RAPID COMMUNICATIONSPHYSICAL REVIEW B 96, 041120(R) (2017)

Three-dimensional band structure of LaSb and CeSb: Absence of band inversion
H. Oinuma,1 S. Souma,2,3 D. Takane,1 T. Nakamura,1 K. Nakayama,1 T. Mitsuhashi,1,4 K. Horiba,4 H. Kumigashira,1,4
M. Yoshida,5 A. Ochiai,1 T. Takahashi,1,2,3 and T. Sato1,2
1

Department of Physics, Tohoku University, Sendai 980-8578, Japan
Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan3
WPI Research Center, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
4
Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
5
Max-Planck-Institute for Solid State Research, Heisenbergstrsse 1, 70569 Stuttgart, Germany(Received 16 June 2017; published 18 July 2017)2

We have performed angle-resolved photoemission spectroscopy (ARPES) of LaSb and CeSb, a candidateof topological insulators. Using soft-x-ray photons, we have accurately determined the three-dimensional bulk
band structure and revealed that the band inversion at the Brillouin-zone corner, a prerequisite for realizing the
topological-insulator phase, is absent in both LaSb and CeSb. Moreover, unlike the ARPES data obtained with
soft-x-ray photons, those with VUV photons were found to suffer significant kz broadening. These results suggestthat LaSb and CeSb are topologically trivial semimetals, and unusual Dirac-cone-like states observed with VUVphotons are not of the topological origin.
DOI: 10.1103/PhysRevB.96.041120

Topological insulators (TIs) manifest a novel quantum
state of matter where a gapless edge or surface states (SSs)appear within an inverted bulk band gap induced by strong
spin-orbit coupling [1–3]. The SSs of three-dimensional (3D)
TIs are characterized by the linearly dispersive Dirac-coneenergy band which can be viewed as a sea of Dirac fermions
whose massless nature is guaranteed by the time-reversal
symmetry. The discovery of TIs ignited the search for Diracfermions associated with other symmetries, as represented
by the discovery of topological crystalline insulators [4–7],
Dirac/Weyl semimetals [8–14], and line-node semimetals[15,16].
Recently, it was predicted from the first-principles bandstructure calculations by Zeng et al. [17] that lanthanum (La)monopnictide with rock-salt structure LaX (X = N, P, As,
Sb, and Bi) becomes either a topological Dirac semimetal(for X = N) or a 3D TI (for X = P, As, Sb, and Bi), with
Dirac fermions at the surface, due to the band inversion
at the X point of the bulk fcc Brillouin zone (BZ). Whilerare-earth monopnictide RX (R: rare earth) was intensively
studied in the 1980–90s in relation to heavy-fermion physics[18–24], the proposal by Zeng et al. [17] renewed the interest
for RX in topological aspects and triggered intensive transport,
spectroscopic, and theoretical studies [25–43], resulting in the
discovery of extremely large magnetoresistance and an unusual
resistivity plateau in LaSb and LaBi [29–32,34–36], as wellas the observation of Dirac-cone-like features in some RX
compounds [38–43].
Specifically, angle-resolved photoemission spectroscopy(ARPES) experiments of LaBi [38,40–42] have identified
unusual Dirac-cone states at M̄ [equivalent to the projectedbulk X point; see Fig. 1(a)] and ¯ of the surface BZ,
pointing to the topologically nontrivial nature due to theband inversion at X. (However, note that some differencesin the number and massless/massive nature of the Diraccones are observed among different groups [38,40–42].) On
the other hand, the electronic structure of LaSb is highly
controversial. The ARPES study with VUV photons by Zeng

2469-9950/2017/96(4)/041120(5)et al. suggested the topologically trivial nature by reporting
the absence of band inversion [37], while the VUV-ARPES
study by Niu et al. proposed the topologically nontrivial
nature by reporting a Dirac-cone-like feature [40]. Another
VUV-ARPES study of CeSb by Alidoust et al. suggested
the nontrivial nature by observing two sets of anisotropic
Dirac-cone-like states [39].
Controversy regarding the topological vs nontopologicalcharacteristics is also found in the first-principles calculationsof LaSb [25]. The generalized gradient approximation (GGA)
calculation with Perdew-Burke-Ernzerhof (PBE) formulas[44] shows the band inversion, while the meta-GGA calculation with modified Becke-Johnson (MBJ) exchange potential[45,46] supports no inversion. These controversies in bothexperiment and theory seriously hinder further understandingof the relationship between the electronic structure and theobserved unusual physical properties in LaSb and CeSb.
It is thus urgently required to experimentally establish thepresence/absence of band inversion at X—a prerequisite forrealizing the TIs.
In this Rapid Communication, we report a soft-x-ray(SX) ARPES study of LaSb and CeSb. By utilizing theenergy-tunable bulk-sensitive SX photons, we are able toovercome the experimental problems that previous VUVARPES experiments encountered, i.e., the surface effectand the large kz (momentum perpendicular to the surface)broadening [24,37,40,42]. We unambiguously demonstrate theabsence of the band inversion in both LaSb and CeSb bycarefully tracing the bulk-band dispersion in whole 3D BZ.
Our results suggest the nontopological nature of LaSb and
CeSb, and lay a foundation for understanding their unusualtransport properties.
LaSb and CeSb single crystals were grown by the Bridgman
method with a tungsten heater furnace. High-purity starting
materials of La/Ce (4N) and Sb (6N) with a ratio of 1:1.005
were sealed in a tungsten crucible using an electron-beamwelder. The crucible was heated above their melting points andthen slowly pulled down from the heater. The obtained crystals

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PHYSICAL REVIEW B 96, 041120(R) (2017)

FIG. 1. (a) Bulk and surface BZs for LaSb and CeSb with the schematic bulk FSs at the  point (green) and the X point (red and blue).
For convenience, different X points are labeled as X1 –X4 . (b) ARPES intensity mapping at EF of LaSb as a function of kx and kz , measured
at T = 40 K, by varying hν from 400 to 630 eV. (c) ARPES intensity plot of LaSb as a function of wave vector and EB , measured along cut
A (X3 cut) in (b). (d) ARPES intensity mapping at EF of LaSb as a function of in-plane wave vector (kx and ky ) at kz = π (hν = 600 eV).
(e) ARPES intensity of LaSb measured along cut B (X3 WX4 cut) in (d). (f) Same as (d) but at kz = 0 (hν = 510 eV). (g) Same as (e) but along
cut C (X1 cut) in (f). (h, i) Same as (f) and (g) but for CeSb.

were characterized by the x-ray diffraction measurements. We
could obtain high-quality single crystals such as LaSb crystal
with the residual resistivity ratio of 490 [47]. SX-ARPES measurements were performed with a Scienta-Omicron SES2002
electron analyzer with an energy-tunable synchrotron light at
BL2 (Musashi) in Photon Factory (PF), KEK. We used linearlypolarized light (horizontal polarization) of 400–630 eV. VUVARPES measurements were performed at BL2 and BL28
with 35–100 eV photons. The energy resolutions for SXand VUV-ARPES measurements were set at 150 meV and
10–30 meV, respectively. Samples were cleaved in situ in an
ultrahigh vacuum of ∼1 × 10−10 Torr along the (100) crystal
plane. The sample temperature was kept at T = 40 K during
measurements. The Fermi level (EF ) of the samples was referenced to that of a gold film evaporated onto the sample holder.
First, we present the overall band structure and Fermisurface (FS) topology of LaSb obtained with SX photons.
Figure 1(b) shows the ARPES intensity mapping at EF of LaSb
as a function of kx and kz [X1 X4 X3 plane (area enclosed bygreen shading) in Fig. 1(a)], measured by varying hν from
430 to 600 eV. One can clearly identify a bright intensity spot
centered at the  point, together with small weak spots at
the X points. The intensity of these spots exhibits a strong kz
dependence, as also seen from the band-structure plot alongthe X3 cut (kz axis) in Fig. 1(c); this demonstrates the bulk
origin of these FSs. When we fix the photon energy at hν =600 eV and map out the ARPES intensity as a function of anin-plane wave vector (kx , ky ) at the kz = π plane [red shading in
Fig. 1(a)], as displayed in Fig. 1(d), the small pocket at X (seeX4 ) is elongated along the X direction. Such an elongatednature is also visible in the ARPES intensity mapping at the kz= 0 plane [blue shading in Fig. 1(a)] in Fig. 1(f), although theintensity is weaker due to the photoelectron matrix-element
effect. We found that the elongated FS is an electron pocket,
since a shallow electronlike band crosses EF around the X4
point of the X3 WX4 cut [cut B in Fig. 1(d)] in Fig. 1(e). In
fact, when we overlaid the electron pocket estimated from thede Haas–van Alphen experiments in Figs. 1(b), 1(d) and 1(f)(dashed curves) [21,22], one can see a reasonable overlap with
the ARPES intensity at each X point.
As shown in the ARPES intensity along the X1 cut[cut C in Fig. 1(f)] in Fig. 1(g), there exist two holelike
bands crossing EF around , which form two hole pockets[24,37,40]. According to the band calculations, these hole
pockets are attributed to the topmost bulk valence band (VB)
with the Sb 5p orbital character, while the electron pocket at
X is assigned to the lowest bulk conduction band (CB) with
the La 5d character [17,25,27,48]. The present SX-ARPES
result thus provides evidence for the semimetallic nature of
LaSb with holes at  and electrons at X. We have also carriedout SX-ARPES measurements on CeSb and found that theoverall FS topology and the band dispersion are very similar
to those of LaSb, as seen from a side-by-side comparison of
the FS [Figs. 1(f) and 1(h)] and the band dispersion [Figs. 1(g)and 1(i)]. (Note that the localized Ce 4f states [39] are
not clearly resolved with this photon energy due to the low
photoionization cross section.)
We compare in Figs. 2(a) and 2(b) the normal-emission
energy distribution curves (EDCs) measured with SX (hν= 400–630 eV) and VUV photons (hν = 35–100 eV),
respectively. One can recognize several dispersive peaks in the
SX data. For instance, a prominent peak at EB ≈ 0.5 eV around (hν ≈ 510 eV) rapidly disperses toward higher EB uponmoving away from , staying at ∼2.5 eV at midway between 
and X (hν ∼ 450 and 550 eV), and then gradually moves backagain toward 2 eV on approaching X (hν = 600 and 410 eV).
On the other hand, in the VUV data shown in Fig. 2(b), themain peaks at 0.5 and 1.0 eV show no dispersion (highlighted
by dashed lines). Such features may appear owing to the sizablekz broadening due to the short escape depth of photoelectrons
excited by VUV photons [24,37,40]. Taking into account thefact that the energy position of these peaks shows a good
agreement with that of relatively flat bands around the X1 pointin the SX data [Fig. 1(g)], the kz broadening would cover a large

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PHYSICAL REVIEW B 96, 041120(R) (2017)

FIG. 2. (a, b) Normal-emission EDCs of LaSb measured with SXand VUV photons, respectively. (c) ARPES intensity at EF around theM̄ point as a function of in-plane wave vector (kx and ky ) measured
with VUV photons (hν = 53 eV). (d) ARPES intensity as a functionof kx and EB measured with hν = 53 eV along a cut shown by thewhite solid line in (c). Red dashed curves in (c) and (d) are a guidefor the eyes to trace FS and band dispersions.

FIG. 3. (a, b) Calculated band structure for LaSb obtained with
GGA calculation with PBE functional (dashed curves) and metaGGA calculation with MBJ potential (solid curves) for X and WXWhigh-symmetry lines, respectively [25]. (c, d) ARPES intensity plotsof LaSb measured along the X1 cut (kz = 0) and the X4 cut (kz =π ), respectively. (e) ARPES intensity plot of LaSb along the WX4 W
cut (kz = π ). (f, g, h) Same as (c)–(e) but for CeSb. Red dots in (c)–(h)indicate the experimental band dispersions estimated by tracing thepeak position in EDCs.

portion of the -X interval. This conclusion is also supportedby the FS mapping at hν = 53 eV in Fig. 2(c), where twopockets originating from the X1 - and X4 -centered FSs withdifferent kz ’s [see Fig. 1(a)] are simultaneously observed. As
a result, when we measure the band dispersion along kx at hν= 53 eV, we accidentally observe two different electronlike
bands with small and large Fermi velocities which cross the
major axis of the X1 -centered pocket and the minor axis of
X4 -centered pocket, respectively, as seen in Fig. 2(d). All
these results strongly suggest that the kz broadening should
be carefully taken into account when discussing the origin ofhν-independent spectral features in terms of the SS. Thus, todiscuss genuine bulk electronic states free from the surface
effects, it is more desirable to use SX photons.
Now we turn our attention to the SX-ARPES data again to
examine the possible bulk-band inversion at X. As shown in
Fig. 3(a), the GGA calculation with PBE formulas for LaSb
(called PBE calculation; dashed curves) [25] predicts that theelectronlike La-5d CB and the Sb-5p VB (called E1 and H1bands, respectively) intersect each other at a point slightly
away from X along the X cut (marked by arrow) due to theband inversion. (Note that a tiny spin-orbit gap opens at theintersection, though it is negligible in the present energy scale.)
Such a band crossing is absent in the meta-GGA calculation
with MBJ exchange potential (called MBJ calculation; solid
curves) [25], since the bottom of E1 band is located at ∼0.2 eV
above the H1 band at the X point. From these considerations,
it can be said that a key to examine the band inversion is toexperimentally verify whether such a band crossing exists or
not in the SX-ARPES data.
Figures 3(c) and 3(d) show the SX-ARPES intensity
mapping along two different X cuts, X1 (kz = 0) andX4 (kz = π ), respectively. We selected these two X cuts
because the intensity ratio between H1 and E1 bands wasfound to strongly depend on the choice of k cut due tothe aforementioned photoelectron matrix-element effect. In
our experimental geometry, the intensity of the E1 bandis dramatically reduced relative to that of the H1 bandfor the X1 cut [Fig. 3(c)], while vice versa for the X4cut [Fig. 3(d)]. Therefore, in order to trace accurately theband dispersions of both H1 and E1 bands, we performed
SX-ARPES measurements in these two X cuts. As seen in
Fig. 3(c), the H1 band exhibits a nearly flat dispersion at EB ≈0.5 eV around the X point. On the other hand, the E1 bandin Fig. 3(d) does not disperse across the H1 band with its
bottom at EB ≈ 0.25–0.3 eV at X. This suggests that the E1
and H1 bands do not cross each other while always keeping
an energy interval of greater than 0.2 eV irrespective of k,
in good agreement with the MBJ calculation but not with the
PBE one [Fig. 3(a)]. As shown in Fig. 3(e), the absence ofband crossing is also confirmed in the cut perpendicular to X(WXW cut) [see also band calculation in Fig. 3(b)]. Moreover,as highlighted in Figs. 3(f)–3(h), we found that CeSb sharesqualitatively the same spectral feature regarding the absenceof band crossing, while the energy position and the shape of041120-3

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the E1 and H1 bands appear to be slightly different between
the two compounds. All these results strongly suggest that thebulk-band inversion does not take place in LaSb or CeSb.
The absence of band inversion casts doubt on the TI nature
proposed for LaSb and CeSb. The observed extremely large
magnetoresistance in LaSb is well explained in terms of thecompensation of electrons and holes due to the semimetallic
nature [25,32,37]. In addition, the observed similarity in theelectronic structure between LaSb and CeSb suggests that thestrong correlation of Ce 4f electrons does not play a role inband inversion or possible TI characteristics. It is thus inferredthat the unusual Dirac-cone-like SSs observed in the previous
VUV-ARPES studies of LaSb and CeSb [39,40,43] may beinterpreted in terms of the trivial SS. Our SX-ARPES result,however, does not exclude the possibility of the TI nature of
LaBi and CeBi, since the band calculations of LaBi commonly
predict a larger overlap of H1 and E1 bands to induce theband inversion [17,25,48], as supported by several previous
VUV-ARPES experiments [38,40–42]. In this regard, the next
important challenge is to perform a bulk-sensitive SX-ARPES
experiment on LaBi/CeBi and clarify similarities and differences in the bulk electronic structure between LaSb and CeSb.

In summary, we performed ARPES experiments on LaSb
and CeSb with bulk-sensitive soft-x-ray photons and determined the 3D band structure and the Fermi surface. In both
LaSb and CeSb, we observed two hole pockets and one electron
pocket at the BZ center and corner, respectively, supporting
the bulk semimetallic nature. In addition, we observed that theelectronlike CB and the topmost VB are well separated aroundthe X point, signifying the absence of bulk-band inversion.
These results strongly suggest that neither LaSb or CeSb are
a TI, and the unusual Dirac-cone-like energy band observedwith VUV-ARPES should be associated with the topologicallytrivial surface states.

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We thank N. Inami and K. Ono for their assistance in the
ARPES measurements. This work was supported by a Grantin-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (JSPS KAKENHI No. JP15H05853),
Grant-in-Aid for Scientific Research (JSPS KAKENHI
No. JP17H01139, No. JP15H02105, No. JP26287071, and
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