# Fermiology of a topological line-nodal compound CaSb2 and its implication to
superconductivity: angle-resolved photoemission study

Chien-Wen Chuang,1 Seigo Souma,2,3 Ayumi Moriya,1 Kosuke Nakayama,1,4
Atsutoshi Ikeda,5 Mayo Kawaguchi,6 Keito Obata,6 Shanta Ranjan Saha,5
Hidemitsu Takahashi,6 Shunsaku Kitagawa,6 Kenji Ishida,6 Kiyohisa Tanaka,7,8
Miho Kitamura,9 Koji Horiba,9,10 Hiroshi Kumigashira,11 Takashi Takahashi,1
Shingo Yonezawa,6 Johnpierre Paglione,5 Yoshiteru Maeno,6 and Takafumi
Sato1,2,3,12 1Department of Physics, Graduate School of Science, Tohoku
University, Sendai 980-8578, Japan
2Center for Science and Innovation in Spintronics (CSIS), Tohoku University,
Sendai 980-8577, Japan
3Advanced Institute for Materials Research (WPI-AIMR), Tohoku University,
Sendai 980-8577, Japan
4Precursory Research for Embryonic Science and Technology (PRESTO), Japan
Science and Technology Agency (JST), Tokyo, 102-0076, Japan
5Maryland Quantum Materials Center and Department of Physics, University of
Maryland, College Park, Maryland 20742-4111, USA
6Department of Physics, Kyoto University, Kyoto 606-8502, Japan
7UVSOR Synchrotron Facility, Institute for Molecular Science, Okazaki
444-8585, Japan
8School of Physical Sciences, The Graduate University for Advanced Studies
(SOKENDAI), Okazaki 444-8585, Japan
9Institute of Materials Structure Science, High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
10National Institutes for Quantum Science and Technology (QST), Sendai
980-8579, Japan
11Institute of Multidisciplinary Research for Advanced Materials (IMRAM),
Tohoku University, Sendai 980-8577, Japan
12International Center for Synchrotron Radiation Innovation Smart (SRIS),
Tohoku University, Sendai 980-8577, Japan

###### Abstract

We performed angle-resolved photoemission spectroscopy with micro-focused beam
on a topological line-nodal compound CaSb2 which undergoes a superconducting
transition at the onset $T_{\rm{c}}\sim$ 1.8 K, to clarify the Fermi-surface
topology relevant to the occurrence of superconductivity. We found that a
three-dimensional hole pocket at the $\Gamma$ point is commonly seen for two
types of single-crystalline samples fabricated by different growth conditions.
On the other hand, the carrier-doping level estimated from the position of the
chemical potential was found to be sensitive to the sample fabrication
condition. The cylindrical electron pocket at the Y(C) point predicted by the
calculations is absent in one of the two samples, despite the fact that both
samples commonly show superconductivity with similar $T_{\rm{c}}$’s. This
suggests a key role of the three-dimensional hole pocket to the occurrence of
superconductivity, and further points to an intriguing possibility to control
the topological nature of superconductivity by carrier tuning in CaSb2.

##  I INTRODUCTION

Initiated by the discovery of topological insulators (TIs) whose surface or
edge hosts gapless states despite the insulating nature of bulk HasanRMP2010 ;
QiRMP2011 ; AndoJPSJ2013 , the search for new quantum states of matter
characterized by the non-trivial topology is becoming one of major challenges
in condensed-matter physics. While TI and topological superconductor (TSC) - a
superconducting analog of TI - commonly contain a finite energy gap in the
bulk (band gap and superconducting gap, respectively), the classification of
band topology has been successfully extended to the systems with gapless bulk
excitations, leading to the discovery of topological semimetals (TSMs). The
first concrete example of TSMs is the three-dimensional (3D) topological Dirac
semimetal such as Na3Bi and Cd3As2 WangPRB2012 ; WangPRB2013 ; NeupaneNC2014 ;
BorisenkoPRL2014 ; LiuScience2014  where a linearly dispersive bulk valence
band (VB) and a conduction band (CB) contact each other at a discrete point in
the 3D k space. Weyl semimetal is also characterized by the point touching of
VB and CB, while the bulk band degeneracy is lifted by the breaking of time-
reversal or space inversion symmetry XuScience2015 ; LvPRX2015 ; YangNP2015 ;
SoumaPRB2016 ; ArmitageRMP2018 . There is another type of TSM called line-
nodal semimetal where the crossing point extends one-dimensionally in the k
space (nodal line or loop), being protected by the crystal symmetry such as
mirror reflection or nonsymmorphic glide mirror symmetry BurkovPRB2011 ;
WuNP2016 ; BianNC2016 ; BianPRB2016 ; YamakageJPSJ2016 ; GuanSciAdv2016 ;
WengPRB2016 ; TakaneNPJQM2018 ; XuPRB2015 ; SchoopNC2016 ; TakanePRB2016 ;
NeupanePRB2016 ; louPRb2016 ; FangCPB2016 ; ChenPRB2017 . While such TSMs, or
more widely, materials containing Dirac/Weyl or line nodes in the bulk-band
structure, are already a useful platform to realize exotic quantum phenomena
such as unusual magneto-transport properties, the coupling of nodal electrons
to superconductivity is another intriguing target of intensive investigations
because such a coupling would provoke the topological superconductivity
KobayashiPRL2015 . However, this essential issue remains highly unexplored,
because superconducting materials whose low-energy excitations are
characterized by Dirac/Weyl or line-nodal electrons are generally rare
BianNC2016 ; ZhangScience2018 ; OrtizPRM2019 ; AggarwalNM2016 .

Figure 1:  (a) Crystal structure (side view) of CaSb2. Two types of Sb atoms
at different sites (Sb1 and Sb2) are indicated by green and orange circles.
(b) Monoclinic bulk Brillouin zone (BZ) of CaSb2. Red lines indicate high-
symmetry lines where the band calculation shown in (c) was carried out.
$k_{x}$, $k_{y}$, and $k_{z}$ axes are also indicated. (c) Calculated band
dispersions along high-symmetry lines in bulk BZ. (d) Calculated FSs in bulk
BZ which incorporate (top panel) no $\mu$ shift and (bottom panel) downward
$\mu$ shift of 210 meV. (e) X-ray Laue diffraction pattern of CaSb2 single
crystal. (f) EDC which includes the Sb 4$d$ and Ca 3$p$ core levels measured
with $h\nu$ = 90 eV. The EDC was obtained by integrating the ARPES spectra
collected within angular window of $\pm$ 15∘ around the surface normal. Inset
shows an expanded view of the Ca 3$p$ core level. (g) Near-$E_{\rm{F}}$ ARPES
intensity crossing the $\Gamma$ point at $k_{z}$ = 0 measured at $T$ = 40 K
with $h\nu$ = 118 eV. (h) Corresponding calculated band structure along the
$\Gamma$Y cut ($k_{z}$ = 0 plane) which takes into account the downward $\mu$
shift of 210 meV. Dashed line indicates the original Fermi-level position,
$E_{\rm{F}}$’.

Recently, the superconductivity with superconducting transition temperature
($T_{\rm{c}}$) of 1.7 K was discovered in a line-nodal compound CaSb2
IkedaPRM2020 . This material crystalizes in the monoclinic structure with
$P2_{1}/m$ space group with Sb zigzag chains running along the $b$-axis and
mirror surfaces in the $a$-$c$ plane, as shown in Fig. 1(a), where one can
recognize two types of Sb atoms, Sb1 and Sb2, at different sites in the unit
cell [note that the bulk Brillouin zone (BZ) is shown in Fig. 1(b)]. First-
principles band-structure calculations of CaSb2 predicted the compensated
semimetallic band structure [Fig. 1(c)] consisting of a 3D hole pocket
extending roughly along the $\Gamma$X direction and quasi-two-dimensional (2D)
cylindrical electron pockets axially centered along the YC line [top panel of
Fig. 1(d)]. Band structure calculations with the spin-orbit coupling (SOC)
predicted the presence of several Dirac points at specific k points such as Y,
C, E, and A points (but not $\Gamma$ and Z points which are related to the 3D
pocket) due to the nonsymmorphic symmetry FunadaJPSJ2019  [some of these Dirac
points at the Y and C points are indicated by black arrows in Fig. 1(c)]. Such
band crossings are connected to the line nodes at the $k_{y}$ = $\pi$ plane
FunadaJPSJ2019  and one of them is associated with the shallow electron pocket
crossing $E_{\rm{F}}$, likely contributing to the transport properties, while
these line nodes and Dirac nodes had to await experimental verification.

Magneto-transport measurements of CaSb2 clarified a resistivity plateau under
a weak magnetic field at 10 K and nonsaturating giant magnetoresistance,
consistent with the existence of line nodes FunadaJPSJ2019 . Electrical
resistivity measurements under pressure revealed the dome-shaped $T_{\rm{c}}$
variation without Lifshitz transition in the normal state KitagawaPRB2021  and
specific heat measurements signified the deviation from the BCS behavior
OudahArXiv2021 , suggestive of the unconventional nature of superconductivity.
On the other hand, 121/123Sb nuclear quadrupole resonance (NQR) measurements
suggested an exponential decrease in the inverse relaxation rate 1/$T_{1}$ at
low temperature, supportive of the conventional $s$-wave superconductivity
with a full gap TakahashiJPSJ2021 . The presence of cylindrical electron
pockets with line nodes has been discussed in favor of topological
superconductivity IkedaPRM2020  associated with the dominant interorbital
pairing interaction with odd-parity pairing within the cylindrical FSs,
similarly to the case of doped TIs SasakiPRL2021  and doped Dirac semimetals
KobayashiPRL2015 ; KawakamiPRX2018 . Topological superconductivity was also
predicted based on the full computation of the $Z_{2}$-enriched symmetry
indicators OnoPRR2021 . Despite such intensive experimental and theoretical
studies, there are no experimental reports on the band structure of CaSb2. It
is thus of great importance to experimentally clarify the electronic states of
CaSb2 to establish the interplay among nodal electrons, superconductivity, and
topology.

In this article, we report micro-focused angle-resolved photoemission
spectroscopy ($\mu$-ARPES) of CaSb2 to clarify the 3D band structure and
Fermi-surface (FS) topology. We observed two different types of FSs in CaSb2;
one is a 3D hole pocket at the $\Gamma$ point and another is a cylindrical
electron pocket at the Y(C) point. We found that the carrier-doping level and
as a result the FS topology are very sensitive to the sample fabrication
condition; the cylindrical electron pocket at the Y(C) point disappears in one
of two samples fabricated by different growth conditions, although both
samples commonly show superconductivity with similar $T_{\rm{c}}$’s. We
discuss implications of the present results in relation to the mechanism of
superconductivity and its relationship with topology.

##  II EXPERIMENTS AND CALCULTIONS

We prepared two different types of single crystalline samples for ARPES
measurements, called here sample A and sample B. The samples A and B were
grown by a self-flux method with molar ratios of Ca:Sb=1:5 and 1:3.1,
respectively. For sample A, Ca (Sigma-Aldrich, 99.99%) and Sb (Alfa Aesar,
99.9999%) were melted at 1000∘C in an alumina crucible inside a sealed quartz
tube, cooled down to 740∘C, and then cooled down to 610∘C at a rate of -1∘C/h.
Crystals were filtered in a centrifuge at this temperature. For sample B, Ca
(Sigma-Aldrich, 99.99%) and Sb (Rare Metallic, 99.99%) were heated in a
similar temperature profile but in a tungsten crucible. We found that typical
size of the single-crystal domains is different between sample A (more than 1
mm size) and sample B (typically a few tens of $\mu$m). From the magnetic
susceptibility measurements, we have confirmed the onset $T_{\rm{c}}$ values
of samples A and B to be $\sim$ 1.8 K, as detailed in Fig. S1 in Section 1 of
Supplemental Material SM .

We performed ARPES measurements at BL28A in KEK-PF KitamuraRSI2022  and BL5U
in UVSOR. We used circularly polarized photons of 30-300 eV at BL28A and
linear horizontally polarized photons of 20-200 eV at BL5U. The energy and
angular resolution was $\sim$ 20 meV and 0.2∘, respectively. The beam size on
sample was 10 $\times$ 12 $\mu$m2 KitamuraRSI2022  and 30 $\times$ 20 $\mu$m2
for BL 28A and BL5U, respectively. Samples were kept at 40 K during
measurements. The Fermi-level ($E_{\rm{F}}$) of samples was referred to that
of a gold film deposited on the sample holder. Laue backscattering
measurements were performed prior to ARPES measurements to determine the
sample geometry. A clear Laue pattern was observed for sample A as shown in
Fig. 1(e), confirming the high single crystallinity of sample (note that it
was difficult to obtain a clear Laue pattern for sample B due to the mixture
of multiple crystal domains. However, we could safely determine the sample
orientation for a small area of sample B on which the micro-ARPES measurement
was performed, by looking at the periodicity and symmetry of obtained band
structure). Since CaSb2 single crystal was very hard to cleave, we tried
cleaving several times in an ultrahigh vacuum (UHV), occasionally obtained a
small flat area on the crystal with a few tens $\mu$m square and then focused
the micro photon beam on it. The cleaving plane is $a$-$b$ plane
(perpendicular to the $c$* axis) according to our x-ray diffraction and ARPES
data. We observed no signature of aging or contamination of sample surface
during ARPES measurements.

We have performed the first-principles band structure calculations by using
Quantum ESPRESSO GiannozziJPCM2009  with generalized gradient approximation
GGA  and have included the SOC. The Perdew-Burke-Ernzerhof (PBE) generalized
gradient approximation was adopted for the exchange-correlation functional.
Lattice constants were referenced from the experimental values IkedaPRM2020
and a $k$ mesh of 18 $\times$ 19 $\times$ 10 was used in the calculations.

##  III RESULTS AND DISCUSSION

To characterize the sample surface cleaved in UHV, we at first carried out
photoemission measurements in a wide energy range with photons of $h\nu$ = 90
eV. The energy distribution curve (EDC) for sample A is shown Fig. 1(f). We
observe two peaks at the binding energy ($E_{\rm{B}}$) of 31.5 and 32.7 eV,
which are attributed to the spin-orbit-split Sb 4$d_{5/2}$ and 4$d_{3/2}$
orbital, respectively. Single-peaked structure of each orbital suggests that
the chemical potential ($\mu$) is almost the same between the Sb1 and Sb2
orbitals. A weak peak at $E_{\rm{B}}$ = 25 eV is assigned to the Ca 3$p$
orbital, as better visualized in the expanded scale in the inset. No other
peaks are observed in this $E_{\rm{B}}$ range, supporting the clean surface.

Figure 2:  (a) Bulk BZ of CaSb2 with the measured k cuts and $k$ planes.
Yellow rectangle represents the $k$ plane ($k_{y}$ \- $k_{z}$ plane) where the
$h\nu$-dependent out-of-plane FS mapping shown in (b) was performed. Red
curves indicate the k cuts (cuts 1-6) where the ARPES measurement shown in (d)
was carried out. The gray rectangles indicate the k slices where in-plane FS
mappings shown in (e) were performed. The slices 7, 8, and 9 correspond to
$k_{z}\sim$ 0, -0.5$\pi$, and -$\pi$, respectively. (b) Out-of-plane FS
mapping in the $k_{y}$ \- $k_{z}$ plane obtained by sweeping $h\nu$. Dashed
red curves are guide for the eyes to trace the $\Gamma$-centered pocket. (c)
Corresponding calculated FSs with (red) and without (blue) taking into account
the downward $\mu$ shift of 210 meV. (d) $h\nu$-dependence of experimental
band dispersions measured along the k cuts (1-6) shown in (a). ARPES data
along cuts 1 and 6 nearly trace the same $k$ region in reduced BZ but measured
with different $h\nu$’s (118 and 88 eV). (e) In-plane FS mapping obtained with
different $h\nu$’s of 118 eV ($k_{z}\sim$ 0: cut 7), 110 eV ($k_{z}\sim$
-0.5$\pi$; cut 8), and 103 eV ($k_{z}\sim$ -$\pi$; cut 9).

Since CaSb2 is a 3D material, it is essential to elucidate the bulk-band
structure in the 3D BZ. For this sake, we have carried out $h\nu$-dependent
ARPES measurements at the normal emission setup to observe the band dispersion
along $k_{z}$ (parallel to the $c$* axis). We at first estimated the inner
potential value to be $V_{0}$ = 13.7 eV from the periodicity of the band
dispersion (for details, see Fig. 2). Then, we performed ARPES measurements at
$h\nu$ = 118 eV which corresponds to the $k_{z}\sim$ 0 plane, along the
$\Gamma$Y ($k_{y}$) cut at $T$ = 40 K. The $\Gamma$Y cut is expected to be
useful to simultaneously observe the holelike band forming a 3D pocket at
$\Gamma$ and an electronlike band forming a quasi-2D pocket at Y, as suggested
from the band calculation displayed in Figs. 1(c) and 1(d). As shown in Fig.
1(g), one can identify a highly dispersive holelike band at $E_{\rm{B}}$ = 0-1
eV which apparently crosses $E_{\rm{F}}$ at $k_{y}$ = $\pm$ 0.18 Å-1 to form a
hole pocket. According to the band calculation OudahArXiv2021 , this band
originates from the Sb2 orbital [see Fig. 1(a)]. Inside this band, another
holelike feature is seen at $E_{\rm{B}}$ = 0.5-1 eV. We found that the energy
dispersion of these bands shows a qualitatively good agreement with the
calculation along the $\Gamma$Y cut shown by red curves in Fig. 1(h), whereas
the calculated bands need to be shifted upward as a whole by 210 meV to obtain
a best matching in the position of Fermi wave vectors ($k_{\rm{F}}$’s) with
the experiment. Surprisingly, we do not observe any signature of electron
pockets at the Y point originating from the Sb1 orbital [see Fig. 1(a)]
OudahArXiv2021 , in sharp contrast to the calculation which does not take into
account the chemical-potential ($\mu$) shift [note that the $E_{\rm{F}}$
position without the $\mu$-shift ($E_{\rm{F}}$’) is indicated by a dashed line
in Fig. 1(h)]. This suggests that sample A is hole-doped probably due to the
off-stoichiometry of the sample, leading to the lift-up of the 2D cylindrical
electron bands into the unoccupied region. We have carefully surveyed the
electron pocket at different in-plane ($k_{x}$ and $k_{y}$) and out-of-plane
wave vectors ($k_{z}$) and found no evidence for it in the entire 3D BZ as
detailed in Fig. 2. Therefore, the transport property of this sample is
expected to be governed by the 3D hole pocket, which is schematically
illustrated by the calculated FS plot including the hole-doping effect in the
bottom panel of Fig. 1(d).

The absence of the electron pocket is suggested from the FS mapping in the
$k_{y}$ \- $k_{z}$ plane [Fig. 2(b)] obtained by changing $h\nu$’s. Although
the band calculation without the $\mu$-shift shown in Fig. 2(c) (blue curves)
predicted the existence of fairly vertical (i.e. quasi-2D) FSs elongated along
the CY cut ($k_{y}\sim$ 0.75 Å-1), the corresponding ARPES intensity is
totally absent as seen in Fig. 2(b). In the experiment, one can see a strong
intensity surrounding the top $\Gamma$ point (at $k_{z}$ = 5.76 Å-1) which
produces an ellipsoidal pocket elongated along the $\Gamma$Z direction (dashed
red curve). This pocket is associated with the holelike band as seen from the
ARPES intensity along the k cut crossing the top $\Gamma$ point (cut 6)
measured at $h\nu$ = 118 eV in Fig. 2(d). On decreasing $h\nu$ (from cut 6 to
cut 4), the separation between two $k_{\rm{F}}$ points indicated by black
arrows gradually becomes narrower due to the downward shift of the holelike
band. Eventually the $k_{\rm{F}}$ points disappear along cut 3 ($h\nu$ = 107
eV) or cut 2 ($h\nu$ = 103 eV), reflecting the 3D closed nature of the hole
pocket as seen from Fig. 2(b). We also observe another hole pocket centered at
the bottom $\Gamma$ point (at $k_{z}$ = 5.04 Å-1) which is equivalent to the
hole pocket centered at the top $\Gamma$ point, as also seen from the ARPES
intensity crossing the bottom $\Gamma$ point along cut 1 in Fig. 2(d).
Intensity of this pocket is weaker probably because of the matrix-element
effect of photoelectron intensity. One can see from a direct comparison of
Figs. 2(b) and 2(c) that the experimental hole pocket is much larger than that
in the calculation without the $\mu$-shift (blue curve at $\Gamma$), but
becomes comparable after the $\mu$-shift (red curve). This is again due to the
aforementioned hole-doping effect.

Now that the absence of 2D electron pocket is established, next we discuss the
shape of 3D hole pocket in more detail. For this sake, we performed the in-
plane ($k_{x}$ \- $k_{y}$) FS mapping at representative $k_{z}$ slices, i.e.
$k_{z}\sim$ 0, -0.5$\pi$ and -$\pi$, as shown in Fig. 2(e). At the slice of
$k_{z}\sim$ 0 ($h\nu$ = 118 eV), one can see a strong intensity concentrated
around the $\Gamma$ point which produces a small pocket slightly elongated
along the $k_{x}$ direction. At the $k_{z}\sim$ -0.5$\pi$ slice ($h\nu$ = 110
eV), this pocket appears to move toward the positive $k_{x}$ region, causing
an apparent asymmetric intensity profile with respect to the $k_{y}$
(horizontal) axis. At the $k_{z}\sim$ -$\pi$ slice ($h\nu$ = 103 eV), the
intensity shows an hourglass shape with two maxima at top and bottom, distinct
from the case of $k_{z}\sim$ 0 plane where intensity is concentrated at the BZ
center. These results suggest that the 3D hole pocket has a rather complicated
“slider” shape in the 3D BZ, as also inferred from the calculated FS shown in
Fig. 1(d). It is noted that the overall $k_{z}$-dependent evolution of the in-
plane FS mapping is consistent with the calculated FS [red curves in Fig.
2(e)]. In particular, the appearance of a small pocket at the $\Gamma$ point
at $k_{z}$ = 0 plane and the movement of this pocket to the positive $k_{x}$
region with increasing $k_{z}$ is well reproduced by the calculation.

Figure 3:  (a) FS mapping at $T$ = 40 K measured with $h\nu$ = 90 eV
(corresponding to $k_{z}$ $\sim$ 0 plane) for sample B. Blue lines indicate
high-symmetry lines in surface BZ. Red lines indicate representative k cuts
(cuts A and B) where the ARPES intensity shown in (b) and (c) was obtained.
(b), (c) ARPES intensity as a function of wave vector and binding energy
measured along cuts A and B, respectively. $k$ in horizontal axis is defined
as the distance between the measured $k$ point and the intersection of red
line and $k_{x}$ ($k_{y}$ = 0) axis. (d) EDC around the Y point which
signifies the peak and metallic Fermi-edge cut-off associated with the
electron pocket.

To clarify to what extent the observed band structure and fermiology is the
intrinsic nature of CaSb2 crystal, we carried out a similar ARPES measurement
for sample B. Figure 3(a) shows the in-plane FS mapping at $T$ = 40 K measured
at $h\nu$ = 90 eV which corresponds to the $k_{z}\sim$ 0 plane. One can see a
dominant intensity around the $\Gamma$ point elongated along the $k_{x}$
direction. This feature originates from the Sb2-orbital-derived 3D hole pocket
OudahArXiv2021  as in the case of sample A, but its intensity distribution is
different from that of sample A at $k_{z}\sim$ 0 shown in the bottom panel
(slice 7) of Fig. 2(e), likely due to the difference in their doping levels as
detailed below. The existence of a hole pocket is recognized from the clear
$E_{\rm{F}}$-crossing of holelike band along a representative k cut (cut A)
shown in Fig. 3(b). Besides the hole pocket, one can see in Fig. 3(a) a weak
intensity around the Y point which is well separated from the hole pocket.
Intriguingly, this feature is absent in sample A as seen in Figs. 2(b) and
2(e). The ARPES intensity along k cut crossing this feature (cut B) in Fig.
3(c) signifies the existence of a shallow electron pocket around the Y point.
The metallic electron pocket is also confirmed by the energy distribution
curve (EDC) at the Y point shown in Fig. 3(d) in which a peak near
$E_{\rm{F}}$ associated with the electron-band bottom accompanied with the
Fermi edge cut-off is clearly seen. We have confirmed the existence of
electron pocket also at $h\nu$ = 120 eV, in line with its quasi-2D nature
predicted from the calculation shown in Figs. 1(c) and 1(d) (for details, see
Section 2 of Supplemental Material SM ). These results indicate that sample B
is relatively more electron doped than sample A, and is situated in a
semimetallic phase with both hole and electron pockets as predicted by the
calculation for stoichiometric CaSb2 (i.e. the calculation without
$\mu$-shift). It is thus suggested that the absence of electron pocket in
sample A is not due to the experimental artifacts such as the strong intensity
suppression associated with the matrix-element effect but due to the
difference in the doping levels. This conclusion is also supported by the
quantitative analysis of the experimental hole-band dispersion, the
photoemission spectra in a wider energy range, and the Sb 4$d$ core-level
energies, as detailed in Section 3 of Supplemental Material SM .

Now we discuss implications of the present results in relation to
superconductivity. Our susceptibility measurements indicate that both samples
A and B show superconductivity with almost the same onset $T_{\rm{c}}$ of
$\sim$ 1.8 K (see Section 1 of Supplemental Material SM ), despite the marked
difference in the carrier-doping level. The fact that the FS of sample A is
composed only of the Sb2-derived 3D hole pocket at the $\Gamma$ point suggests
that the main player of superconductivity is the hole carriers in this pocket.
It is thus inferred that the electron carriers in the Sb1-derived quasi-2D FS
centered at the Y(C) point is not essential for the occurrence of
superconductivity. This argument puts a constraint on the microscopic origin
of superconductivity as well as its possible non-trivial nature in CaSb2,
because the occupancy of the electron band hosting the line nodes was
suggested to be important for promoting topological superconductivity
associated with the dominant interorbital pairing interaction with odd-parity
pairing IkedaPRM2020 . Also, it is worth noting that CaSb2 maintains
superconductivity regardless of the existence or absence of the electron
pocket, which points to an intriguing possibility that one can tune the
topological nature of superconductivity by simply controlling the carrier
concentration in CaSb2, although its validation needs further experimental
studies that directly connects the fermiology and the superconducting pairing
symmetry. We leave such an experiment as a challenge in future.

##  IV CONCLUSION

We reported results of a photon-energy-tunable micro-focused ARPES study on a
topological line-nodal material CaSb2. We found two different types of FSs;
one is a three-dimensional hole pocket at the $\Gamma$ point and another is a
cylindrical electron pocket at the Y(C) point which is predicted to host line
nodes. When the doping level is changed to a more hole-doped region, the
electron pocket at the Y(C) point disappears while the hole pocket at the
$\Gamma$ point survives, although the superconductivity keeps to emerge
regardless of the doping level. This suggests a dominant role of the 3D hole
pocket at the $\Gamma$ point for the occurrence of superconductivity. The
present result lays the foundation for understanding the nature of
superconductivity and its relationship with topology in CaSb2.

###### Acknowledgements.

We thank M. Tomikawa for his assistance in the sample characterization. This
work was supported by JST-CREST (No: JPMJCR18T1), JST-PRESTO (No: JPMJPR18L7),
Grant-in-Aid for Scientific Research (JSPS KAKENHI Grant Numbers JP21H04435,
JP20H01847, JP20H00130, JP20KK0061, JP21K18600, and JP22H04933), the US
Department of Energy Award for low temperature sample characterization (No.
DE-SC0019154), the Gordonand Betty Moore Foundation’s EPiQS Initiative for
sample synthesis (No. GBMF9071), the Maryland Quantum Materials Center, KEK-PF
(Proposal number: 2021S2-001), and UVSOR (Proposal number: 21-658 and 21-679).
C.-W. C. acknowledges support from GP-Spin and JSPS.

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