvature-induced LMT can be identified as
summarized in Table 1. It is found that 66 MPGs support
$\chi_{\alpha\beta\gamma}$ among which 31 also support $\chi_{\alpha,\beta}$.
Table 1 is a guiding principle to search for materials supporting Berry-
curvature-induced LMT.

Figure 2: (a)-(b) Schematics of band-resolved LMT tensor
$\chi_{\alpha\beta\gamma}$ for (a) untilted and (b) tilted Weyl cones,
respectively. Red (Blue) color represents the plus (minus) sign of
$\chi_{zxx,n\bm{k}}{\sim}v_{n\bm{k}}^{z}v_{n\bm{k}}^{x}{\Omega}_{n\bm{k}}^{x}$
and the thickness of color represents its magnitude. Orange circles represent
Fermi surfaces with their top view shown by insets. (c)-(d) Calculated LMT
tensors of the tilted Weyl cone model [i.e., Eq. (3)] with $\hbar v_{\rm
F}=6.6$ eV$\cdot\mathrm{\AA}$. $\bar{\chi}$ is dimensionless, defined as
$\chi/\chi_{0}$ with $\chi_{0}=e^{3}\tau v_{\rm F}/2h^{2}$. (c) LMT tensors as
functions of the tilting parameter $t=v_{\rm t}/v_{\rm F}$ with chemical
potential $\mu=0.1$ eV. (d) LMT tensors as functions of chemical potential for
a type-II Weyl cone with $t=1.5$. Figure 3: Berry-curvature-induced LMT
conductivities in magnetic Weyl semimetals (a)-(c) Co3Sn2S2 and (d)-(f) FM
MnBi2Te4. (a)(d) Crystal structure (left panel) and distribution of Weyl
points (right panel) for Co3Sn2S2 and FM MnBi2Te4. Gray arrows represent
magnetic moments, and red (blue) dots within Brillouin zone represent Weyl
points with positive (negative) chirality. $\theta^{\rm CSS}$ and $\theta^{\rm
MBT}$ are angles between magnetization and $z$ axis, used in the following.
$\theta^{\text{CSS}}=\theta^{\text{MBT}}=0$ here. (b)(e) Band structures
including spin-orbit coupling. Size of the red dots indicates the magnitude of
Berry curvature $|\bm{\Omega}_{n\bm{k}}|$. (c)(f) Independent nonzero
components of $\sigma^{\text{LMT}}_{\alpha\beta\gamma}$ as functions of
chemical potential $\mu$.

LMT in tilted Weyl cone model.—The fact that Berry-curvature-induced LMT
requires TRS breaking further motivates us to study magnetic WSMs. We start
from considering a Weyl cone model with TRS broken by finite tilting:

$H_{\bm{k}}=s\hbar v_{\rm F}\bm{k}\cdot\bm{\sigma}+s\hbar v_{\rm t}k_{z},$ (3)

where $s=\pm$ refers to the chirality of Weyl point (WP), $v_{\text{F}}$ is
the Fermi velocity, and $t=v_{\rm t}/v_{\rm F}$ is a parameter describing the
tilting of Weyl cone which is assumed along the $z$ direction. The Weyl cone
model which is isotropic in the $k_{x}k_{y}$ plane allows only 4 independent
nonzero LMT tensor components: $\chi_{xxz}$, $\chi_{zxx}$, $\chi_{zzz}$ and
$\chi_{z}$, whose analytical expressions are calculated explicitly in section
S3 of SM SM . Their tilting dependence is shown in Fig. 2(c). For an untilted
Weyl cone with $t=0$, LMT tensors vanish because of the cancellation of
$v_{n\bm{k}}^{\alpha}v_{n\bm{k}}^{\beta}{\Omega}_{n\bm{k}}^{\gamma}$ between
$\pm\bm{k}$ when integrating over the Fermi surface [Fig. 2(a)]. After
increasing tilting breaks such a cancellation [Fig. 2(b)], LMT tensors exhibit
an overall increase and reverse sign between $\pm t$ for both type-I ($|t|<1$)
and type-II ($|t|>1$) Weyl cones. On the other hand, LMT tensors are
independent of chemical potential $\mu$ for a type-I Weyl cone and insensitive
to $\mu$ for a type-II Weyl cone as shown in Fig. 2(d). This is because the
Berry curvature is proportional to $1/\mu^{2}$ while the Fermi surface area is
proportional to $\mu^{2}$. Figure 2(d) only shows the $\mu>0$ region because
LMT tensors are invariant between $\mu$ and $-\mu$. In magnetic WSMs, a pair
of Weyl cones related by inversion symmetry contribute to LMT equally because
of their simultaneously opposite tiltings and chiralities.

LMT in magnetic WSM materials.—Then we investigate LMT concretely in magnetic
WSMs Co3Sn2S2 and FM MnBi2Te4 (see details of first-principles calculations in
section S4 of SM SM ) whose structures and Brillouin zones are shown in Figs.
3(a) and (d), respectively. They have attracted much attentions because of
their correlated magnetism and band topology Xu  _et al._ (2018); Liu  _et
al._ (2018); Wang  _et al._ (2018); Morali  _et al._ (2019); Liu  _et al._
(2019); Li  _et al._ (2019a, b); Zhang  _et al._ (2019); Gong  _et al._
(2019); Liu  _et al._ (2020); Deng  _et al._ (2020). They both belong to MPG
$\overline{3}$m′ including inversion $\mathcal{P}$, three-fold rotation
$C_{3z}$ and the combined mirror-time-reversal $M_{x}\mathcal{T}$ symmetries,
where $\chi_{\alpha\beta\gamma}$ and $\chi_{\alpha,\beta}$ both exist as shown
in Table 1. Co3Sn2S2 is one of the few experimentally confirmed magnetic WSMs
with an out-of-plane FM ground state Liu  _et al._ (2018); Wang  _et al._
(2018); Morali  _et al._ (2019); Liu  _et al._ (2019). There are totally three
pairs of WPs related by $\mathcal{P}$ and $C_{3z}$ at about 60 meV above the
Fermi level Xu  _et al._ (2018). MnBi2Te4 possesses extraordinarily rich
topological phases with an out-of-plane antiferromagnetic (AFM) ground state
Li  _et al._ (2019a, b); Zhang  _et al._ (2019); Gong  _et al._ (2019); Liu
_et al._ (2020); Deng  _et al._ (2020) but can also be tuned to FM under a
moderate magnetic field due to the weak interlayer AFM coupling Zhu  _et al._
(2020); Li  _et al._ (2021); Huan  _et al._ (2021); Jiang  _et al._ (2021b);
Lee  _et al._ (2021); Lei  _et al._ (2022). FM MnBi2Te4 possesses a pair of
$\mathcal{P}$-related WPs tilting along $z$ on -Z-$\Gamma$-Z near the Fermi
level as predicted by calculations Li  _et al._ (2019a, b) and evidenced by
experiments Zhu  _et al._ (2020); Li  _et al._ (2021); Huan  _et al._ (2021);
Jiang  _et al._ (2021b); Lee  _et al._ (2021); Lei  _et al._ (2022).

Figure 3(b) gives the band structure and band-resolved Berry curvature
distribution of Co3Sn2S2 including spin-orbit coupling with a WP shown along
$\Gamma$-A and L-B. Except for bands near WPs, considerable Berry curvature
also distributes on bands near quasi-degenerate points, thus significantly
contributing to LMT. Relaxation time of Co3Sn2S2 is estimated as 1 ps by
$\tau=m^{\ast}\mu_{\rm c}/e$, where effective mass $m^{\ast}$ and mobility
$\mu_{\rm c}$ are adopted from experiments Liu  _et al._ (2018); Ding  _et
al._ (2021, 2019); Shen  _et al._ (2019); Zhou  _et al._ (2020). MPG
$\overline{3}$m′ allows four independent nonzero components of
$\sigma_{\alpha\beta\gamma}^{\rm LMT}$ including $\sigma^{\rm LMT}_{xxy}$,
$\sigma^{\rm LMT}_{xxz}$, $\sigma^{\rm LMT}_{xzx}$ and $\sigma^{\rm
LMT}_{zzz}$ ind . Their chemical potential dependence is shown in Fig. 3(c),
reaching an order of $10^{4}~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$ and showing a
sign reversal around $\mu=0$. Calculated LMT tensors in section S5 of SM SM
show that the only symmetry allowed rank-1 tensor component $\chi_{z}$ is much
smaller than rank-3 tensor $\chi_{\alpha\beta\gamma}$ due to the cancellation
between $\chi_{zxx}=\chi_{zyy}$ and $\chi_{zzz}$, indicating that Berry
curvature induces LMT in Co3Sn2S2 mainly by modifying DOS.

In FM MnBi2Te4, LMT is mainly induced by Berry curvature distributed around
WPs as shown by band structure in Fig. 3(e). Relaxation time of FM MnBi2Te4 is
estimated as 0.04 ps from experiments Lee  _et al._ (2021); Jiang  _et al._
(2021b). Figure 3(f) shows calculated $\sigma^{\rm LMT}_{\alpha\beta\gamma}$,
reaching an order of $10^{2}~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$. In addition the
$\sigma^{\text{LMT}}_{xxy}$ is significantly smaller compared with other
components, which is consistent with our previous model analysis where
$\chi_{xxy}=-\sigma^{\rm LMT}_{xxy}$ vanishes due to the isotropy of ideal
Weyl cone within the $k_{x}k_{y}$ plane. Small $\sigma^{\rm LMT}_{xxy}$ in FM
MnBi2Te4 comes from weak anisotropy of WPs due to the three-fold rotation
symmetry $C_{3z}$ along $z$ axis. According to the calculated LMT tensors in
section S5 of SM SM , mechanisms of modified DOS, chiral anomaly and
$\bm{B}$-induced anomalous velocity all give significant contribution to LMT.

Figure 4: Effects of magnetization canting (see the definition of angles
$\theta^{\rm CSS}$ and $\theta^{\rm MBT}$ in the insets of Figs. 3(a) and (d),
respectively) on Berry-curvature-induced LMT of (a) Co3Sn2S2 and (b) FM
MnBi2Te4. $\chi_{y,z}$ are taken as examples and other tensor components are
shown in section S7 of SM SM .

Effects of magnetization canting.—Although both Co3Sn2S2 and FM MnBi2Te4 have
easy axes along $z$, their magnetization directions can be canted away from
the $z$ axis by external magnetic fields. In Co3Sn2S2 and FM MnBi2Te4,
required magnetic fields to overcome the magnetic anisotropy energy are less
than 10 T and 2 T respectively (see section S6 of SM SM ), which are
experimentally achievable. Figure 4 shows calculated $\chi_{y}$ and $\chi_{z}$
of both materials as functions of canting angle and chemical potential. Other
LMT tensor components exhibit similar qualitative features as shown in section
S7 of SM SM . Berry-curvature-induced LMT is generally robust against small
magnetization canting introduced by perturbative magnetic fields, while is
tunable by larger canting and greatly enhanced at certain canting angles. Our
further analyses show that Berry-curvature-induced LMT is tuned by
magnetization canting due to the coupling between Berry curvature and
magnetization canting in Co3Sn2S2 and also the change of band structure in FM
MnBi2Te4 (see details in section S8 of SM SM ). The tunable LMT is promising
for future experimental investigations.

Characteristic LMT signatures.—Then we give all characteristic signatures to
detect Berry-curvature-induced LMT experimentally. As aforementioned, Berry
curvature only induces symmetric part of conductivity, i.e., the linear
magnetoconductance (MC). While for resistivity, Berry curvature could induce
both the symmetric linear MR and antisymmetric linear Hall resistivity, due to
the mixture between Drude conductivity, anomalous Hall conductivity and linear
MC. In section S9 of SM SM , all conductivities and resistivities constrained
by MPG $\overline{3}$m′ are listed explicitly and discussed in detail.

Interestingly, we identify intrinsic components of linear MC and linear MR
that are independent of relaxation time $\tau$, thus irrelevant to the quality
of samples in experiments and solely determined by the intrinsic electronic
structure. They serve as ideal quantities for comparison between theory and
experiment. These components are

$\displaystyle\begin{split}\mathrm{MC}_{\alpha\alpha}&=\frac{\sigma_{\alpha\alpha}(\bm{B})-\sigma_{\alpha\alpha}(0)}{\sigma_{\alpha\alpha}(0)}=\frac{\sigma^{\text{LMT}}_{\alpha\alpha\gamma}B_{\gamma}}{\sigma^{\rm
Drude}_{\alpha\alpha}},\end{split}$
$\displaystyle\begin{split}\mathrm{MR}_{zz}&=\frac{\rho_{zz}(\bm{B})-\rho_{zz}(0)}{\rho_{zz}(0)}=\frac{\sigma^{\text{LMT}}_{zz\gamma}B_{\gamma}}{\sigma^{\rm
Drude}_{zz}},\end{split}$ (4)

where $\alpha=x,y,z$. Their dependence on $\tau$ is eliminated because Drude
conductivity $\sigma^{\rm Drude}_{\alpha\alpha}$ and LMT conductivity
$\sigma^{\text{LMT}}_{\alpha\beta\gamma}B_{\gamma}$ are both proportional to
$\tau$. For MnBi2Te4 whose ground state is AFM, $\sigma_{\alpha\alpha}(0)$ and
$\rho_{zz}(0)$ of FM MnBi2Te4 can be extrapolated from data at higher magnetic
fields where FM state is stabilized. According to Eq. (4), materials with a
large $\sigma^{\text{LMT}}_{\alpha\alpha\gamma}$ but a small $\sigma^{\rm
Drude}_{\alpha\alpha}$, i.e., materials with large Berry curvature but small
Fermi surface, such as magnetic WSMs, are favored by these intrinsic
signatures. Figure 5(a) and (b) show the ${\rm MC}_{\alpha\alpha}$ and ${\rm
MR}_{zz}$ for Co3Sn2S2 and FM MnBi2Te4, respectively, exhibiting an
enhancement when $\mu$ approaches the energy of WPs. Due to large Fermi
surfaces contributed by bands irrelevant to WPs, they are small in Co3Sn2S2.
While for FM MnBi2Te4 with small Fermi surfaces, $\mathrm{MR}_{zz}$ and
$\mathrm{MC}_{zz}$ reach a large value exceeding 100% per tesla, which can be
easily examined by future experiments.

Figure 5: Intrinsic linear magnetoconductance and magnetoresistance components
$\mathrm{MC}_{\alpha\alpha}$ ($\alpha=x,y,z$) and
$\mathrm{MR}_{zz}=\mathrm{MC}_{zz}$ of (a) Co3Sn2S2 and (b) FM MnBi2Te4 when
magnetic field and magnetization both point along $z$ axis. Because of
$C_{3z}$ symmetry, $\mathrm{MC}_{xx}=\mathrm{MC}_{yy}$.

Comparison with experiments.—Finally, we consider recent LMT experiments Jiang
_et al._ (2021a); Li  _et al._ (2021); Lei  _et al._ (2020); Zhu  _et al._
(2020); Huan  _et al._ (2021), which can not be explained by previous theories
Parish and Littlewood (2003, 2005); Abrikosov (1998, 2000). In Co3Sn2S2,
linear MR components ${\rm MR}_{yx}(B_{x})$ and ${\rm MR}_{xx}(B_{y})$ are
observed Jiang  _et al._ (2021a). Corresponding components of $\sigma^{\rm
LMT}_{\alpha\beta\gamma}$ are $\sigma^{\rm
LMT}_{yxx}{=}1360~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$ and $\sigma^{\rm
LMT}_{xxy}{=}1300~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$ from experimental data met .
In our calculations, $\sigma^{\rm LMT}_{yxx}=\sigma^{\rm LMT}_{xxy}$ reaches a
maximum of $6600~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$ when $\mu$ is near the energy
of WPs and becomes several times smaller after $\mu$ shifts slightly away can
, in agreement with the experiment. In FM MnBi2Te4 and MnSb2Te4 whose band
structure is similar to that of MnBi2Te4, ${\rm MR}_{xx}(B_{z})$ is observed
Li  _et al._ (2021); Lei  _et al._ (2020); Zhu  _et al._ (2020); Huan  _et
al._ (2021). Corresponding $\sigma^{\rm LMT}_{xxz}$ in our calculations (about
$60~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$ when $\mu$ is near the energy of WPs) is
similar to that in six-layer MnBi2Te4 (from $8$ to
$200~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$) but much smaller than that in thick
MnBi2Te4 flakes and MnSb2Te4 bulk (about
$2000~{}{\rm\Omega^{-1}m^{-1}T^{-1}}$). Such differences may originate from
the variation of relaxation time $\tau$. ${\rm MC}_{xx}(B_{z})$ insensitive to
$\tau$ ranges from $0.23\%$ to $8\%$ per tesla from experiments, equaling to
our results when $\mu$ is away from the energy of WPs by several or tens of
meV [Fig. 5(b)]. Our results also agree with the observed dependence of linear
MR on magnetic field direction and chemical potential (see details in section
S10 of SM SM ). Moreover, from Eq. (1), only the rank-3 tensor
$\chi_{\alpha\beta\gamma}$ contributes to
$\sigma^{\text{LMT}}_{\alpha\beta\gamma}$ components above because the
relevant rank-1 tensor components $\chi_{y}$ vanish due to the $C_{3z}$
symmetry. Since our numerical calculations based purely on Berry curvature
effect already agree well with currently available experimental data, we
conclude that Berry curvature effect dominates linear MR observed in these
materials and the rank-3 tensor $\chi_{\alpha\beta\gamma}$ (i.e., the Berry-
curvature-modified DOS) plays a major role.

Summary.—In summary, the crucial role of Berry curvature in LMT of realistic
magnetic materials is revealed. Berry-curvature-induced LMT is a general
phenomenon existing in 66 out of 122 MPGs according to the presented symmetry
guideline. Focusing on representative magnetic WSMs Co3Sn2S2 and FM MnBi2Te4,
the contribution of Berry curvature to LMT is estimated concretely, which is
tunable by magnetization canting. Berry-curvature-induced LMT can be justified
by various characteristic experimental signatures, especially an intrinsic MR
exceeding 100% per tesla. Our results suggest that observed LMT in recent
experiments on Co3Sn2S2 and FM MnBi2Te4 are actually dominated by Berry
curvature through modifying DOS.

###### Acknowledgements.

We acknowledge fruitful discussions with Prof. Binghai Yan and Prof. Yong Xu.
This work was supported by the Basic Science Center Project of NSFC (Grant No.
51788104), the Ministry of Science and Technology of China, and the Beijing
Advanced Innovation Center for Future Chip.

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# Spectroscopic analysis of the argon scintillation with a wavelength
sensitive particle detector

R. Santorelli  E. Sanchez Garcia  P. Garcia Abia  D. González-Díaz  R. Lopez
Manzano  J.J. Martinez Morales  V. Pesudo  and L. Romero

###### Abstract

We performed a time-resolved spectroscopic study of the VUV/UV argon
scintillation as a function of pressure and electric field, by means of a
wavelength sensitive detector operated with different radioactive sources. Our
work conveys new evidence of distinctive features of the argon light which are
in contrast with the general assumption that, for particle detection purposes,
the scintillation can be considered to be largely monochromatic at 128 nm
(second continuum). The wavelength and the time-resolved analysis of the
photon emission reveal that the dominant component of the argon scintillation
during first tens of ns is in the range [160, 325] nm. This light is
consistent with the third continuum emission from highly charged argon
ions/molecules. This component of the scintillation is field-independent up to
25 V/cm/bar and shows a very mild dependence with pressure in the range [1,
16] bar. The dynamics of the second continuum emission is dominated by the
excimer formation time, whose variation as a function of the pressure has been
measured. Additionally, the time and pressure-dependent features of electron-
ion recombination, in the second continuum band, have been measured. This
study opens new paths toward a novel particle identification technique based
on the spectral information of the noble-elements scintillation light.

##  1 Introduction

Over the last decade, argon and xenon detectors have attracted a lot of
interest for their use in direct dark matter search [1, 2, 3, 4, 5] and
neutrino experiments [6, 7, 8], given their unique ionization and
scintillation properties. In these experiments, the high-purity noble element
bulk is used as target, as well as active and tracking medium for particles
[9, 10], attaining overall performances better than the ones reachable with
other technologies.

A central aspect of the single or dual (gas-liquid) phase noble element
detectors is the efficient collection and detection of the vacuum ultraviolet
(VUV) scintillation photons, which provides calorimetric data, event time for
the 3D event reconstruction, and particle identification capability [11, 12].
However, the details of the photon production mechanisms as well as the
wavelength and temporal spectra are not fully understood. Experimental
information, obtained largely from the closely related fields of photo-
chemistry, plasma and laser physics, provides abundant evidence that the light
emission mechanism relies on the bond created between excited and ground state
atoms through 3-body collisions. As densities is similar or above those of
noble gases at standard (STP) conditions, Ar${}_{2}^{*}$ and Xe${}_{2}^{*}$
_excimers_ , Rydberg states with a dimer core and a binding electron, form.
Singlet and triplet excimer states undergo radiative de-excitation, giving
rise to the so-called _second excimer continuum_. This feature dominates the
scintillation spectrum for gas pressures above 100 mbar, and results in
relatively narrow emission bands ($\approx$ 10 nm wide) at 128 nm (argon) and
172 nm (xenon).

Under the above paradigm, there has been so far little motivation towards
exploiting spectroscopic information in this kind of particle detectors. As a
consequence, the light detection systems of argon and xenon chambers are based
on broad-band optical sensors, possibly coupled to photon wavelength-shifters,
that effectively integrate the light signal over a wide spectral range,
missing the potential information provided by the scintillation wavelength.

Some studies were carried out (mostly prior to the 90’s) to investigate the
temporal evolution of characteristic spectral components of the argon and
xenon scintillation. This experimental program was performed through
irradiation with strong X-ray [13], electron [14, 15], proton [16] or heavy
ion [17, 18] beams. Although a high intensity beam can produce, in a
relatively simple way, the photon yield required for the study of
scintillation in pure gases, spurious effects (associative processes,
interactions with walls and emission from the window) are often introduced.
Comparatively, it is more difficult to study the time-resolved spectroscopy
with individual particles, and, for this reason, the systematic investigation
of the spectral characteristics and absolute scintillation yields in particle
detectors is much scarcer, and seems to be almost entirely circumscribed to
$\upalpha$-particles [19, 20, 21].

With regard to the particle detectors field, the demonstration of a light
emission mechanism more complex than the one so far considered in the
literature, with well separated emission bands for different particle types,
could trigger the interest on a novel detector concept sensitive to the photon
wavelength. This technology would allow to exploit distinctive features of the
noble gases scintillation emission, a possibility currently not conceived by
the present experiments.

To this aim, we have built a high-pressure gas detector in the CIEMAT
laboratory (Sec. 3). The use of photon sensors with different spectral
sensitivities allowed us to detect the Ar scintillation in the near, middle
and far UV ranges, and to investigate, in detail, aspects of the photon
production mechanism and light emission spectrum particularly relevant for
particle detectors based on noble elements.

Results obtained with $\upalpha$ and $\upbeta$ sources deployed in the gas
chamber, operated up to 20 bar, evidenced a substantial emission in the
middle-UV region, which is consistent with the so-called third continuum
emission (Secs. 2 and 4). Despite being still sub-dominant, overall, compared
to the second continuum, the third continuum is markedly fast, hence
representing the main contribution to the photon signal during the first tens
of ns (Secs. 4 and 5) below 10 bar.

To the best of our knowledge, this is the first systematic study of the third
continuum carried out with $\upalpha$ and $\upbeta$ sources operated in a
noble-gas chamber. Our findings significantly boost the importance of the
spectral information in noble-element detectors. Although the two continua can
be unambiguously differentiated spectroscopically, the widespread use of
wavelength shifter coatings in dark matter and neutrino detectors spoils any
possibility of exploiting the spectroscopic information of the argon
scintillation.

##  2 Brief review of the scintillation in noble gases

In this section we revisit briefly the experimental situation, starting with
the $1^{\textnormal{st}}$ and $2^{\textnormal{nd}}$ continuum, that have their
origin on the emission from vibrationally-relaxed singlet
($\textnormal{Ar}_{2}^{*}(^{1}\Sigma_{u})$) and triplet
($\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u})$) excimer states, when transitioning
to the dissociative ground state of the Ar dimer
($\textnormal{Ar}_{2}(^{1}\Sigma_{g})$). The importance of this emission stems
from the fact that, for pressures above few 100’s of mbar, low-lying excited
atomic states (resonant: $\textnormal{Ar}^{*}(s_{4})$, metastable:
$\textnormal{Ar}^{*}(s_{5})$) are quickly and predominantly populated through
a collision-dominated atomic cascade; given that singlet and triplet excimer
states are formed from those atomic states through termolecular (3-body)
reactions, this emission displays a high universality. Focusing on the
$\textnormal{Ar}^{*}(s_{4})$ state, the scintillation process can be
characterized in general through the following (dominant) pathways:

$\displaystyle\textnormal{Ar}^{**}+\textnormal{Ar}$
$\displaystyle\xrightarrow{\textnormal{(cascade)}}~{}~{}\textnormal{Ar}^{*}(s_{4})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
collisional quenching (2.1) $\displaystyle\textnormal{Ar}^{**}$
$\displaystyle\xrightarrow{\textnormal{(cascade)}}~{}~{}\textnormal{Ar}^{*}(s_{4})+h\nu\textnormal{'s}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
atomic radiation (2.2)
$\displaystyle\textnormal{Ar}^{*}(s_{4})+\textnormal{Ar}+\textnormal{Ar}$
$\displaystyle\xrightarrow{K_{s_{4}\rightarrow{0_{u}}}}~{}~{}\textnormal{Ar}_{2}^{*}(0_{u}^{+})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
(weakly bound) exc. form. (2.3)
$\displaystyle\textnormal{Ar}_{2}^{*}(0_{u}^{+})$
$\displaystyle\xrightarrow{K_{0_{u}\rightarrow{s_{4}}}}~{}~{}\textnormal{Ar}^{*}(s_{4})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
$\displaystyle\textnormal{exc. dissociation to}~{}s_{4}$ (2.4)
$\displaystyle\textnormal{Ar}_{2}^{*}(0_{u}^{+})$
$\displaystyle\xrightarrow{K_{0_{u}\rightarrow{s_{5}}}}~{}~{}\textnormal{Ar}^{*}(s_{5})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
$\displaystyle\textnormal{exc. dissociation to}~{}s_{5}$ (2.5)
$\displaystyle\textnormal{Ar}_{2}^{*}(0_{u}^{+})$
$\displaystyle\xrightarrow{1/\tau_{{}_{0_{u}}}}~{}~{}~{}\textnormal{Ar}+\textnormal{Ar}+h\nu~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
first continuum (2.6)
$\displaystyle\textnormal{Ar}_{2}^{*}(0_{u}^{+})+\textnormal{Ar}$
$\displaystyle\xrightarrow{K_{bind,1}}~{}~{}\textnormal{Ar}_{2}^{*}(^{1}\Sigma_{u}(v))+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
exc. binding (2.7)
$\displaystyle\textnormal{Ar}_{2}^{*}(^{1}\Sigma_{u}(v))+\textnormal{Ar}$
$\displaystyle\xrightarrow{K_{cool,1}}~{}~{}\textnormal{Ar}_{2}^{*}(^{1}\Sigma_{u}(v=0))+\textnormal{Ar}~{}~{}~{}~{}$
exc. cooling/relaxation (2.8)
$\displaystyle\textnormal{Ar}_{2}^{*}(^{1}\Sigma_{u}(v=0))$
$\displaystyle\xrightarrow{1/\tau_{e_{2}}^{s}}~{}~{}~{}~{}\textnormal{Ar}_{2}(^{1}\Sigma_{g})+\textnormal{Ar}+h\nu~{}~{}~{}~{}~{}~{}$
second continuum (2.9)

Here $\textnormal{Ar}^{**}$ refers to any excited atomic state above the two
lowest ones, $\textnormal{Ar}_{2}^{*}(0_{u}^{+})$ is the weakly bound
$\textnormal{Ar}_{2}^{*}$ excimer associated with
$\textnormal{Ar}_{2}^{*}(^{1}\Sigma_{u}(v))$, in Hund’s notation corresponding
to _case c_ , and the quantum number $v$ refers to the vibrational state, with
$v=0$ corresponding to the bottom of the potential well. If considering,
instead, that the cascade proceeds through the $\textnormal{Ar}^{*}(s_{5})$
state, the situation is analogous:

$\displaystyle\textnormal{Ar}^{**}+\textnormal{Ar}$
$\displaystyle\xrightarrow{\textnormal{(cascade)}}~{}~{}\textnormal{Ar}^{*}(s_{5})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
collisional quenching (2.10) $\displaystyle\textnormal{Ar}^{**}$
$\displaystyle\xrightarrow{\textnormal{(cascade)}}~{}~{}\textnormal{Ar}^{*}(s_{5})+h\nu\textnormal{'s}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
atomic radiation (2.11)
$\displaystyle\textnormal{Ar}^{*}(s_{5})+\textnormal{Ar}+\textnormal{Ar}$
$\displaystyle\xrightarrow{K_{s_{5}\rightarrow{0_{u}}}}~{}~{}\textnormal{Ar}_{2}^{*}(1_{u}/0_{u}^{-})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
(weakly bound) exc. form. (2.12)
$\displaystyle\textnormal{Ar}_{2}^{*}(1_{u}/0_{u}^{-})$
$\displaystyle\xrightarrow{K_{0_{u}\rightarrow{s_{5}}}}~{}~{}~{}\textnormal{Ar}^{*}(s_{5})+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
$\displaystyle\textnormal{dissociation to}~{}s_{5}$ (2.13)
$\displaystyle\textnormal{Ar}_{2}^{*}(1_{u}/0_{u}^{-})$
$\displaystyle\xrightarrow{1/\tau_{{}_{1_{u}}}}~{}~{}~{}~{}\textnormal{Ar}+\textnormal{Ar}+h\nu~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
first continuum (2.14)
$\displaystyle\textnormal{Ar}_{2}^{*}(1_{u}/0_{u}^{-})+\textnormal{Ar}$
$\displaystyle\xrightarrow{K_{bind,3}}~{}~{}\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u}(v))+\textnormal{Ar}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}$
exc. binding (2.15)
$\displaystyle\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u}(v))+\textnormal{Ar}$
$\displaystyle\xrightarrow{K_{cool,3}}~{}~{}\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u}(v=0))+\textnormal{Ar}~{}~{}~{}~{}$
exc. cooling/relaxation (2.16)
$\displaystyle\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u}(v=0))$
$\displaystyle\xrightarrow{1/\tau_{e_{2}}^{t}}~{}~{}~{}~{}\textnormal{Ar}_{2}(^{1}\Sigma_{g})+\textnormal{Ar}+h\nu~{}~{}~{}~{}~{}~{}$
second continuum (2.17)

and $\textnormal{Ar}_{2}^{*}(1_{u}/0_{u}^{-})$ refers to the degenerate weakly
bound excimers associated with $\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u}(v))$. A
detailed diagram compiling these pathways can be found for instance in [22].
Reaction rates ($K$) will be assumed in this work to be in units of [t-1],
therefore being number density ($N$) dependent. Experimentally, it is has been
determined that, for pressures above 100 mbar, the dominant time constants are
the (3-body) formation times $\tau_{f_{2}}=1/K_{s_{5(4)}\rightarrow 0_{u}}$,
and the decay times $\tau_{e_{2}}^{s}$, $\tau_{e_{2}}^{t}$.

At high ionization densities, characteristic of high pressures and/or highly
ionizing radiation, charge recombination provides additional scintillation
channels [23, 24]. From

$\displaystyle\textnormal{Ar}^{+}+\textnormal{Ar}+\textnormal{Ar}$
$\displaystyle\rightarrow$
$\displaystyle\textnormal{Ar}_{2}^{+}+\textnormal{Ar}$ (2.18)
$\displaystyle\textnormal{Ar}_{2}^{+}+e$ $\displaystyle\rightarrow$
$\displaystyle\textnormal{Ar}_{2}^{**}$ (2.19)
$\displaystyle\textnormal{Ar}_{2}^{**}$ $\displaystyle\rightarrow$
$\displaystyle\textnormal{Ar}^{**}+\textnormal{Ar}$ (2.20)

the $1^{\textnormal{st}}$ and $2^{\textnormal{nd}}$ continua follow, according
to reactions 2.1, 2.2, 2.10, 2.11. This leads to a perfect correlation between
recombined charge and excess scintillation, with reaction 2.19 being regulated
by the external electric field [25]. As a result, the effective energy to
create a UV photon at zero-field varies, under $\upalpha$-particles, from
$W_{sc}$=50.6 eV at 2 bar to $W_{sc}$=25.3 eV at 10 bar [26].

On the other hand, mechanisms leading to scintillation mainly in the region
[180, 300] nm are grouped under the generic denomination of “$3^{rd}$
continuum”, despite it is possible that a number of different species
contribute, as hinted by the study in [18]. The identification of the
precursors to this continuum has been subject of hot debates throughout the
80’s and 90’s [27, 28]. The most complete study to date, combining the two
leading hypothesis, doubly ionized (Ar++) and excited (Ar+∗) ions, seems to be
[18], however it does not allow quantitative predictions of the scintillation
yields, nor it has been fully substantiated. In a nutshell, doubly ionized
states would lead to scintillation around 200 nm through three-body reactions,
as:

$\displaystyle\textnormal{Ar}^{++}+\textnormal{Ar}+\textnormal{Ar}$
$\displaystyle\rightarrow$
$\displaystyle(\textnormal{Ar}_{2})^{++}+\textnormal{Ar}$ (2.21)
$\displaystyle(\textnormal{Ar}_{2})^{++}$ $\displaystyle\rightarrow$
$\displaystyle\textnormal{Ar}^{+}+\textnormal{Ar}^{+}+h\nu$ (2.22)

At high pressures, the presence of new peaks in the range [200, 300] nm led to
the consideration of additional contributions, finding a good theoretical
correspondence with $\textnormal{Ar}^{+*}$ decays:

$\displaystyle\textnormal{Ar}^{+*}$ $\displaystyle\rightarrow$
$\displaystyle\textnormal{Ar}^{+}+h\nu$ (2.23)

Contrary to the $1^{\textnormal{st}}$ and $2^{\textnormal{nd}}$ continua, the
pathways leading to formation of $\textnormal{Ar}^{+*}$ species have not been
unambiguously identified. According to experimental data obtained in [19] for
$\upalpha$-particles, electron-ion recombination is not competing with process
2.21, so the $3^{\textnormal{rd}}$ continuum would be largely field-
independent except perhaps for very highly ionizing radiation.

##  3 Experimental setup

Figure 1: (Left) Photograph of the experimental setup. (Right) Top view of
detector. The pressurized region with the radioactive source is in the centre
of the chamber.

The wavelength-sensitive chamber is shown in Fig 1. It consists of a 7 cm side
stainless steel cube with one CF-40 flange on each face. The top and bottom
flanges are connected to the service lines for the vacuum and the gas filling.
The lateral flanges are equipped with four custom-made optical view-ports
necessary to decouple the pressurized region from the optical readout system.
A custom-designed steel frame keeps the windows in place. Grooves in the
mechanical assembly hold viton o-rings which seal the window, making the view-
port vacuum and pressure-tight up to 20 bar. The windows are made of 8.0 mm
thick UV-grade MgF2 crystals (38.1 mm–$\varnothing$), whose transmission is
$\approx$ 95% for wavelengths above 180 nm (Fig. 2-left). A transmission of
$\approx$ 33% at 128 nm is measured comparing the light detected with and
without the MgF2 crystals installed in the chamber.

Four 1” Hamamatsu photomultipliers (PMT) are hosted in canisters attached to
the optical view-ports. They are built with KF-40 tee and cross fittings and
equipped with a connection for the vacuum line, separated from the main
pressure chamber, and two electrical feedthroughs for the HV and PMT signals.

PMTs with different spectral sensitivities are used in the experiment. Two
Hamamatsu R7378A phototubes are placed in opposite sides of the central
chamber. In the other two confronting faces, one Hamamatsu R6095 and one
Hamamatsu R6835 are set. The Hamamatsu R6095 PMT is coated with a 200
$\upmu$g/cm2 layer of tetraphenyl butadiene (TPB), a wavelength shifter that
converts the UV photons to 420 nm with approximately 100 % efficiency [29].
The nominal quantum efficiencies (QE) of these phototubes and the MgF2
window’s transmission coefficient are plotted in Fig. 2-right as a function of
the photon wavelength [30, 31].

The TPB coating makes the R6095 response independent of the wavelength of the
incident photon in the VUV-UV region, so its spectral sensitivity is
considered constant in the range of interest ($[100,~{}300]$ nm). The QE of
this tube is considered equal to half of the nominal value at 420 nm (30 %) to
take into account the 50 % probability of backward emission of the TPB-
converted photons. The CsI photocathode of the R6835 is solar blind, thus the
420 nm photons, diffused backwards by the TPB coating of the R6095 placed in
front of it, do not produce a signal. Specific tests performed in our
laboratory with the R6835 PMT and a blue LED proved that this phototube is not
sensitive to the 420 nm light. The geometry of the setup reduces the optical
cross-talk between the 420 nm photons and the R7378 phototubes to a level
which is negligible for our purposes.

Figure 2: (Left) Curves of light transmission as a function of wavelength, for
the windows and filters used in the experiment. (Right) Quantum efficiencies
of the PMTs used in the detector, measured by Hamamatsu as a function of the
wavelength of the incident photons.

Special runs with 1” ($\varnothing$) Al2O3 (Sapphire) crystals from Thorlabs
[32] and long-pass filters form Asahi [33]), placed in front of the R6835 and
R7378 respectively, are also taken in order to narrow the spectral sensitivity
of these phototubes. The cross-comparison of the signals with and without the
filters placed in front of the PMTs allows to study the Ar scintillation in
well defined UV ranges. This work investigates the argon scintillation in the
spectral ranges $[110,~{}140]$ nm (called UV2 region in the following) and
$[160,~{}325]$ nm (UV3 region) using the signals of the R6835 PMT with the
Al2O3 window and of the R7378 PMT with the Asahi filters, respectively (Table
1). The upper limits are identified by the fact that no light signal is
detected with the filters placed in front of the PMTs.

The detector is equipped with two pressure sensors (ITR-90) and a set of 1/2”
VCR valves that allow to set the pressure in the chamber and the optical
readout system independently. The optical filters can be put or removed
without the need to open or evacuate the pressure chamber. Before each run,
the system is pumped with a TURBOVAC 350i for 24 hours and a pressure of
$2\times 10^{-5}$ mbar is typically reached in the central volume. Pure argon
gas (AirLiquide ALPHAGAZ™-2, purity $\geq$ 99.9999 %) is used to fill the
chamber. The PMT region is evacuated and continuously pumped during the data
taking (pressure $<$9$\times$10-5 mbar) to minimize the absorption of the UV-
VUV photons by the air between the optical view-port and the PMT window.

The PMTs are powered independently with a negative bias voltage through
custom-made bleeder circuits with SMD components mounted on PCBs. The signal
is amplified 10 times with a CAEN N979 module. One of the two outputs of the
fast amplifier goes to a leading edge discriminator (CAEN N841), with a
threshold set to 0.5 photoelectrons. Different trigger logics (CAEN N455 quad
logic unit), based on the coincidence of the R6095 and R7378 phototubes, are
used in the experiment. The second output of the fast amplifier is fed to a
CAEN DT5725 sampling ADC (14-bit resolution and 250 MS/s sampling rate).
Different runs are taken with digitization windows from 4 $\upmu$s to 16
$\upmu$s. The data are transferred via optical link to a computer for the
analysis. The gain of the PMTs is obtained from dark-rate data taken in
vacuum, by fitting the single photoelectron peak with a Gaussian function. The
calibration of the R6835 is performed directly with the tail of the argon
light pulse, given its very low dark pulse rate. The high voltage of the PMTs
is set independently, in order to equalize the gains to the level of 500 ADC
counts per photoelectron.

Region | Range | Lower bound | Upper bound
---|---|---|---
UV2 |  $[110,~{}140]$ nm | R6835 lower spectral sensitivity limit | R6835 + Al2O3 crystal
UV3 |  $[160,~{}325]$ nm | R7378 lower spectral sensitivity limit | R7378 + XUL0325 filter
Table 1: Definition of the UV2 and UV3 spectral ranges. The lower bounds are
set by the spectral sensitivity of the PMTs. The upper limits are defined from
the filters’ transmission edge.

The gas purity is assessed through the decay time of the slow component of the
argon second continuum emission. Values of $\approx$ 3 $\upmu$s were obtained
depending on the gas pressure and flow. Simple selection criteria are applied
to reject a few percent of the total triggers which are produced by electronic
noise and cross-talk events.

The results presented in this study are obtained with 241Am (activity
$\approx$ 500 Bq) and $\rm{}^{90}Sr/Y$ (activity $\approx$ 100 Bq) radioactive
sources electrodeposited on stainless steel disks. The pressure chamber is
equipped with a PTFE support structure able to host one radioactive source in
the centre.

##  4 Wavelength-resolved UV/VUV emission with a 241Am source

Figure 3: (Left) Integrated charge signal of the four different PMTs used in
the experiment, obtained with the 241Am $\upalpha$ source in argon at 2 bar.
The signal in the UV3 region is detected with two R7378 PMTs (UV3-PMT1 and
UV3-PMT2). The light collected on the four photo detectors (Sum) is around 220
PE. (Right) Asymmetry between the two R7378 PMTs for different pressures. The
Gaussian functions fitted to the data are overlaid.

Initial measurements were carried out with a 241Am $\upalpha$-source in argon
gas up to 16 bar using two R7378 (UV3-PMT1 and UV3-PMT2 in the following), one
R6835 (UV2-PMT) and one TPB-coated R6095 PMT (TPB-PMT). Taking into account
the W-values reported in [26], 1.1$\times$ 106 photons are produced in argon
at 2 bar. Considering the solid angle between the PMTs photocathode and the
source, the MgF2 transmission coefficient and the nominal PMTs QE, (1.0 $\pm$
0.2) $\times$ 102 photoelectrons (PE) are expected to be detected by the TPB-
PMT, which is sensitive to the entire spectral range. The average solid angle
between the PMTs photocathode and the source is estimated by means of a toy
Monte Carlo which includes the detailed description of the chamber geometry
and takes into account the refraction of the light on the MgF2 crystals.
Values in the range [0.008, 0.011] are obtained for the different PMTs
depending on the nominal photocathode size and the average length of the alpha
track as a function of the gas pressure.

The $\upalpha$-peak is clearly visible in the integrated charge spectra (Fig.
3-left). Depending on the gas purity and pressure, more than two hundreds of
photoelectrons (PE) are detected in the full energy peak (green histogram)
produced by the $\approx$ 5.5 MeV $\upalpha$ particles, allowing wavelength
and time-resolved analysis of the light pulses. The TPB-PMT detects $\approx$
90 PE on average (blue histogram in Fig. 3-left), a value which is in good
agreement with the expected one. The UV2-PMT (red histogram) mean value is
approximately 60 PE, while the two UV3-PMTs (black histograms), which are only
sensitive to wavelengths above 160 nm, detect $\approx$ 30 PE each on average.
This clearly establishes that there is a significant component of the argon
scintillation light at wavelengths significantly longer than the 128 nm line
from the second continuum.

Figure 4: Typical Ar scintillation signals from 5.5 MeV $\upalpha$-particle
interaction detected in three spectral regions, with argon gas at 1.5 bar. A
clear separation of the components is possible by wavelength discrimination.

The signal asymmetry, defined as the ratio between the difference and the sum
of a pair of PMTs integrated signals, is plotted in Fig. 3-right for the two
UV3 phototubes at different pressure values. The data are fitted with a
Gaussian function with a mean value compatible with zero, confirming that the
source is at the centre of the chamber. The width of the distribution
decreases with pressure due to the reduction of the mean range of the
particles in the gas, indicating that the influence of any geometrical
correction in the measured scintillation is negligible above 3 bar.

The pulse shape of a typical signal, produced by an $\upalpha$ event in argon
at 1.5 bar, is presented in Fig. 4, as registered by the different PMTs. The
TPB-PMT detects the characteristic fast and slow components of the argon
emission. However, only the slow component of the scintillation is detected in
the UV2 region, in form of a long train of pulses ($\mu$s scale) at the single
photoelectron level. The UV3 sensitive phototubes are able to detect only the
prompt emission, with a pulse amplitude similar to the one detected by the
TPB-PMT.

A signal consistent with dark current is registered by the UV2-PMT with the
sapphire crystal placed between the PMT window and the MgF2 optical view-port,
proving that the slow component of the Ar scintillation is entirely in the
range $[110,~{}140]$ nm. The light signal detected by the UV3-PMTs with the
250 nm long-pass filter is of the order of 20 % of the total signal without
filter. No light is detected with the 325 nm long-pass filter.

The 1.5 bar argon scintillation pulses, averaged over $3\times 10^{4}$ events,
are displayed in Fig. 5 in two time ranges. Only the $\upalpha$-particle
interactions from the 241Am source are considered, using an energy threshold
cut. LED calibration runs taken in vacuum evidenced an after-pulsing
component, between 60 ns and 100 ns after the maximum pulse height, in the
UV3-PMTs signal. This second pulse is removed from the analysis with a
software cut, after confirming that the impact in our study is negligible.

Figure 5: Pulse shapes of the argon scintillation signals averaged over
$3\times 10^{4}$ events per PMT type, registered with the 241Am source in Ar
at 1.5 bar, in two time windows: (left) $[0,3000]$ ns and (right) $[0,~{}400]$
ns.

Figure 6: (Left) Integrated charge spectrum obtained in the PMT with the
wavelength shifter compared with the sum of the spectra in the UV2 and UV3
regions, with 241Am data in argon gas at 1.5 bar. (Right) Average argon pulse
detected with the TPB and sum of the UV2 and UV3 pulses at 1.5 bar.

In this analysis, only the raw number of PEs have been reported without any
signal correction. The combination of the plots in Figs. 3 (left) and 5
suggests that the amplitude of the signal detected by the TPB-PMT, which is
sensitive to the entire spectral range, is very similar to the sum of the
signals of two other PMTs, sensitive only to either of the two UV2 and UV3
regions. In Fig. 6, the integrated charge spectra (left) and the average pulse
shape of the argon scintillation (right) are shown with the 241Am source in
argon gas at 1.5 bar, selecting the events in the center of the detector
through two symmetry cuts between the different couples of confronting PMTs.
Given the symmetry of the setup and the similar size of the PMTs, the fact
that the tube signals are similar in the two regions UV2 and UV3 respectively
also suggests that the QEs are comparable.

These results prove that the two components of the scintillation with Ar gas
at 1.5 bar are characterized by distinct wavelengths and can be unambiguously
differentiated spectroscopically. The slow component is consistent with the
second continuum emission (Sec. 2), which gives rise to the 128 nm photons.
The fast component of the scintillation, on the other hand, is entirely in the
UV3 region and it is compatible with the third continuum emission.

In our experiment the actual purity of the argon gas was estimated through the
decay time constant of the triplet excimer states
$\textnormal{Ar}_{2}^{*}(^{3}\Sigma_{u})$. The values obtained between 2.5 and
3 $\upmu$s set the level of impurities in the range 0.1–1 ppm [34], which is
consistent with the gas contamination certified by the producer. The measured
triplet decay time rejects the possible explanation of the UV3-photon
production in terms of parasitic re-emissions from N2, H2O and O2
contamination, which can only produce a sub-dominant component in the UV band
and over a wide time scale. Any explanation, other than the third continuum
emission, in terms of unusual Ar contaminants is considered implausible.

The fast/slow component ratio obtained at 1.5 bar gas pressure and maximum
purity (3.2 $\upmu$s) is 5.4, in good agreement with the value 5.5 $\pm$ 0.6
at 1.1 bar absolute pressure measured in [35].

##  5 Spectroscopic analysis of the argon scintillation as a function of the
gas pressure

In order to quantitatively compare signals in the two spectral regions UV2 and
UV3, we calculate the total numbers of photons produced by the $\upalpha$
interactions considering the MgF2 transmission values (33% for the UV2 region
and 95% for the UV3), the nominal QEs (0.15 for the UV2-PMT and TPB-PMT, 0.18
for the UV3-PMT) and the solid angle estimated through the toy Monte Carlo
(Sec. 3). The analog manometer introduces an uncertainty of 0.2 bar on the
pressure measurement.

The variation of the average 241Am signal, defined as the mean value of a
Gaussian fit to the $\upalpha$ peak, is presented in Fig. 7-left as a function
of the gas pressure. The light yield of the chamber is sufficient to clearly
identify the alpha peak in the charge spectra (Fig. 3-left), and the
statistical uncertainty from the fit is negligible for all the PMTs. The
fluctuations in the number of photons are taken into account with a pressure
independent systematic uncertainty of $\pm~{}3-5$ %, that is related to the
uncertainty on the gain calibration and to the different spectral responses of
the PMTs.

The light in the UV2 region (red square in Fig. 7-left) increases to more than
twice the initial value in the [1.5, 16] bar pressure range, an effect which
is consistent with the enhanced electron-ion recombination probability at
higher gas pressure [21]. On the other hand, the signal in the UV3 region
(black triangles) is stable within the uncertainties in that pressure range:
this result suggests that the recombination light is consistent only with 128
nm photons production and no other emission is observed at longer wavelengths.

In Fig. 7-right the evolution of the charge signal in a fixed 90 ns time
window after the trigger (“fast” component) is shown as a function of the gas
pressure. The UV2 signal rises up to 25 PE and gets nearly stable at pressures
above 7 bar, demonstrating that more photons are emitted promptly in the UV2
region (red dots) when the gas pressure increases. The UV3 component (black
dots) barely depends on the pressure and represents the dominant light
emission during the first 90 ns, up to 5 bar.

Figure 7: (Left) Mean $\upalpha$ signal detected in the different spectral
ranges as a function of the pressure. (Right) Variation with the pressure of
the fast component (first 90 ns) of the argon scintillation. In both graphs,
the bands indicate the systematic uncertainties.

A typical signal from an $\upalpha$ interaction in argon at 16 bar is plotted
in Fig. 8. When it is compared with the signal at 1.5 bar (Fig. 4), a fast
component can be now observed in the UV2 region. In the UV3 region, though,
the pulse shape and the amplitude of the signal is similar to the 1.5 bar
case. This is consistent with the fast component of the scintillation signal
detected by the TPB-PMT being significantly larger at 16 bar than at 1.5 bar.

Figure 8: Typical Ar scintillation signals from 5.5 MeV $\upalpha$-particle
interaction detected in three spectral regions, for argon gas at 16 bar.
Compared to the typical signal at 1.5 bar (Fig. 4), a fast component appears
in the UV2 region when the pressure is increased.

The argon scintillation pulse, averaged over $3\times 10^{4}$ $\upalpha$
interactions, is depicted in Fig. 9 for different pressures and spectral
regions. The pulse heights are normalized to the maximum values, which are
observed at 1.5 bar for the UV3 and 16 bar for the UV2 emissions,
respectively. A relatively small decrease of the UV3 signal is evident as the
pressure increases from 5 to 16 bar (Fig. 9-right). The enhancement of the
fast argon scintillation component at higher pressure is evident in the UV2
region (Fig. 9-left). This effect is consistent with the reduction of the
average distance among the argon molecules at higher pressure, which allows
the formation of the excimer in shorter time and leads to an increase in the
fast component through the decay of the singlet ${}^{1}\sum_{u}$ states. This
result is in agreement with an old study that evidenced the dependence of the
Ar${}^{*}_{2}$-excimer formation-time on the gas pressure [36]. The change of
slope around 6 bar in Fig. 7-right can be explained by the singlet state
excimer formation time becoming smaller than the 90 ns fast signal integration
window.

Figure 9: Average signals in the [1.5, 16] bar pressure range for the (left)
UV2 and (right) UV3 regions. For UV3, only slight variations on the shapes are
observed for different pressures. In the UV2 region, the fast component is
more significant at higher pressure.

The use of sensors with different spectral sensitivity allows to study the
second and the third continuum emissions separately. The average light pulse
(from $2\times 10^{4}$ events) in the UV3 region with argon at 1.5 bar is
shown in Fig. 10-left. Data are fitted using the following expression:

$I_{\scriptscriptstyle
UV3}(t)=\frac{L}{\tau_{f_{3}}-\tau_{e_{3}}}(e^{-t/\tau_{e_{3}}}-e^{-t/\tau_{f_{3}}})\otimes
G(t-t_{0},\sigma),$ (5.1)

where $L$ is a normalization constant, $G$ a gaussian function, with mean
$t_{0}$ and width $\sigma$, that accounts for the detector response and
$\tau_{f_{3}}$, and $\tau_{e_{3}}$ are the time necessary for the formation of
the third continuum precursors and their characteristic photon emission time.
In each bin of Fig. 10-left the pulse error is calculated through the
statistical distribution of the set of waveforms and a fixed uncertainty of
$\pm$ 2 ns is introduced by the sampling rate of the ADC.

The $\tau_{f_{3}}$ time constant is fast and it cannot be precisely measured
from the fit due to the 250 MHz maximum sampling rate of our ADC, thus a limit
$\tau_{f_{3}}\lesssim 1$ ns is set on the molecular-ions formation time. The
photon emission time constant $\tau_{e_{3}}$ is independent of the gas
pressure in the range [1, 16] bar (Fig. 10-right) and its value is 5.02 $\pm$
0.11 ns, calculated as the average of the fit results in the pressure range of
interest. This result is compatible with previous works [27, 20], where values
of $\approx$ 5 ns have been obtained for the lifetime of these radiative
molecular states.

Figure 10: (Left) Result of the fit (red line) of the mean pulse for $2\times
10^{4}$ $\upalpha$ interactions in argon at 1.5 bar in the UV3 region (black)
using Eq. 5.2. (Right) Dependence of the emission time constant with pressure
in the 1.5 to 16 bar range.

The time constants of the argon second continuum in the UV2 region are
obtained in the [1.5, 8] bar pressure range, fitting the average light pulse
in the UV2 region with the following function [35]:

$I_{\scriptscriptstyle
UV2}(t)=\left[\frac{L_{1}}{\tau_{f_{2}}-\tau_{e_{2}}^{s}}(e^{-t/\tau_{f_{2}}}-e^{-t/\tau_{e_{2}}^{s}})+\frac{L_{2}}{\tau_{f_{2}}-\tau_{e_{2}}^{t}}(e^{-t/\tau_{f_{2}}}-e^{-t/\tau_{e_{2}}^{t}})\right]\otimes
G(t-t_{0},\sigma),$ (5.2)

The two exponential differences account for the singlet ($s$) and triplet
($t$) contributions, independently, with the corresponding $\tau_{e_{2}}$
parameters labeled accordingly. The formation times have been assumed to be
identical for both contributions. The result of the fit of the UV2-PMT average
charge spectrum at 1.5 bar (Fig. 11-left) proves that Eq. 5.2 represents an
accurate description of the argon scintillation signal at that pressure.

Figure 11: Results of the fits (red lines) of the mean pulses for $2\times
10^{4}$ $\upalpha$ interactions in argon at (left) 1.5 bar and (right) 16 bar,
in the UV2 region (black dots). A 4 ns binning is used up to 100 ns and it is
increased to 160 ns for larger times. Eq. 5.2 is used for the fit on the left,
and Eq. 5.2 \+ Eq. 5.3 for the fit on the right.

At pressures larger than 8 bar, the UV2 signal shape is characterized by a new
structure a few $\upmu$s after the maximum pulse height, and Eq. 5.2 no longer
describes the spectrum. A tentative explanation of this feature is taken from
the model proposed in [37], that addresses the electron-ion recombination
luminescence in the absence of electric field. This model considers a region
of uniform ionization density and neglects the diffusion process out of the
$\upalpha$ track for the thermalized electrons. The recombination time
$\tau_{r}$ is proportional to $P^{-2.7\pm 0.3}$ for pressures larger than 10
bar [21] and it becomes shorter at larger pressures. In liquid argon, this
time is below 1 ns, where the time dependence of the recombination is
dominated by the molecular de-excitation time.

A new term is added to Eq. 5.2 in order to describe the scintillation from the
charge recombination, $I_{\scriptscriptstyle UV2}^{\scriptscriptstyle R}$,
which depends on the characteristic recombination time, $t_{r}$, and the
excimer lifetime, $\tau_{e}$, (discussed in Sec. 2):

$\begin{split}I_{\scriptscriptstyle UV2}^{\scriptscriptstyle
R}(t)&=\;L_{3}\;(e^{-t/\tau_{e}^{t}}-e^{-2t/t_{r}}),\qquad\textnormal{for}\;t<t_{r},\\\
I_{\scriptscriptstyle UV2}^{\scriptscriptstyle
R}(t)&=\;L_{3}\;e^{-t/\tau_{e}^{t}},\hskip
54.06023pt\qquad\textnormal{for}\;t>t_{r},\end{split}$ (5.3)

where $L_{3}$ is a normalization constant. The result of the UV2 signal fit to
Eq. 5.2, after including the additional term $I_{\scriptscriptstyle
UV2}^{\scriptscriptstyle R}(t)$, is shown in Fig. 11-right. The signal is
successfully described by the fit above 8 bar up to 16 bar. The dependence of
the excimer formation time and the singlet decay time in the UV2 region are
summarized in Fig. 12-left for different pressures.

Figure 12: (Left) Dependence of the excimer formation time constant (red dots)
and singlet de-excitation lifetime (blue triangles) with pressure in the 1.5
to 16 bar range. (Right) Dependence of the luminescence with the electric
field intensity in the UV2 (red dots) and UV3 (black triangles) regions. The
UV3 signal is not affected by the electric field.

The excimer formation time has a strong pressure dependence, decreasing from
46 ns at 1.5 bar to 2.6 ns at 16 bar. On the other hand, the singlet decay
time emission is independent of the pressure with values around 4-5 ns. The
triplet lifetime is measured to be $\approx$ 3 $\upmu$s depending on the gas
flow as expected. These results are in good agreement with previous studies
[36]. At argon pressures below 5 bar, the excimer formation time is the
dominant factor that determines the photon emission during the first hundred
of ns. In this case, the singlet component of the second continuum emission is
smeared over tens of ns. At higher gas pressure, the typical excimer formation
time decreases.

##  6 Electric field dependence of the scintillation and spectroscopic studies
of the electron-ion recombination

With the aim of establishing the nature of the new structure that appears in
the UV2 range at large pressures and to study the field dependence of the UV3
emission, a small field cage (2 cm height) with the $\rm{}^{241}Am$ source on
the anode plate was introduced in the central volume of the pressure chamber.

Data at 10 bar of pressure were taken in order to fully contain the $\upalpha$
track in the field region. In this setup the anode is grounded and the reduced
electric field (E/P) applied in the range from 0 to 25 V/cm/bar. The number of
PE measured with the $\rm{}^{241}Am$ peak as a function of the electric field
is shown in Fig. 12-right, evidencing that the emission in the UV2 wavelength
range decreases with electric fields up to 4 V/cm/bar and then remains
constant. The saturation in the collection of the charge above this field
value is consistent with the measurements reported in [21] for the second
continuum. On the other hand, the emission in the UV3 spectral region is not
affected by the electric field up to 25 V/cm/bar.

The scintillation pulses at 10 bar with and without a 100 V/cm field, averaged
over $2\times 10^{4}$ events and normalized to the maximum value of the
distribution, are shown in Fig. 13, both for the UV2 and UV3 spectral ranges.
The bump over 1 $\upmu$s in the UV2 range (left graph) disappears by
increasing the amplitude of the reduced field. This result confirms the
interpretation of this structure in terms of electron-ion recombination given
in Sec. 5. When a sufficiently strong field is applied, the charge
recombination is suppressed and the overall signal shape is similar to the
scintillation pulse at pressures below 8 bar. In these conditions, the argon
slow component is well described by a single exponential function.

The distribution for UV3 (right plot) proves that the photon emission in this
spectral region is not affected by the electric field. This result
demonstrates that the recombination light is consistent only with the second
continuum emission at 128 nm.

Figure 13: Mean pulse shape of the UV2 (left) and UV3 (right) signals with
(blue line) and without (black line) electric field with argon at 10 bar. The
bump in the UV2 graph disappears when the electric field is applied. The UV3
signal is not affected by the electric field.

##  7 First evidence of the third continuum emission with a $\mathbf{\beta}$
source

Our experiments with $\upalpha$ particles in argon at different pressures have
proved that a substantial component of the scintillation is in the range [160,
325] nm and is not related to the radiative de-excitation of the singlet and
triplet excimers. We interpret this photon production through the mechanism
responsible for the third continuum emission (Sec.2). Additional studies have
been performed replacing the $\rm{}^{241}Am$ $\upalpha$ source with a weak
$\rm{}^{90}Sr/Y$ $\upbeta$ source (activity $\approx$ 100 Bq), with 546 keV
and 2280 keV Q-values of the decays. We collected several runs with argon in
the pressure range [15, 21] bar. The $\upbeta$’s from the source are typically
not fully contained in our detector, unlike for the case of $\upalpha$
interactions. To increase the light collection, the UV2-PMT (R6835) is
replaced by another phototube coated with TPB (R6095). In this configuration,
the trigger is produced by the coincidence of the two TPB-PMTs.

The integrated charge spectrum of one TPB-PMT, obtained with the
$\rm{}^{90}Sr/Y$ $\upbeta$ source and gas argon at 20 bar is compared with a
background spectrum taken without any source (Fig. 14). A prominent excess is
present at low energy, between 6 and 25 PE, giving us a solid evidence of the
actual identification of the $\upbeta$ interactions. A typical signal produced
by one UV-PMT and one TPB-PMT in this region is displayed in Fig. 15. A clear
pulse, similar to the one detected with the $\upalpha$ source but with an
amplitude consistent with the different energy scale, is shown in the UV3
region in coincidence with the TPB-PMT signal. To the best of the authors
knowledge, this result is the first evidence of the third continuum emission
produced by a $\upbeta$ interaction in argon gas.

This demonstration of the third continuum emission from $\upalpha$ and
$\upbeta$ interactions in argon, provides evidence that the temporal and
spectroscopic information of the argon scintillation are strongly related, and
can be used independently or complementary for particle identification. New
studies focused on a novel particle identification technique based on the
spectroscopic analysis of the light pulses are currently on-going [38].

Figure 14: Integrated charge for events collected without (red line) and with
(blue line) the $\rm{}^{90}Sr/Y$ $\upbeta$ source in the center of the
detector. The number of events is normalized to the same acquisition time.
Figure 15: Typical Ar scintillation signals detected for a $\upbeta$ event in
two spectral regions, with argon gas at 20 bar.

##  8 Conclusions

Conventional dark matter and neutrino detectors based on noble element time-
projection chambers are built with fast light detection devices coupled with
photon wavelength-shifters that integrate the light signal over a wide
spectral range, missing the potential information provided by the
scintillation wavelength.

We have studied the primary and the recombination scintillation of the argon
gas with a wavelength sensitive detector operated with $\upalpha$ and
$\upbeta$ sources electrodeposited on stainless steel disks. Our results
evidence the emission of photons at wavelengths larger than the 128 nm line
through a production mechanism which is not based on the excimer formation
associated to the low-lying atomic states. We interpret this component of the
argon scintillation as the third continuum emission.

We have proven that up to 20% of the scintillation obtained with an 241Am
source in 1.5 bar argon gas is in the range $[160,~{}325]$ nm. The photon
yield and the typical emission time of this component are largely independent
from the gas pressure up to 16 bar, and the emission is not significantly
affected by an external electric field. Compared to the second continuum,
which is dominated by the excimer formation time, the third continuum is
remarkably fast and represents the main contribution to the argon light signal
during the first tens of ns, for pressures below 10 bar. Evidence of the third
continuum emission produced by $\upbeta$ interactions in argon gas has been
also obtained for the first time using a $\rm{}^{90}Sr/Y$ source. The
spectroscopic studies of the electron-ion recombination light revealed that
this component is consistent with the 128 nm emission.

We have established that the argon second and the third continuum
scintillation can be distinguished experimentally by means of sensors with
different spectral sensitivities, making possible to exploit distinctive
features of the noble gases photon emission that are not envisaged by the
present experiments. Particularly, our investigations open new paths toward a
novel particle identification technique based on the spectral information of
the noble-elements scintillation light.

## Acknowledgments

This research is funded by the Spanish Ministry of Economy and Competitiveness
(MINECO) through the grant FPA2017-92505-EXP. The authors are also supported
by the “Física de partículas” Unit of CIEMAT through the grant MDM-2015-0509.
DGD is supported by the Ramon y Cajal program (Spain) under contract number
RYC-2015-18820.

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