RAPID COMMUNICATIONS
PHYSICAL REVIEW B 88, 121102(R) (2013)
Surface and bulk electronic structure of the strongly correlated system SmB
6
and implications for a topological Kondo insulator
N. Xu,
1,*
X. Shi,
1,2
P. K. Biswas,
3
C. E. Matt,
1,4
R. S. Dhaka,
1,5
Y. Huang,
1
N. C. Plumb,
1
M. Radovi
´
c,
1,6
J. H. Dil,
7,1
E. Pomjakushina,
8
K. Conder,
8
A. Amato,
3
Z. Salman,
3
D. McK. Paul,
9
J. Mesot,
1,5
H. Ding,
2
and M. Shi
1,†
1
Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
2
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
3
Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
4
Laboratory for Solid State Physics, ETH Z
¨
urich, CH-8093 Z
¨
urich, Switzerland
5
Institut de la Matiere Complexe, EPF Lausanne, CH-1015, Lausanne, Switzerland
6
SwissFEL, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
7
Physik-Institut, Universit
¨
at Z
¨
urich, Winterthurerstrauss 190, CH-8057 Z
¨
urich, Switzerland
8
Laboratory for Developments and Methods, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
9
Physics Department, University of Warwick, Coventry CV4 7AL, United Kingdom
(Received 16 June 2013; published 10 September 2013)
Recent theoretical calculations and experimental results suggest that the strongly correlated material SmB
6
may be a realization of a topological Kondo insulator. We have performed an angle-resolved photoemission
spectroscopy study on SmB
6
in order to elucidate elements of the electronic structure relevant to the possible
occurrence of a topological Kondo insulator state. The obtained electronic structure in the whole three-dimensional
momentum space reveals one electron-like 5d bulk band centered at the X point of the bulk Brillouin zone that is
hybridized with strongly correlated f electrons, as well as the opening of a Kondo band gap (
B
∼ 20 meV) at
low temperature. In addition, we observe electron-like bands forming three Fermi surfaces at the center
¯
point
and boundary
¯
X point of the surface Brillouin zone. These bands are not expected from calculations of the bulk
electronic structure, and their observed dispersion characteristics are consistent with surface states. Our results
suggest that the unusual low-temperature transport behavior of SmB
6
is likely to be related to the pronounced
surface states sitting inside the band hybridization gap and/or the presence of a topological Kondo insulating
state.
DOI: 10.1103/PhysRevB.88.121102 PACS number(s): 73.20.−r, 71.20.−b, 75.70.Tj, 79.60.−i
A three-dimensional (3D) topological insulator (TI) is an
unusual topological quantum state associated with unique
metallic surface states that appear within the bulk band gap.
1,2
Owing to the peculiar spin texture protected by time-reversal
symmetry, the Dirac fermions in TIs are forbidden from
scattering due to nonmagnetic impurities and disorder.
3,4
Hence they carry dissipationless spin current,
5
making it
possible to explore fundamental physics, spintronics, and
quantum computing.
1,2
However, even after extensive ma-
terials synthesis efforts,
6–10
impurities in the bulk of these
materials make them metallic, prompting us to search for new
types of TIs with truly insulating bulks.
The 3D Kondo insulator SmB
6
may open a new route to
realizing topological surface states. SmB
6
is a typical heavy-
fermion material with strong electron correlation. Localized
f electrons hybridize with conduction electrons, leading to
a narrow band gap on the order of 10 meV opening at
low temperatures, with the chemical potential lying in the
gap.
11–14
Due to the opening of the band gap, the conductivity
changes from metallic to insulating behavior with decreasing
temperature. It saturates to a constant value below about 1 K,
which is thought to be caused by in-gap states.
15
Theoretical
studies have proposed that SmB
6
may host three-dimensional
topological insulating phases.
16,17
Recently, transport exper-
iments employing a novel geometry
18,19
showed convincing
evidence of a distinct surface contribution to the conductiv-
ity that is unmixed with the bulk contribution, suggesting
SmB
6
is an ideal topological insulator with a perfectly
insulating bulk. Point-contact spectroscopy revealed that the
low-temperature Kondo insulating state harbors conduction
states on the surface, in support of predictions of nontrivial
topology in Kondo insulators.
20
Moreover, Lu et al. used
the local-density approximation combined with the Gutzwiller
method to investigate the topological physics of SmB
6
from
the first principles.
17
They found a nontrivial Z
2
topology,
indicating that SmB
6
is a strongly correlated topological
insulator. They calculated the topological surface states and
found three Dirac cones, in contrast to most known topological
insulators. At present, topological insulators are essentially
understood within the theory of noninteracting topological
theory.
1,2
SmB
6
, as one candidate for a topological Kondo
insulator, potentially offers us an opportunity to investigate
the interplay between topological states and strong many-body
interactions.
As a surface-sensitive technique, angle-resolved photoe-
mission spectroscopy (ARPES) is one of the best probes to
investigate the surface states and attest to their topological
nature. However, previous ARPES studies did not resolve the
surface dispersion from bulk states, possibly due to the system
resolution and sample surface condition.
21,22
In this Rapid
Communication, we report high-resolution ARPES results
from SmB
6
in the whole three-dimensional Brillouin zone
(BZ) by tuning the incident photon energy. Due to the high
resolution of the ARPES system and good sample quality, we
are able to clearly identify electron-like bands forming three
Fermi surfaces (FS), which are distinct from the expected bulk
121102-1
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RAPID COMMUNICATIONS
N. XU et al. PHYSICAL REVIEW B 88, 121102(R) (2013)
FIG. 1. (Color online) (a) The first Brillouin zone of SmB
6
and
the projection on the cleaving surface. High-symmetry points are also
indicated. (b), (c) Fermi surface mapping at T = 17 K by integrating
ARPES intensity within E
F
± 5 meV with hν = 26 and 46 eV,
corresponding to k
z
= 4π and 5π at
¯
, respectively. (d), (e) ARPES
intensity plots at
¯
and
¯
X for the k
B
z
= 4π plane at T = 17 K. The red
and blue curves are the dispersions of the β and γ bands extracted
by MDC fitting. (f), (g) Analogous to (d) and (e), but for the k
B
z
=
5π plane.
states, and we discuss the possible topological property of
those surface states.
High-quality single crystals of SmB
6
weregrownbythe
flux method. ARPES measurements were performed at the
Surface/Interface Spectroscopy (SIS) beam line at the Swiss
Light Source using a VG-Scienta R4000 electron analyzer
with photon energies ranging from 22 to 110 eV. The energy
resolution ranged from ∼10meVat22eVto∼15 meV at
110 eV. The angular resolution was around 0.2
o
. Clean surfaces
for the ARPES measurements were obtained by cleaving the
crystalsin situ in a working vacuum better than 5 × 10
−11
mbar.
Shiny mirrorlike surfaces were obtained after cleaving the
samples, confirming their high quality.
Figure 1 displays the Fermi surface and band dispersions
of SmB
6
measured at T = 17 K with various photon
energies, corresponding to different k
z
points in the bulk
BZ (k
B
z
). The first BZ of bulk SmB
6
and its projection on
the cleaving surface are shown in Fig. 1(a),withallthe
high-symmetry points labeled. In Figs. 1(b) and 1(c),we
plot the FS mappings obtained using hν = 26 and 46 eV,
corresponding to approximately k
B
z
= 4π and 5π , allowing
direct comparisons with previous work.
21,22
In making the
maps, we integrated the ARPES intensity within E
F
± 5meV.
As seen in Figs. 1(b) and 1(c), the same FS topology is
observed at different k
B
z
high-symmetry points of the bulk BZ:
one small circular FS, α, is located at the surface BZ center
¯
point and an additional ellipse-shaped FS, β, is located at the
surface BZ boundary
¯
X point. We also observed a folded band
β
caused by a 1 × 2 reconstruction of the surface, which is also
observed in low-energy electron diffraction (LEED) patterns.
21
Figures 1(d) and 1(e) show photoemission E vs k intensity
plots at the
¯
and
¯
X points for the k
B
z
= 4π plane at T = 17 K.
Similarly, data recorded for the k
B
z
= 5π plane are shown in
Figs. 1(f) and 1(g). One can see that the highly renormalized
4f
6
electrons form three flat bands, located at E
B
= 960, 160,
and 20 meV. One electron-like band, γ , hybridizes with three
4f
6
bands at low temperature. The γ band, which is attributed
to the 5d orbital as suggested by Ref. 17, is seen at
¯
X for k
B
z
=
4π and at
¯
for k
B
z
= 5π, which in the bulk BZ are equivalent
at the X point, as seen in Fig. 1(a). This strongly three-
dimensional feature indicates that γ is a bulk band located
at the X point in the bulk BZ, consistent with the theoretical
calculation.
17
In order to investigate the low-energy excitations, band
dispersions near E
F
at
¯
and
¯
X for the k
B
z
= 4π plane are
shown in Figs. 2(a) and 2(b). In addition, we plot the ARPES
intensity near E
F
at the center of the second surface BZ
¯
point and
¯
X point for the k
B
z
= 5π plane in Figs. 2(d) and 2(e).
As seen in Figs. 2(b) and 2(d), the bulk band γ hybridizes
with the flat 4f band near E
F
, leading to a Kondo band gap.
The gap size is
B
∼ 20 meV based on the peak position
of the energy distribution curve (EDC) taken at the position
marked by the vertical red line in Fig. 2(b). Moreover, as
FIG. 2. (Color online) (a), (b) ARPES intensity plots for cuts
through
¯
-
¯
X and
¯
X-
¯
M, respectively, for the k
B
z
= 4π plane. Note the
narrow energy window. The data were collected at T = 17 K. The red
and blue curves are dispersions for the β and γ bands extracted by
fitting the MDCs. The curves on the top are the MDCs taken at E
F
,
with labels for the peak positions. An EDC at the location in k space
marked by the red vertical line is also displayed. From this, the Kondo
band gap is estimated to be
B
∼ 20 meV. (c), (d) Analogous to
(a) and (b), but for the k
B
z
= 5π plane. (e)–(g) Plots of the curvatures
of the MDC intensities along
¯
-
¯
X in either the first or second BZ
(
¯
−
¯
X
) evaluated in the k
B
z
= 4π,5π,and6π planes, respectively.
(h) MDC curvature analysis at the second BZ center
¯
’ point for the
k
B
z
= 6π plane. (i)–(l) Corresponding MDC plots for (e)–(h).
121102-2
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70
60
50
40
30
-0.5 0.0 0.5 -0.5 0.0 0.5
22 eV
24 eV
26 eV
28 eV
30 eV
32 eV
34 eV
37 eV
40 eV
43 eV
46 eV
75 eV
Momentum (Å
-1
)
Photon Energy (eV)
Intensity (a. u.)
(b) (c)
-0.3 0.0 0.3 -0.3 0.0 0.3 -0.3 0.0 0.3 -0.3 0.0 0.3 -0.3 0.0 0.3 -0.3 0.0 0.3
50 eV
-0.3 0.0 0.3
XMMXMM
______
E - E
F
(meV)
0
-50
(a)
hν = 22 eV
26 eV 30 eV 34 eV
k
z
= 4π
-0.3 0.0 0.3
40 eV 46 eV 50 eV 60 eV
k
z
= 5π
-0.3 0.0 0.3
k
z
= 6π
70 eV
Momentum (Å
-1
)
-0.3 0.0 0.3
Momentum (Å
-1
)
-100
0
-50
(d)
E - E
F
(meV)
22 eV
26 eV
30 eV
34 eV
40 eV
46 eV
50 eV
60 eV
70 eV
X
_
M
_
M
_
110
100
90
80
70
-0.1 0.0 0.1
Intensity (a. u.)
Photon Energy (eV)
Momentum (Å
-1
)
22 eV
24 eV
26 eV
65 eV
70 eV
90 eV
95 eV
100 eV
105 eV
-0.3 0.0 0.3
(e)
Γ
MM
___
Γ
MM
___
55 eV
-0.1 0.0 0.1
B B B
110 eV
(f)
FIG. 3. (Color online) (a) ARPES intensity along the
¯
X-
¯
M direction measured at T = 17 K with various photon energies. (b) Plot of the
ARPES intensity along
¯
X-
¯
M as a function of photon energies from 22 to 75 eV, covering more than 1.5 BZs along k
B
z
. (c) Corresponding
MDCs at E
F
. (d) Extracted dispersions of the β band for different photon energies. (e) Plot of the curvature of the MDC intensity along
¯
-
¯
M
for each photon energy. (f) Corresponding MDCs at E
F
.
seen in Figs. 2(b) and 2(d), the electron-like band β appears
inside the band gap and crosses E
F
at the
¯
X point, forming
an ellipse-shaped FS at the BZ boundary. For the β band,
its Fermi momentum k
F
measures 0.39 and 0.28
˚
A
−1
along
the
¯
X-
¯
and
¯
X-
¯
M directions, respectively. The folded band
β
can be seen in Figs. 2(a) and 2(c), located at about
¯
,
with a folding wave vector (π, 0) caused by the 1 × 2 surface
reconstruction. Additionally, we observe one weak band α at
the
¯
point, which corresponds to the small FS at the BZ
center. To better visualize the weak α band, in Figs. 2(e)–2(h)
we plot the curvature of the MDC intensity
23
along
¯
-
¯
M
for different photon energies approximately corresponding to
the k
B
z
= 4π,5π, and 6π planes. The corresponding raw
momentum distribution curves (MDCs) are also plotted in
Figs. 2(i)–2(l). From the curvature plots, we can see that the
electron-like α band crosses E
F
around the
¯
point, which
can also be observed in the MDC plots. The MDCs at E
F
in Figs. 2(a) and 2(c) confirm that the α and β bands indeed
cross E
F
.
From bulk band calculations,
16,17
the in-gap bands α and
β are totally unexpected at any k
B
z
value. However, both
theoretical and experimental results
16–18,20
suggest that SmB
6
exhibits metallic surface states that make it a candidate for
a strongly correlated Kondo topological insulator. To further
examine whether the in-gap states are surface or bulk bands,
we have carried out an ARPES measurement along the cut
crossing the
¯
X point for different k
B
z
values by tuning photon
energy. In Fig. 3(a) we plot ARPES spectra with k
||
oriented
along the
¯
X-
¯
M line taken with different photon energies from
22 to 70 eV, which cover more than 1.5 bulk BZs along
k
B
z
. One can see that, although the spectral weight of the β
band varies with photon energy due to photoemission matrix
element effects, the dispersion of the β band stays highly
fixed. MDCs at E
F
obtained with different photon energies are
plotted in Fig. 3(c), and the corresponding hν-k
||
FS intensity
plot is shown in Fig. 3(b). As one immediately recognizes from
Fig. 3(c), the peak positions of the MDCs at E
F
, which indicate
the k
F
values of the β band, are stationary with respect to hν.
Thus the β band forms a two-dimensional FS in the hν-k
||
plane shown in Fig. 3(b). In fact, when we plot the extracted
dispersions for different photon energies in Fig. 3(d), their
linear dispersions overlap each other within the experimental
uncertainties, demonstrating the two-dimensional nature of the
β band. This two-dimensional feature is different from the
bulk γ band, indicating the surface origin of the β band. We
likewise studied the photon energy dependence of the small α
band to check its surface/bulk origin. While the weak intensity
and shallow dispersion make detailed quantitative analysis of
the α band difficult, we consistently find anomalous spectral
weight at E
F
connected to this band, independent of the photon
energy. This is consistent with a shallow 2D state that is
nondispersive along k
z
. In light of the fact that the α band
is not predicted from bulk band structure calculations, the data
strongly suggest that the α band, like the β band, has a surface
origin.
We have also performed temperature-dependent measure-
ments to study the evolution of both the bulk and surface
bands. Figures 4(a)–4(f) show ARPES intensity plots at the
¯
X point measured at temperatures ranging from 17 to 280 K.
Figures 4(g)–4(i) show similar plots at the
¯
point measured
121102-3
RAPID COMMUNICATIONS
N. XU et al. PHYSICAL REVIEW B 88, 121102(R) (2013)
17 K
30 K 45 K 70 K 110 K 280 K
(a)
XMM
___
Momentum (Å
-1
)
17 K
(b) (f)(e)(c) (d)
β
β
α
β'
E - E
F
(meV)
0
-50
-100
30 K 45 K 70 K 110 K 150 K
Γ
XX
___
(h) (l)(k)(i) (j)
0
-50
-100
0.30-0.30.30-0.30.30-0.30.30-0.30.30-0.30.30-0.3
(g)
γ
FIG. 4. (Color online) (a)–(f) ARPES intensity plots along
¯
M-
¯
X-
¯
M measured at T = 17, 30, 45, 70, 110,and 280 K, respectively.
(g)–(l) ARPES intensity plots along
¯
X-
¯
-
¯
X measured at T = 17, 30,
45, 70, 110, and 150 K, respectively.
at temperatures ranging from 17 to 150 K. The hybridization
between the 5dγband and 4f flat band is destroyed around
T = 110 K. Meanwhile, the surface bands α and β,aswell
as the folding band β
, vanish. The temperature dependence
suggests that the surface states can only exist when the Kondo
band gap opens.
Our ARPES results demonstrate that SmB
6
is a strongly
correlated Kondo insulator with metallic surface states located
inside the Kondo band gap. The observed surface bands at
both the
¯
and
¯
X points show good agreement with the
topologically nontrivial surface states found in calculations,
17
suggesting that SmB
6
is a topological Kondo insulator as
predicted theoretically.
16,17
Three surface bands (α contributes
one FS at the
¯
point and β contributes two FSs at the
¯
X point)
enclose an odd number of time-reversal-invariant momenta,
which is a very strong indication of a topologically nontrivial
phase. We also note that no clear Dirac point is observed in
our ARPES measurements; for the α band, the intensity is
too dim to see a potential Dirac point clearly. One possible
reason is that the cleaving surface is the B-terminated layer,
and the α band may originate from Sm, making the signal
very weak. For the β band, the intensity diminishes suddenly
at E
B
∼ 20 meV, corresponding to the hybridization gap edge
between f and d electrons, which may prohibit observing
the Dirac point formed by the bands crossing each other.
Thus the apparent absence of a clear Dirac point may be a
signature of interactions between topological surface states
and the strongly correlated bulk f electrons. Such nontrivial
many-body interactions have recently been observed in other
topological insulators studied by ARPES.
24
This hints that
SmB
6
may offer an opportunity to understand topological
insulators beyond the noninteracting topological theory. It
should also be mentioned that the identified surface states in
our ARPES experiments are robust. As a test, after acquiring
ARPES data from a fresh surface right after cleaving at low
temperature (18 K), we have warmed the sample to room
temperature and placed the sample in 5 × 10
−8
mbar for 48 h.
After cooling down to 18 K, the surface states were still clearly
visible.
In summary, we reported high-resolution ARPES results
from the strongly correlated Kondo insulator SmB
6
.Wefirst
identified two anomalous bands, α located at the BZ center
¯
and β at the BZ boundary
¯
X, that are distinct from the
expected bulk band structure. While the shallow dispersion of
the α band prevents clear analysis of its shape as a function
of k
z
, we managed to explicitly show that the β band is a
2D surface state. The observation of these states agrees well
with the topologically nontrivial surface states predicted by
theoretical calculations.
16,17
We also observe that the α and
β bands disappear when the hybridization between the bulk
γ band and the heavily correlated f electrons vanishes at
high temperature. Our results uphold the possibility that SmB
6
is a topological Kondo insulator, consistent with theoretical
calculations.
16,17
We acknowledge Z. Fang for stimulating discussions. This
work was supported by the Sino-Swiss Science and Tech-
nology Cooperation (Project No. IZLCZ2138954), the Swiss
National Science Foundation (Grant No. 200021-137783),
and MOST (Grant No. 2010CB923000) and NSFC. The
experiment was carried out at the Swiss Light Source of the
Paul Scherrer Institut in Villigen, Switzerland, and we thank
the SIS beam line staff for their excellent support.
*
nan.xu@psi.ch
†
ming.shi@psi.ch
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