Electronic address<EMAIL_ADDRESS>
# Pressure suppression of the excitonic insulator state in Ta2NiSe5 observed
by
optical conductivity

H. Okamura  [  T. Mizokawa1 K. Miki  Y. Matsui  N. Noguchi  N. Katayama2 H.
Sawa2 M. Nohara3 Y. Lu4 H. Takagi5,6 Y. Ikemoto7 T. Moriwaki7 Department of
Applied Chemistry, Tokushima University, Tokushima 770-8506, Japan
1Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan
2Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
3Department of Quantum Matter, Hiroshima University, Higashi-Hiroshima
739-8503, Japan  4College of Materials Science and Engineering, National
Engineering Research Center for Magnesium Alloys, Chongqing University,
Chongqing 400044, China  5Department of Physics, University of Tokyo, Tokyo
113-0013, Japan  6Max Planck Institute for Solid State Research, 70569
Stuttgart, Germany  7Japan Synchrotron Radiation Research Institute, Sayo
679-5198, Japan

###### Abstract

The layered chalcogenide Ta2NiSe5 has recently attracted much interest as a
strong candidate for the long sought excitonic insulator (EI). Since the
physical properties of an EI are expected to depend sensitively on the
external pressure, it is important to clarify the pressure evolution of
microscopic electronic state in Ta2NiSe5. Here we report the optical
conductivity [$\sigma(\omega)$] of Ta2NiSe5 measured at high pressures to 10
GPa and at low temperatures to 8 K. With cooling at ambient pressure,
$\sigma(\omega)$ develops an energy gap of about 0.17 eV and a pronounced
excitonic peak at 0.38 eV, as already reported in the literature. Upon
increasing pressure, the energy gap becomes narrower and the excitonic peak is
broadened. Above a structural transition at $P_{s}\simeq$ 3 GPa, the energy
gap becomes partially filled, indicating that Ta2NiSe5 is a semimetal after
the EI state is suppressed by pressure. At higher pressures, $\sigma(\omega)$
exhibits metallic characteristics with no energy gap. The detailed pressure
evolution of $\sigma(\omega)$ is presented, and discussed mainly in terms of a
weakening of excitonic correlation with pressure.

##  I Introduction

Excitonic insulator (EI) is an unconventional insulator in which the
attractive correlation between electrons and holes results in a collective
condensation of electron-hole ($e$-$h$) pairs (excitons) and an energy gap at
the Fermi level ($E_{\rm F}$). EI was first predicted theoretically in the
1960s,EI-review  with a phase diagram schematically shown in Fig. 1.

Figure 1: Schematic phase diagram of EI in terms of the temperature ($T$) and
the one-particle band gap in the absence of $e$-$h$ correlation ($E_{g}$).
Positive and negative values of $E_{g}$ correspond to semiconducting and
semimetallic states, respectively. An EI state is expected in the vicinity of
$E_{g}$=0 below the transition temperature ($T_{c}$), with a characteristic
flattening of the band edges as indicated.

The starting material for EI can be either a semimetal ($E_{g}<$ 0) or
semiconductor ($E_{g}>$ 0), where $E_{g}$ indicates the one-particle band gap
in the absence of $e$-$h$ correlation. An EI state is expected in the vicinity
of $E_{g}$=0 below the transition temperature $T_{c}$ if the exciton binding
energy $E_{b}$ is larger than $|E_{g}|$. Another feature of the EI is a
characteristic flattening of the bands as indicated in Fig. 1.

Despite the theoretical interest on EI, only a few compounds had been
considered as candidates for EI, including TmSe1-xTexwachter  and
1$T$-TiSe2.TiSe2  In 2009, Wakisaka et al.wakisaka  suggested that Ta2NiSe5
should be an EI on the basis of angle-resolved photoemission spectroscopy
(ARPES) data. Ta2NiSe5 has a layered crystal structure, and exhibits a
structural phase transition at $T_{c}$=328 K, where the crystal symmetry
changes from orthorhombic to monoclinic with decreasing temperature
($T$).sunshine ; salvo  Below $T_{c}$, the resistivity increases rapidly with
cooling, indicating an energy gap of about 0.2 eV.salvo  The ARPES study at
low $T$ found an unusually flat dispersion at the top of valence band, which
was ragarded as strong evidence for an EI.wakisaka  Further ARPES studyseki
and band calculationseki ; kaneko  indicated that the flat band feature
persisted even above $T_{c}$, and suggested the low-$T$ phase of Ta2NiSe5 to
be an EI in the strong coupling regime caused by a condensation of preformed
excitons.kaneko ; seki  It was pointed out that above $T_{c}$ the
hybridization between the Ta 5d conduction band and Ni 3d valence band at
$\Gamma$ point should be forbidden by symmetry. It was also suggested that the
structural change below $T_{c}$ was mainly driven by the exciton condensation,
rather than by a structural instability due to electron-lattice ($e$-$l$)
coupling.kaneko  Lu et allu  reported transport and optical data of
Ta2Ni(Se,S)5 and Ta2Ni(Se,Te)5, where the chemical substitution and external
pressure were used to control $E_{g}$ of Ta2NiSe5. The optical conductivity
[$\sigma(\omega)$] of Ta2NiSe5 at low $T$ clearly exhibited a pronounced peak
of excitonic origin at about 0.4 eV, and an energy gap of about 0.16 eV. An
experimental phase diagram of Ta2NiSe5 was constructed from the transport
data, which was indeed consistent with the predicted one depicted in Fig. 1
and strongly suggested Ta2NiSe5 to be an EI.lu  Detailed $\sigma(\omega)$
databoris  were analyzed by a theoretical study,sugimoto  which again
suggested that Ta2NiSe5 should be an EI in the strong coupling regime below
$T_{c}$, and it should be a semiconductor ($E_{g}>$ 0) above $T_{c}$.sugimoto

Many more works on Ta2NiSe5 have also been reported, including ARPES,mor1 ;
okazaki1 ; mizokawa ; tang ; okazaki2 ; saha ; fukutani1 ; chen ; watson ;
fukutani2  optical conductivity,seo ; matsubayashi  Raman scattering,yan ;
raman-MPI ; sood ; kim ; volkov  ultrafast laser spectroscopy,weudehausen ;
mor2 ; okamoto  resonant inelastic X-ray scattering,rixs1 ; rixs2  high
pressure studies,matsubayashi ; sood ; sawa  scanning tunneling
spectroscopy,STM  and theoretical analyses.watson ; subedi ; mazza  While many
of these works support that the transition at $T_{c}$ is driven by exciton
condensation, some of them question such scenario.watson ; rixs2 ; subedi  For
example, a semimetallic ($E_{g}<$ 0) band dispersion around $E_{\rm F}$ has
been reported by an ARPES study above $T_{c}$.watson  Theoretically, it has
been shown that a flat valence band may be obtained by a band calculation
without $e$-$h$ correlation,watson  and that there can be a sizable ($\sim$
0.1 eV) hybridization with the mirror symmetry breaking below $T_{c}$ but
without $e$-$h$ correlation.subedi

Following the above development, it is important to carefully evaluate effects
of both the $e$-$h$ correlation and $e$-$l$ coupling in Ta2NiSe5. An important
aspect is the response of Ta2NiSe5 to changes in the ratio $E_{b}/E_{g}$,
since the physical properties of EI should sensitively depend on
$E_{b}/E_{g}$. In this regard, photo-excited experiments, which are probed by
either ARPESmor1 ; okazaki1 ; mizokawa ; tang ; okazaki2 ; saha  or
laser,weudehausen ; mor2 ; okamoto  have the advantage of being able to tune
the carrier density, and hence to control $E_{b}$ through the Coulomb
screening of $e$-$h$ attraction. In fact, photo-induced gap closing and
semimetallic states in Ta2NiSe5 have been observed and analyzed. mor1 ;
okazaki1 ; mizokawa ; tang ; okazaki2 ; saha ; okamoto  Another effective way
of tuning an EI state is the application of external pressure ($P$),lu ; sood
; sawa ; matsubayashi  since an applied pressure usually broadens the
conduction and valence bands, and increases (reduces) their overlap
(separation). Detailed high-$P$ studiessawa ; matsubayashi  have been
performed on the crystal structure, resistivity ($\rho$), Hall coefficient,
and $\sigma(\omega)$ of Ta2NiSe5. They revealed a rich $P$-$T$ phase diagram
of Ta2NiSe5 as depicted in Fig. 2.

Figure 2: Temperature ($T$)-pressure ($P$) phase diagram of Ta2NiSe5
reproduced from Matsubayashi et al.matsubayashi  $T_{c}$, $T^{\ast}$, and
$P_{s}$ indicate the structural transition temperatures and pressure, and
$T_{sc}$ the superconducting transition temperature. The green arrows and dots
indicate the ($P,T$) paths and points where $\sigma(\omega)$ was measured in
this work.

Above the first order structural transition at $P_{s}\simeq$ 3 GPa, the $ac$
plane becomes flatter with a less rippling of $ac$ plane along the $c$
axis.sawa ; matsubayashi  $\rho(T)$ is reduced with increasing $P$, showing a
crossover from semiconducting $T$ dependence below $P_{s}$ to a completely
metallic one well above $P_{s}$, with quite large and dramatic change of
$\rho(T)$ around $P_{s}$. A superconductivity with $T_{c}$=2 K appears at
about 8 GPa. Above $P_{s}$, from $\rho(T)$ and $\sigma(\omega)$ data, it has
been shown that Ta2NiSe5 is a semimetal with a partial energy gap, in contrast
to the full energy gap below $P_{s}$. It has been suggested that the
electronic transition at $T^{\ast}$ to the low-$T$ semimetallic state is
caused by $e$-$l$ coupling, while that at $T_{c}$ below $P_{s}$ is caused by
both excitonic correlation and $e$-$l$ coupling.matsubayashi

In this paper, we present a full account of the $\sigma(\omega)$ and
reflectance data of Ta2NiSe5 at high $P$ and low $T$, which have been obtained
at the ($P$, $T$) points indicated in Fig. 2. The data reveal how the well-
developed energy gap and excitonic peak at $P$=0, which have been taken as
evidence for an EI, are suppressed as the applied pressure reduces the
excitonic correlation.

##  II Experimental

The samples of Ta2NiSe5 used were single crystals grown with the chemical
vapor transport method as reported previously.lu  The reflectance spectrum at
zero external pressure [$R_{0}(\omega)$] was measured at 0.015-4.5 eV photon
energy rangeokamura-chapter  on an as-grown, specular surfaces.
$\sigma(\omega)$ was derived from the measured $R_{0}(\omega)$ using the
standard Kramers-Kronig (KK) analysis.dressel  Below the measured energy
range, $R_{0}(\omega)$ was extrapolated by the Hagen-Rubens function or a
constant, depending on the data.dressel  Above the measured range, it was
extrapolated by a function of the form $\omega^{-d}$.gaisou  $T$ dependence of
$R_{0}(\omega)$ were measured below 1.4 eV, and above 1.4 eV the
$R_{0}(\omega)$ at 295 K was connected. Reflectance spectra at high $P$ were
measured using a diamond anvil cell (DAC).pressure-review  Type IIa diamond
anvils with a 0.8 mm culet diameter and a stainless steel gasket were used to
seal the sample with KBr as the pressure transmitting medium. An as-grown
surface of a sample was directly attached on the culet surface of the diamond
anvil, and the reflectance at the sample/diamond interface [$R_{d}(\omega)$]
was measured. A gold film was also sealed with the sample as the reference of
reflectance. The pressure in the DAC was measured with the ruby fluorescence
method.NBS  $R_{d}(\omega)$ at high $P$ and low $T$ were measured at photon
energies between 0.025 and 1.1 eV, using synchrotron radiation as a bright
infrared sourceJPSJ-review  at the beamline BL43IR of SPring-8.micro  The
measured $R_{d}(\omega)$ spectra below 1.1 eV were connected to the
$R_{d}(\omega)$ above 1.1 eV given by the KK analysis of measured
$R_{0}(\omega)$ at 295 K and the refractive index of diamond ($n_{d}$=2.4).
Then the connected $R_{d}(\omega)$ spectra were used to obtain
$\sigma(\omega)$ by a modified KK analysis.okamura-kk  More details of the
high pressure infrared experiments are reported elsewhere.pressure-review

##  III Results and Discussions

In the crystal structure of Ta2NiSe5, the (-Ta-Se-) and (-Ni-Se-) chains
extend along the $a$ axis in the $a$-$c$ layers stacked along the $b$
axis.sunshine ; salvo  Therefore, characteristic optical responses of EI are
expected with $E\parallel a$ polarization where $E$ is the electric field of
the incident light. $R_{0}(\omega)$ and $\sigma(\omega)$ spectra of Ta2NiSe5
measured at ambient pressure ($P$=0) are indicated in Figs. 3(a) and 3(b),
respectively.

Figure 3: (a) Optical reflectance [$R_{0}(\omega)$] and (b) conductivity
[$\sigma(\omega)$] of Ta2NiSe5 at different temperatures and at ambient
pressure. $E\parallel a$ and $E\parallel c$ denote incident light polarized
along $a$ and $c$ axes, respectively. The broken line in (b) is a guide to the
eye, indicating the onset at 0.17 eV. (c) Schematic diagrams indicating the
optical transitions in an EI (red curves) and a band insulator (green curves).

In the $E\parallel a$ data, with cooling, $R_{0}(\omega)$ exhibits large $T$
dependences. $\sigma(\omega)$ develops a clear energy gap with the onset at
about 0.17 eV, as indicated by the broken line in Fig. 3(b), and a pronounced
peak centered at $\simeq$ 0.38 eV.footnote1  The sharp spikes below 0.05 eV
are due to optical phonons and the periodic oscillations below 0.1 eV are due
to interference caused by internal reflections from the rear surface of the
sample. In contrast, in the $E\parallel c$ data, both $R_{0}(\omega)$ and
$\sigma(\omega)$ are much lower than those in the $E\parallel a$ data, and
their $T$ dependence is much smaller. At 8 K, the onset of $\sigma(\omega)$
appears to be located around 0.3 eV, with only a gradual increase of
$\sigma(\omega)$ above the onset. These results are very similar to previously
reported $P$=0 data in the literature.lu ; boris ; seo  The development of the
energy gap and the pronounced peak with $E\parallel a$ have been interpreted
as the result of EI state formation below $T_{c}$. The peak at 0.38 eV is an
excitonic peak, as already discussed in Introduction, and its origin can be
basically understood in terms of a band flattening as illustrated in Fig.
3(c).

Figure 4: (a) Optical reflectance [$R_{d}(\omega)$] and (b)(c) conductivity
[$\sigma(\omega)$] of Ta2NiSe5 at 295 K under high pressure ($P$).
$R_{d}(\omega)$ in the 0.235-0.285 eV range has been interpolated by a
straight line since it could not be measured well due to strong absorption by
diamond.pressure-review  In (c), the same spectra as those in (b) are
vertically offset, and the broken line indicates the shift and suppression of
the excitonic peak. (d)-(f) $R_{d}(\omega)$ of Ta2NiSe5 measured at $P$=2.5,
3.5, and 6.5 GPa and at different temperatures. (g)-(j) $\sigma(\omega)$ of
Ta2NiSe5 at $P$=0, 2.5, 3.5, and 6.5 GPa and at low temperatures. The red
vertical arrows indicate the onset of $\sigma(\omega)$ discussed in the text.
The same temperature labels (the colors of the curves) apply in (d)-(f) and
(g)-(j).

In a conventional insulator, the optical excitation between the band edges
lead to the increase of $\sigma(\omega)$ above the band gap, as indicated by
the green curves in Fig. 3(c). The spectrum in this case is actually similar
to that measured with $E\parallel c$ in Fig. 3(b). In the case of EI, in
contrast, the band edges are flattened by excitonic correlation. This results
in a larger density of states (DOS) at the band edges, which should cause an
enhancement in $\sigma(\omega)$ as shown by the red curves in Fig. 3(c). The
spectrum in this case is very similar to that observed with $E\parallel a$ in
Fig. 3(b). The $T$ evolution of $\sigma(\omega)$ in Ta2NiSe5 has also been
discussed in terms of exciton-phonon Fano effectboris  and exciton superfluid
formation.seo  The shifts of the onset and the transfer of spectral weight in
$\sigma(\omega)$ will be discussed later.

Pressure evolution of $R_{d}(\omega)$ and $\sigma(\omega)$ at 295 K with
$E\parallel a$ is shown in Figs. 4(a)-4(c). Upon applying pressure, both
$R_{d}(\omega)$ and $\sigma(\omega)$ below 0.2 eV exhibit large increases. In
particular, $\sigma(\omega)$ below $\sim$ 0.2 eV, which is reduced by the
energy gap at $P$=0, rapidly increases with $P$. In addition, the excitonic
peak is broadened and red-shifted with $P$, and is almost suppressed at 3 GPa
and above. This is more clearly seen in Fig. 4(c) where the spectra are
vertically offset. The large spectral change at around 3 GPa is almost
coincident with the structural transition at $P_{s}$ (Fig. 2). Since $P_{s}$
is believed to be the boundary of EI phase,matsubayashi  it is reasonable that
the excitonic peak is suppressed above $P_{s}$. The broadening and red shift
of the excitonic peak below $P_{s}$ probably indicate the weakening of
excitonic correlation even within the EI phase below $P_{s}$. As discussed in
Appendix, Raman spectra of Ta2NiSe5 at high $P$ were also measured, using the
same DAC and sample condition. The Raman spectra (Fig. 7) exhibit a sudden
shift and disappearance of phonon peaks around 3 GPa, which should result from
the first order structural transition at $P_{s}$. This Raman result further
supports that the observed spectral changes in $\sigma(\omega)$ indeed result
from the structural transition at $P_{s}$. With increasing $P$ above 3 GPa,
$\sigma(\omega)$ further increases and shows metallic characteristics with a
rising (Drude) component toward zero energy.

Temperature dependent $R_{d}(\omega)$ spectra at $P$=2.5, 3.5 and 6.5 GPa are
indicated in Figs. 4(d)-(f), and the corresponding $\sigma(\omega)$ spectra in
Figs. 4(h)-4(j). First, note that the large $T$ dependences of $R_{d}(\omega)$
and $\sigma(\omega)$ observed at $P$=0 are progressively reduced with
increasing $P$. Accordingly, both the energy gap and excitonic peak at low $T$
are progressively suppressed with $P$. At 2.5 GPa, $\sigma(\omega)$ develops a
clear energy gap with cooling [Fig. 4(h)], but the onset of $\sigma(\omega)$
at 8 K is located at 0.062 eV, which is much smaller than that at $P$=0 [Fig.
4(g)]. Namely, a clear energy gap still exists at $P$=2.5 GPa, but its width
is significantly reduced from that at $P$=0. At 3.5 GPa, $\sigma(\omega)$
below 0.2 eV is still strongly reduced with cooling, but unlike those at $P$=0
and 2.5 GPa, it is not completely depleted even at 8 K. A rising component
toward zero energy is observed 8 K, which should be a Drude component due to
free carriers. The thermal energy $k_{\rm B}T$, where $k_{\rm B}$ is the
Boltzmann constant, is about 0.7 meV at 8 K, while the tail of the Drude
component at 8 K extends to much higher energy, $\sim$ 50 meV. Therefore, the
electronic state at 3.5 GPa and 8 K is difficult to understand as a
semiconductor with thermally excited free carriers. Instead, it should be a
semimetal with a band overlap of the order of 50 meV. Accordingly, the energy
gap at 3.5 GPa should be a partial one, which is open only in certain portions
of the Brillouin zone.matsubayashi  At 6.5 GPa, the spectra show only minor
$T$ dependences, and $\sigma(\omega)$ below 0.4 eV is almost unchanged from
295 to 8 K. Clearly, at 6.5 GPa there is no energy gap in Ta2NiSe5 and its
electronic structure is quite metallic.

To examine more closely the variations of energy gap with $P$ and $T$, the
low-energy portion of $\sigma(\omega)$ at $P$=0 and 2.5 GPa are displayed in
Figs. 5(a) and 5(b), respectively.

Figure 5: Low-energy portion of $\sigma(\omega)$ in $E\parallel a$
polarization at (a) $P$=0 and (b) $P$=2.5 GPa. The broken lines indicate
extrapolations to the linear-in-energy portion of the spectra, and the
vertical arrows indicate the onset given by the zero crossing. (c) The onset
energy in (a) and (b) plotted as a function of temperature ($T$). The broken
curves indicate $\Delta(T)=\Delta(0)\\{1-(T/T_{c})^{\alpha}\\}$ with the
indicated values of $\alpha$. $\Delta(0)$=0.175 eV and $T_{c}$=328 K are used
for $P$=0, and $\Delta(0)$=0.062 eV and $T_{c}$=170 K for $P$=2.5 GPa.

The broken lines are extrapolations to the linear-in-energy portion in
$\sigma(\omega)$. Their zero crossings, marked with the vertical arrows,
indicate the onset of $\sigma(\omega)$. Here we regard the onset energy as the
gap width $\Delta$, following a previous $\sigma(\omega)$ work on Ta2NiSe5
(Ref. [seo, ]) and other optical studies on strongly correlated electron
systems.basov  At $P$=0 [Fig. 5(a)], the extrapolation crosses zero at 295 K
and below, but not at 320 K. Namely, the gap in $\sigma(\omega)$ becomes fully
open at 295 K and below, which is reasonable since the gap formation starts
below $T_{c}$=328 K and the gap is not well developed yet at 320 K. The $T$
dependence of the onset energy is plotted in Fig. 5(c). The result is similar
to that previously reported by Ref. [seo, ], which reported a $T$ dependence
of the form $\Delta(T)=\Delta(0)\\{1-(T/T_{c})^{\alpha}\\}$ with $\alpha$=2.
For comparison, in Fig. 5(c) we also plot this function with $T_{c}$=328 K and
$\alpha$=2, 2.5, and 3. It is seen that the present data is close to
$\alpha$=2.5, but cannot be well described by a single exponent. At 2.5 GPa
[Fig. 5(b)], the extrapolation crosses zero at 160 K and below, but not at 200
K. Namely, the gap becomes fully open at 160 K and below, which is much lower
than $T_{c}\simeq$ 290 K at 2.5 GPa. This is in contrast to the $P$=0 case
above, where the gap in $\sigma(\omega)$ is already open at 295 K which is
below but still close to $T_{c}$=328 K. Namely, it seems that the $P$
dependence of the energy gap in $\sigma(\omega)$ is different from that of
$T_{c}$. The $T$ dependence of the onset at 2.5 GPa is also plotted in Fig.
5(c). It is similar to that at $P$=0, but to fit with the form
$\Delta(T)=\Delta(0)\\{1-(T/T_{c})^{\alpha}\\}$, $T_{c}\simeq$ 170 K and
$\alpha\simeq$ 2.5 are required as shown by the broken curve in Fig. 5(c).
Note that the use of this functional form is only phenomenological, and not
based on a microscopic model for EI. The much stronger suppression of energy
gap by pressure than that of $T_{c}$ will be discussed again later.

To analyze the spectral weight (SW) transfer in $\sigma(\omega)$ with $P$ and
$T$, the effective electron number $N^{\ast}(\omega)$ per formula unit (fu) of
Ta2NiSe5, expressed as dressel

$N^{\ast}(\omega)=\frac{n}{m^{\ast}}(\omega)=\frac{2m_{0}}{\pi
e^{2}N_{0}}\int_{0}^{\omega}\sigma(\omega^{\prime})d\omega^{\prime},$ (1)

is plotted in Fig. 6.

Figure 6: Effective electron number $N^{\ast}(\omega)$ per formula unit (fu)
of Ta2NiSe5, calculated with Eq. (1) and the measured $\sigma(\omega)$ spectra
at different pressures and temperatures.

Here, $n$, $m^{\ast}$ and $e$ are the electron density, effective mass in
units of the rest mass $m_{0}$, and the elementary charge. $N_{0}$ is the
number of fu’s per unit volume, which was calculated using the high $P$
crystal structure data.sawa ; footnote4  $N^{\ast}(\omega)$ can be regarded as
the number of electrons that contribute to $\sigma(\omega)$ between 0 and
$\omega$, therefore it directly reflects the SW transfer up to $\omega$. At
all $P$ and $T$ in Fig. 6, $N^{\ast}(\omega)$ at 1 eV is of the order of 1
fu-1, which is reasonable compared with the total DOS within 1 eV from $E_{\rm
F}$ given by band calculations.matsubayashi  At $P$=0, $N^{\ast}(\omega)$
varies with $T$ over a wide energy range. The $N^{\ast}(\omega)$ spectra at
different temperatures do not converge even at 1 eV, showing that the
electronic structure reconstruction in the EI phase occurs over a wider energy
scale than the gap width (0.17 eV) and the excitonic peak energy (0.4 eV). At
2.5 and 3.5 GPa, however, $N^{\ast}(\omega)$ varies with $T$ only up to about
0.6 eV, indicating that the SW transfer is complete within 0.6 eV. At 6.5 GPa,
$N^{\ast}(\omega)$ is almost independent of $T$. These results show that both
the amount and energy range of the SW transfer are progressively suppressed by
$P$, which is closely related with the suppression of energy gap.

As discussed in Introduction, it has been pointed out that the gap formation
in Ta2NiSe5 below $P_{s}$ may be partly due to $e$-$l$ coupling, rather than
being solely due to $e$-$h$ (excitonic) correlation. If their relative
contributions do not change with $P$, and if both the structural transition at
$T_{c}$ and the gap opening below $T_{c}$ are driven by a common mechanism,
then one would naively expect that $\Delta$ and $T_{c}$ should have similar
$P$ dependences. This is in contrast to the present results, in which the
reduction of $\Delta$ by pressure is much greater than that of $T_{c}$ (from
$\Delta$=0.17 eV and $T_{c}$=328 K at $P$=0 to $\Delta$=0.062 eV and
$T_{c}\simeq$ 290 K at 2.5 GPa). Namely, in terms of the $P$ dependence,
$\Delta$ is not scaled with $T_{c}$. Interestingly, a pressure decoupling
between electronic and structural transitions has been observed in
BaFe2As2,Ba122  which is another pressure-induced superconductor. The present
results for Ta2NiSe5 may suggest that, somehow, the $e$-$h$ correlation is
more responsible for the gap development below $T_{c}$, while the $e$-$l$
coupling is more responsible for the structural transition at $T_{c}$. This
would naturally lead to a stronger suppression of $\Delta$ than $T_{c}$ by
pressure, since the $e$-$h$ correlation is likely more reduced by pressure
than the $e$-$l$ coupling as long as the structure does not change. An
understanding of these $P$ dependences based on a specific microscopic model
is beyond the scope of the present study. It is hoped that effects of both the
$e$-$h$ correlation and the $e$-$l$ coupling with symmetry breaking-induced
hybridization are both included in a microscopic model to understand the
pressure evolution of electronic states in Ta2NiSe5.

##  IV Summary

$\sigma(\omega)$ spectra of Ta2NiSe5, a strong candidate for an EI, have been
measured at high pressures and at low temperatures. A clear energy gap of
about 0.17 eV and a marked excitonic peak at 0.38 eV at $P$=0 are suppressed
with increasing $P$, which is especially marked across the structural
transition at $P_{s}$=3 GPa. At 2.5 GPa ($<P_{s}$), the gap is still clearly
open with a reduced width of 0.062 eV, but at 3.5 GPa ($>P_{s}$), the gap is
partially filled, indicating that the ground state above $P_{s}$ is
semimetallic. At 6.5 GPa, $\sigma(\omega)$ shows very metallic characteristics
with no energy gap. These results have been discussed in terms of a
progressive weakening of excitonic correlation with pressure. Also, it is
noted that the reduction of energy gap with pressure is much greater than that
of $T_{c}$. This result may suggest that the relative importance of $e$-$h$
correlation and $e$-$l$ coupling in the gap formation changes with pressure.

###### Acknowledgements.

We would like to thank Prof. K. Matsubayashi, Prof. Y. Ohta, and Prof. K.
Sugimoto for useful discussions. Experiments at SPring-8 were performed under
the approval by JASRI (Proposal numbers 2013A1085, 2015B1698, 2016A1166,
2017A1163, 2017A1164.) This work was supported by KAKENHI (21102512, 23540409,
26400358, 19H00659, 17H06456)

*

##  Appendix A Raman spectra at high pressures

Raman scattering spectra of Ta2NiSe5 measured at high pressures and at 295 K
are shown in Fig. 7.

Figure 7: Raman spectra of Ta2NiSe5 measured at high pressures ($P$) and at
295 K. The spectra are vertically offset for clarity. The excitation was made
at 532 nm with $E\parallel a$ polarization. The broken lines are guide to the
eye, emphasizing the sudden changes at around 3 GPa.

The measurement was made under a back scattering geometry on an as-grown
sample surface containing the $ac$ plane. A standard micro-Raman apparatus was
used with a 532 nm laser source polarized along the $a$ axis. High pressures
were applied using the same DAC as that used for the $\sigma(\omega)$ studies,
with exactly the same procedure for sample loading. In Fig. 7, the Raman peaks
are due to optical phonons.yan ; raman-MPI ; sood  As indicated by the broken
lines in Fig. 7, the peak near 100 cm-1 is blue shifted and the peak near 125
cm-1 disappears in the spectra at 3.1 GPa and above. These sudden changes
should result from the first-order structural phase transition at $P_{s}$
(Fig. 2), where the rippling of the $ac$ plane along $c$ axis is reduced above
$P_{s}$.sawa ; matsubayashi

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