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4f Crystal Field Ground State of the Strongly Correlated Topological Insulator SmB6

TL;DR: In this article, the crystal-electric field ground state of the manifold in strongly correlated topological insulator was investigated using core-level nonresonant inelastic x-ray scattering.
Abstract: We investigated the crystal-electric field ground state of the $4f$ manifold in the strongly correlated topological insulator ${\mathrm{SmB}}_{6}$ using core-level nonresonant inelastic x-ray scattering. The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the ${\mathrm{\ensuremath{\Gamma}}}_{8}$ quartet state of the Sm ${f}^{5}\text{ }\text{ }J=5/2$ configuration governs the ground-state symmetry and, hence, the topological properties of ${\mathrm{SmB}}_{6}$. Our findings contradict the results of density functional calculations reported so far.
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4f Crystal Field Ground State of the Strongly Correlated Topological Insulator SmB
6
M. Sundermann,
1,2
H. Yavaş,
3
K. Chen,
1,
D. J. Kim,
4
Z. Fisk,
4
D. Kasinathan,
2
M. W. Haverkort,
5
P. Thalmeier,
2
A. Severing,
1,2,*
and L. H. Tjeng
2,
1
Institute of Physics II, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
2
Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
3
PETRA III, Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, 22607 Hamburg, Germany
4
Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
5
Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, 69120 Heidelberg, Germany
(Received 20 June 2017; revised manuscript received 25 September 2017; published 5 January 2018)
We investigated the crystal-electric field ground state of the 4f manifold in the strongly correlated
topological insulator SmB
6
using core-level nonresonant inelastic x-ray scattering. The directional
dependence of the scattering function that arises from higher multipole transitions establishes unambig-
uously that the Γ
8
quartet state of the Sm f
5
J ¼ 5=2 configuration governs the ground-state symm etry
and, hence, the topological properties of SmB
6
. Our findings contradict the results of density functional
calculations reported so far.
DOI: 10.1103/PhysRevLett.120.016402
It was recently proposed that the intermediate valent
Kondo insulator SmB
6
[15] could be a topological
insulator [611]. Indeed, topologically protected metallic
surface states would be an attractive explanation for the
low-temperature conductance that has been puzzling sci-
entists for decades. The proposal is appealing since, in
particular, rare earth Kondo insulators have the necessary
ingredients for strong spin-orbit coupling and electrons of
opposite parity, namely, the 4f and 5d. The concept of
strongly correlated topological insulators is exciting not
only because the surface may have massless charge carriers
with locked helical spin polarization, but also because the
surface of such a strongly correlated system may host novel
phenomena not present in semiconductor-based topological
insulators [1215]. With the bulk being truly insulating,
SmB
6
has experienced a tremendous renewed interest
and many experimental techniques like angle-resolved
photoelectron spectroscopy (ARPES) [1624], scanning
tunneling spectroscopy [2529], and resistivity and sur-
face conductance measurements [3037] have been applied
to unveil its topological properties. Please see also
Refs. [38,39] and references therein.
In SmB
6
, the strong hybridization of the low lying 4f
states with conduction band d states gives rise to a
hybridization gap of the order of 20 meV [1621]. The
Fermi level lies in this hybridization gap so that the material
is an insulator when the hybridization becomes effective at
low temperatures. The strong hybridization also leads to a
partial occupation of the 4f shell or a mixture of the Sm f
6
ð2þÞ and f
5
ð3þÞ configurations. For the valence at low
temperatures, values of 2.5 to 2.7 are given according to
different sources in the literature [4046]. Hence, the
electronic structure is described by the Hunds rule ground
states of the Sm f
6
ð2þÞ and f
5
ð3þÞ configurations with
total orbital momenta of J ¼ 0 and 5=2, respectively. The
J ¼ 5=2 multiplet is further split into a Γ
7
doublet and Γ
8
quartet due to the cubic crystal-electric field (CEF).
Figure 1 shows the ground state and first excited state of
the two Sm configurations plus their electron charge
density distributions. The charge densities of the J ¼ 0
and 1 states are spherical since neither the J ¼ 0 or 1 are
split in a cubic potential [47]. This is contrasted by the
charge densities of the CEF split J ¼ 5=2 multiplet (and
J ¼ 7=2, not shown) that are anisotropic.
FIG. 1. Sm
2þ
and Sm
3þ
total energy level diagram. The Sm
2þ
configuration is split into a J ¼ 0 and J ¼ 1, and the Sm
3þ
into a
J ¼ 5=2 and J ¼ 7=2 multiplet. The label n indicates the
degeneracy. The Sm
3þ
multiplets are further split (Γ
i
) by the
cubic crystal-electric field. The insets show the corresponding
charge densities for six and five electrons and their 2D projec-
tions, respectively.
PHYSICAL REVIEW LETTERS 120, 016402 (2018)
0031-9007=18=120(1)=016402(6) 016402-1 © 2018 American Physical Society

Information of the surface topology can be unambigu-
ously inferred from the symmetries and parities of the bulk
states involved. Knowledge about the CEF ground state
symmetry of SmB
6
therefore plays an essential role. For
example, theoretical predictions for the spin texture of the
sought-after topological surface states depend very much
whether the ground state of the f
5
J ¼ 5=2 configuration is
the Γ
8
quartet or the Γ
7
doublet CEF state [4850].
Surprisingly, after forty years of research, the CEF
scheme of SmB
6
has still to be determined. The classical
tool inelastic neutron scattering has not been able to identify
the CEF states, possibly due to the superposition of both Sm
f
5
and f
6
configurations in this mixed valent compound and
the strong neutron absorption despite double isotope sam-
ples [5153]. From inelastic neutron scattering, a sharp
excitation at 14 meV close to the hybridization gap was
reported. It was assigned to a spin exciton and not to a CEF
excitation since its intensity does not follow the 4f magnetic
form factor. Further magnetic intensities at about 35, 115,
and 85 meV have been assigned to the inter-multiplet
transitions of the Sm
2þ
configuration and of the CEF split
Sm
3þ
configuration (see Fig. 1), and to some magnetoelastic
coupling, respectively. In-gap transitions at about 15 meVin
Raman spectra could be interpreted as CEF excitations but
Raman does not yield the information about which state
forms the ground state [54,55]. A semi-empirical extrapo-
lation method can predict CEF parameters across the rare
earth series for highly diluted systems [56]. Applying such
an extrapolation to the measured CEF schemes of REB
6
with
RE ¼ Ce, Pr, and Nd [57,58] yields for SmB
6
aCEF
splitting of the order of 15 meV with the Γ
8
quartet as
the ground state. However, the Kondo insulator SmB
6
is not
a highly diluted system and it is definitely not an ionic
system but highly intermediate valent instead, questioning
the validity of such an extrapolation.
We, therefore, performed bulk-sensitive, core-level non-
resonant inelastic hard-x ray scattering (NIXS) measure-
ments that target specifically the ground state symmetry of
SmB
6
. NIXS is a powerful tool to determine the ground
state wave function of 4f and 5f systems [5962]. This
bulk sensitive and element specific spectroscopic method is
carried out with large momentum transfers j
qj so that the
transition operator e
i
q·
r
in the scattering function Sð
q; ωÞ
contains contributions of higher multipole terms, giving
information that is not accessible in a dipole experiment
[6374]. Here, the dependence of Sð
q; ωÞ on the direction
of vector
q with respect to the crystallographic lattice
provides the symmetry information of the ground state
wave function, even for cubic compounds thanks to the
multipole terms [67,75].
The NIXS measurements on the Sm and Eu N
4;5
core
level (4d
10
4f
5
4d
9
4f
6
and 4d
10
4f
6
4d
9
4f
7
, respec-
tively) were performed at the beam line P01 of PETRA-III
with a fixed final energy of 9690 eV, an energy resolution
of 0.7 eV full width at half maximum (FWHM), and
an averaged momentum transfer of j
qj¼ð9.6 0.1Þ Å
1
.
Further experimental details can be found in the
Supplemental Material [76].
The SmB
6
single crystals were grown by the aluminum
flux method [34], the polycrystalline commercial reference
samples Sm
2
O
3
(4f
5
) and Eu
2
O
3
(4f
6
) were pressed pellets
with a purity of 99.9% and 99.99%, respectively. All
samples were mounted in a vacuum cryostat with Kapton
windows and measured at 16 K. Two SmB
6
single crystals
with (100) and (110) surfaces were oriented such that for
q½100 and
q½110 a specular scattering geometry was
realized. For the
q½111 direction one of the crystals was
turned accordingly with respect to the scattering triangle.
Figure 2 shows the NIXS spectra across the N
4;5
edges of
SmB
6
(blue dots) and of the two reference compounds
Sm
2
O
3
and Eu
2
O
3
(purple and dark yellow) after sub-
traction of a linear background and scaling to the Compton
background. Spectra over a larger energy interval showing
also the elastic lines and the Compton background are
given in Fig. S1 of the Supplemental Material [76]. The Eu
edge appears at a higher energy transfer than in the case of
Sm because Eu has a higher atomic number.
We first investigate whether the SmB
6
spectrum can be
interpreted using those of Sm
2
O
3
and Eu
2
O
3
. For this
purpose we construct a spectrum made up of the weighted
sum of Sm
2
O
3
and Eu
2
O
2
. The best reproduction of the
data is obtained weighing the Sm reference with a factor 0.6
and the Eu data with a factor of 0.4. In addition, the Eu
2
O
3
spectrum is shifted by 6.8 eV to lower energies in order to
account for the higher atomic number. The resulting
spectrum reproduces the SmB
6
spectrum very satisfactorily
[see dark cyan line in Fig. 3(a)]. The weights used for the
sum correspond to a Sm valence of 2.6, in good agreement
with other studies using a variety of different experimental
methods [4046]. This provides us with confidence to carry
out further analysis using full multiplet calculations based
on the 4f
5
and 4f
6
configurations of Sm.
FIG. 2. Energy scans at the N
4;5
edges of SmB
6
,Sm
2
O
3
, and
Eu
2
O
3
after subtracting a linear background.
PHYSICAL REVIEW LETTERS 120, 016402 (2018)
016402-2

Figure 3(b) shows the full multiplet simulation of the
Sm
3þ
N
4;5
edges (purple line) resulting from a fit to the
Sm
2
O
3
data (see Fig. S2 in the Supplemental Material [76]).
The N
4;5
edge of Sm
2þ
(dark yellow line) was calculated
using the same adjustable parameters as for Sm
3þ
(see
below). The weighted sum (60% and 40%) of the simulated
curves (dark cyan) describes the SmB
6
spectrum very well in
the energy re gion between 120 and 135 eV. This is the region
where the high multipole scattering dominates (see Fig. S3
of the Supplemental Material [76] and Ref. [66] for further
explanation). In the region above 135 eV, where the
spectrum is given mostly by the dipole transitions (see
Fig. S3 and Ref. [66]) the simulation produces spectral
features that are too sharp with respect to the experiment
because the interference with the continuum states is not
included in the calculations. The high multipole excitations
are more realistically reproduced since they are lower in
energy and, therefore, further away from the continuum
states and consequently more excitonic [77].
The 4d 4f transitions were simulated with the full
multiplet code
Q
uanty which includes Coulomb and spin-
orbit interactions [78]. A Gaussian and a Lorentzian
broadening of 0.7 and 0.4 eV FWHM, respectively, account
for the instrumental resolution and lifetime effects. The
atomic 4f-4f and 4d-4f Coulomb interactions were
calculated using the Hartree-Fock scheme and a reduction
of about 20% [79] has been applied to obtain the best
agreement between the calculated and measured peak
positions [80]. Further details about the simulation can
be found in the Supplemental Material [76].
Figure 4 shows the direction dependence of the Sm N
4;5
of SmB
6
. Although the effect is small, there are clear
differences between the spectra in the energy regions
marked with red arrows. At about 126 eV energy transfer
the scattering of the
q½110 (light green dots) and
q½111
(dark green dots) directions are both stronger than for the
q½100 (blue dots), and at about 140 eV it is opposite. To
show these directional differences in a more transparent
manner, we also present in Fig. 4 the difference spectrum
between the
q½100 and
q½111 (black dots): this so-
called dichroic spectrum has unambiguously a negative
peak at 126 eV whereas it displays positive intensity in a
broader region around 140 eV.
To interpret the observed direction dependence, it is
important to know how each CEF state or multiplet
component contributes to the dichroic signal. Therefore,
Sð
q; ωÞ has been calculated taking into account a cubic
CEF for the Sm
3þ
f
5
ground state multiplet with J ¼ 5=2
assuming a Γ
8
quartet or a Γ
7
doublet ground state, and for
the Sm
2þ
f
6
multiplets with J ¼ 0 or J ¼ 1 (see Fig. 1),
[81]. The calculations were performed for the two direc-
tions
q½100 and
q½111 and in Fig. 5(a) the resulting
dichroic signals are plotted. The calculated dichroism for
the [110] and [111] direction is shown in the Supplemental
Material [76], Fig. S4. Here only the multipole scattering
contributes to the dichroism, the dipole does not because
the Sm site symmetry is cubic.
FIG. 3. (a) Experimental SmB
6
data for
q½100 (blue dots)
together with the weighted sum (dark cyan line) of the exper-
imental Sm
2
O
3
(f
5
) (purple dots) and energy shifted experimen-
tal Eu
2
O
3
(f
6
) (dark yellow dots). (b) Full multiplet simulation of
Sm
3þ
(purple line) and Sm
2þ
spectra (dark yellow line) and their
weighted sum (dark cyan line).
FIG. 4. SmB
6
NIXS data at 16 K for
q½100 (blue dot s),
q½110 (dark green dot s), and
q½111 (light green dots). The
difference spectrum between the
q½100 and
q½111 directions
is also displayed (black dots).
PHYSICAL REVIEW LETTERS 120, 016402 (2018)
016402-3

The first important finding is that the Sm
2þ
configuration
does not show any dichroism at all (see dark red and green
lines at zero dichroism) as we would expect for states with
spherical charge densities (see Fig. 1 and Direction
Dependence in NIXS in the Supplemental Material [76],
which includes Refs. [82,83]). Hence, the observed
direction dependence of the signal is solely due to the
initial state of the Sm
3þ
Hunds rule ground state. The
second important finding is that the Γ
8
and Γ
7
CEF states
exhibit different and opposite dichroism (see orange and
light blue lines), consistent with their opposite anisotropy
in the charge densities (see Fig. 1). The opposite dichroism
at 125 and 140 eV reduces the experimental challenge to a
simple yes-no experiment and makes the determination of
the CEF ground state of Sm
3þ
in SmB
6
straightforward.
Figure 5(b) shows the experimental dichroic spectrum
(black dots) together with the calculated ones. The two
possible CEF states of the J ¼ 5=2 configuration have now
been scaled down to 60% to quantitatively account for the
Sm
3þ
component in intermediate valent SmB
6
. We can
clearly observe that in the regions of pronounced dichroism
(see red arrows) the sign of the experimental dichroic
signal is correctly explained by the Γ
8
quartet (orange line)
but not at all by the Γ
7
doublet state (light blue line). In
addition, the Γ
8
reproduces the experimental dichroism
quantitatively in the high multipole region (see red arrow
1). The dichroism also fits quantitatively in the dipole
region (see red arrow 2) when an extra broadening is
applied (FWHM 4 eV beyond 135 eV energy transfer)
to mimic the interference with continuum states. Note that
sum rules still apply; i.e., the interference with the
continuum states does not change the polarization, it only
affects the broadening. The dashed lines correspond to the
dipole calculation without the extra broadening. These
results unambiguously establish that the CEF ground state
of the Sm f
5
component in SmB
6
is the Γ
8
quartet.
We would like to point out that the down scaling to 60%
of the Sm f
5
component gives a good quantitative agree-
ment in the magnitude of the dichroic signal. This provides
confidence that the NIXS method is indeed reliable since
this 60% number is fully consistent with the existing
valence determination in the literature [4046] as well as
with the above analysis of the total N
4;5
NIXS spectra. We
also would like to note that possible errors in the alignment
of the Sm
2þ
NIXS signal with respect to that of the Sm
3þ
do not affect the dichroic signal and hence the analysis of
the CEF ground state since the Sm
2þ
is silent in terms of
directional dependence.
Our finding of the Γ
8
quartet forming the ground state
supports very much the results of spin resolved APRES
[22].Xuet al. find spin polarized surface states, fulfilling
time reversal as well as crystal symmetry, that have spins
locked to the crystal momenta k such that at opposite
momenta the surface states have opposite spins. The
anticlockwise spin texture is in agreement with spin
expectation values that are calculated by Baruselli and
Vojta for a Γ
8
ground state [48,50]. Note, for a Γ
7
the spin
directions should be reversed.
Our finding of a Γ
8
local ground-state symmetry contra-
dicts the outcome of several density functional band
structure calculations [9,8486]. In band theory, the search
for the ground state symmetry in SmB
6
translates into the
question in which band the hole in the J ¼ 5=2 manifold
resides. Kang et al. reported for the X point an unoccupied
4f state of Γ
7
origin [86]. Also their k-integrated 4fJ¼
5=2 partial density of states (pDOS) shows the hole
residing in the Γ
7
band, in line with the fact that the center
of gravity of the Γ
7
pDOS is higher in energy than that of
the Γ
8
, and despite the fact that the Γ
7
band is lower than the
Γ
8
at the Γ point. Our experiments showed instead that the
X
7
band at the X point that is above the Fermi level
originates from the Γ
8
and not from the Γ
7
.
To summarize, we have utilized the high multipole
contributions in the core-level nonresonant inelastic
x-ray scattering process to determine the symmetry of
the Sm crystal field ground state 4f wave function in
SmB
6
. We have found a clear directional dependence of the
spectra that allows for the unambiguous identification of
FIG. 5. (a) Simulation of the
q½100 vs
q½111 dichroic
spectrum for the J ¼ 0 (brown) and J ¼ 1 (green) multiplet state s
of the Sm
2þ
configuration as well as for the Γ
8
quartet (orange)
and Γ
7
doublet (light blue) of the J ¼ 5=2 Sm
3þ
configuration.
(b) Experimental dichroic spectrum (black dots) and simulated
dichroic spectra for the Γ
8
quartet (orange) and Γ
7
doublet (light
blue) scaled with the factor of 0.6 to account for the Sm
3þ
component of the ground state; dashed lines with energy
independent broadening, solid lines with extra broadening in
the dipole region (see text).
PHYSICAL REVIEW LETTERS 120, 016402 (2018)
016402-4

the Γ
8
quartet state of the Sm f
5
J ¼ 5=2 configuration as
the state which governs the topological properties of SmB
6
.
Follow-up calculations should be performed within a
reduced basis of only Γ
8
states for the construction of a
low-energy many-body Hamiltonian.
K. C., M. S., A. S., and D. K. benefited from the financial
support of the Deutsche Forschungsgemeinschaft under
projects SE 1441 and SPP 1666. Parts of this research were
carried out at PETRA III at DESY, a member of the
Helmholtz Association (HGF). We thank C. Becker and
T. Mende from MPI-CPfS, and F.-U. Dill, S. Mayer, H. C.
Wille, and M. Harder from PETRA III at DESY for their
skillful technical support.
*
Corresponding author.
severing@ph2.uni-koeln.de
Corresponding author.
Hao.Tjeng@cpfs.mpg.de
Present address: Synchrotron SOLEIL, LOrme des
Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette
edex, France.
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016402-5

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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Journal ArticleDOI
TL;DR: In this paper, a redox pair of Ce4+ and Ce3+ complexes has been prepared that is stabilized by the [(NP(1,2-bis-tBu-diamidoethane)(NEt2))]1− ligand.
Abstract: A redox pair of Ce4+ and Ce3+ complexes has been prepared that is stabilized by the [(NP(1,2-bis-tBu-diamidoethane)(NEt2))]1− ligand. Since these complexes are isostructural to the recently reported isovalent terbium analogs, a detailed structural and spectroscopic comparative analysis was pursued via Voronoi–Dirichlet polyhedra analysis, UV-vis-NIR, L3-edge X-ray absorption near edge spectroscopy (XANES), cyclic voltammetry, and natural transitions orbital (NTO) analysis and natural bond orbital (NBO) analysis. The electrochemical studies confirm previous theoretical studies of the redox properties of the related complex [K][Ce3+(NP(pip)3)4] (pip = piperidinyl), 1-Ce(PN). Complex 1-Ce(PN*) presents the most negative Epc of −2.88 V vs. Fc/Fc+ in THF of any cerium complex studied electrochemically. Likewise 1-Tb(PN*) has the most negative Epc for electrochemically interrogated terbium complexes at −1.79 V vs. Fc/Fc+ in THF. Complexes 1-Ce(PN*) and 2-Ce(PN*) were also studied by L3-edge X-ray absorption near edges spectroscopy (XANES) and a comparison to previously reported spectra for 1-Tb(PN*), 2-Tb(PN*), 1-Ce(PN), and, [Ce4+(NP(pip)3)4], 2-Ce(PN), demonstrates similar nf values for all the tetravalent lanthanide complexes. According to the natural bond orbital analysis, a greater covalent character of the M–L bonds is found in 2-Ce(PN*) than in 1-Ce(PN*), in agreement with the shorter Ce–N bonds in the tetravalent counterpart. The greater contribution of Ce orbitals in the Ce–N bonding and, specifically, the higher participation of 4f electrons accounts for the stronger covalent interactions in 2-Ce(PN*) as compared to 2-Tb(PN*).

24 citations

Posted Content
TL;DR: A review of surface and bulk properties of Samarium hexaboride can be found in this paper, with an emphasis on the role of crystal growth and sample preparation, and the remaining mysteries and open questions in the field.
Abstract: Samarium hexaboride crystallizes in a simple cubic structure (space group #221, Pm-3m), but its properties are far from being straightforward. Initially classified as a Kondo insulator born out of its intriguing intermediate valence ground state, SmB6 has been recently predicted to be a strongly correlated topological insulator. The subsequent experimental discovery of surface states has revived the interest in SmB6, and our purpose here is to review the extensive and in many aspects perplexing experimental record of this material. We will discuss both surface and bulk properties of SmB6 with an emphasis on the role of crystal growth and sample preparation. We will also highlight the remaining mysteries and open questions in the field.

19 citations

References
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TL;DR: In this article, the effect of cubic crystal field Hamiltonians with both fourth and sixth degree terms and acting on an angular momentum J, has been investigated as a function of the ratio between the fourth and six degree terms.

1,466 citations

Journal ArticleDOI
TL;DR: A topological classification of emergent band structures for Kondo insulators is developed and it is shown that these materials may host three-dimensional topological insulating phases.
Abstract: This article reviews recent theoretical and experimental work on a new class of topological material—topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of Kondo insulators is reviewed along with the theoretical models used to describe these heavy fermion compounds. The Fu-Kane method of topological classification of insulators is used to show that hybridization between the conduction electrons and localized f electrons in these systems gives rise to interaction-induced topological insulating behavior. Finally, some recent experimental results are discussed, which appear to confirm the theoretical prediction of the topological insulating behavior in samarium hexaboride, where the long-standing puzzle of the residual low-temperature conductivity has been shown to originate from robust surface states.

570 citations

Journal ArticleDOI
TL;DR: In this paper, the authors review the properties of heavy fermion semiconductors and show how they can be interpreted in terms of an electronic band structure, with a temperature dependent hybridization gap together with temperature dependent quasi-particle lifetimes.
Abstract: The heavy fermion semiconductors, or Kondo insulators, are very narrow gap semiconductors in which the properties show unusual temperature dependencies. We shall review their properties and show how they can be interpreted in terms of an electronic band structure, with a temperature dependent hybridization gap together with temperature dependent quasi-particle lifetimes. The properties of these semiconductors are very sensitive to impurities, which can enhance the incipient antiferromagnetic correlations and precipitate a magnetic instability.

349 citations

Journal ArticleDOI
Feng Lu1, Jianzhou Zhao1, Hongming Weng1, Zhong Fang1, Xi Dai1 
TL;DR: The local density approximation+Gutzwiller method incorporating a Green's function scheme is applied to typical mixed valence materials SmB(6), finding its nontrivial Z(2) topology, indicating that SmB (6) is a strongly correlated topological insulator.
Abstract: We propose the local density approximation+Gutzwiller method incorporating a Green's function scheme to study the topological physics of correlated materials from the first principles. Applying this method to typical mixed valence materials SmB(6), we find its nontrivial Z(2) topology, indicating that SmB(6) is a strongly correlated topological insulator. The unique feature of this compound is that its surface states contain three Dirac cones in contrast to most known topological insulators.

294 citations

Journal ArticleDOI
TL;DR: The authors' observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, collectively provide strong evidence for protected surface metallicity with a Fermani surface whose topology is consistent with the theoretically predicted topological FermI surface.
Abstract: The Kondo insulator SmB6 has long been known to exhibit low-temperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the anomalous transport regime by combining state-of-the-art laser and synchrotron-based angle-resolved photoemission techniques. We observe clear in-gap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB6.

291 citations

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