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Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States
in Bi2Te3and Sb2Te3
D. Hsieh,
1
Y. Xia,
1
D. Qian,
1
L. Wray,
1
F. Meier,
2,3
J. H. Dil,
2,3
J. Osterwalder,
3
L. Patthey,
2
A. V. Fedorov,
4
H. Lin,
5
A. Bansil,
5
D. Grauer,
6
Y. S. Hor,
6
R. J. Cava,
6
and M. Z. Hasan
1,
*
1
Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544, USA
2
Swiss Light Source, Paul Scherrer Institute, CH-5232, Villigen, Switzerland
3
Physik-Institut, Universita
¨tZu
¨rich-Irchel, 8057 Zu
¨rich, Switzerland
4
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
5
Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
6
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
(Received 18 June 2009; published 28 September 2009)
We show that the strongly spin-orbit coupled materials Bi2Te3and Sb2Te3and their derivatives belong
to the Z2topological-insulator class. Using a combination of first-principles theoretical calculations and
photoemission spectroscopy, we directly show that Bi2Te3is a large spin-orbit-induced indirect bulk band
gap (150 meV) semiconductor whose surface is characterized by a single topological spin-Dirac
cone. The electronic structure of self-doped Sb2Te3exhibits similar Z2topological properties. We
demonstrate that the dynamics of spin-Dirac fermions can be controlled through systematic Mn doping,
making these materials classes potentially suitable for topological device applications.
DOI: 10.1103/PhysRevLett.103.146401 PACS numbers: 71.20.b, 71.10.Pm, 73.20.At, 73.23.b
Topological insulators are a new phase of quantum
matter that host exotic Dirac electrons at their edges owing
to a combination of relativistic and quantum entanglement
effects [1]. They were recently proposed [2–4] and shortly
afterwards discovered in the Bi1xSbx[5,6] and Bi2Se3
[7,8] materials. In these systems, spin-orbit coupling
(SOC) gives rise to electrically insulating states in the
bulk and robust conducting states along the edges. In
contrast to graphene, which has four Dirac cones (2 doubly
degenerate cones at the Kand K0points in momentum
space) [9], the remarkable property of topological edge
states is that their dispersion is characterized by an odd
number of nondegenerate Dirac cones. Such odd Dirac-
cone edge metals are predicted to exhibit a host of uncon-
ventional properties including a fractional (half-integer)
quantum Hall effect [2,10] and immunity to Anderson
localization due to spin-texture and pi Berry’s phases on
their surfaces [2,5–7,11]. The most exciting physics, how-
ever, may occur at the interface between a topological
insulator and an ordinary ferromagnet or superconductor,
where electromagnetic responses that defy Maxwell’s
equations [10,12,13] and excitations that obey non-
Abelian statistics [14,15] have been predicted.
The surging number of interesting experimental pro-
posals involving odd Dirac-cone surface metals [10,14–
17] has ignited a search for the most elementary form of a
topological insulator, namely, one with a large bulk band
gap and a single surface Dirac cone. Although Bi1xSbx
has a room temperature direct band gap (>30 meV)[5],
a small effective mass of its bulk electrons is known to
cause the system to form conducting impurity bands even
in high purity samples [18], which dominate over conduc-
tion through the surface states. More importantly, Bi1xSbx
has multiple surface states of both topological and non-
topological origin [5], which makes isolating any trans-
port signal from a single topological surface state particu-
larly challenging. More recently, angle-resolved photo-
emission spectroscopy (ARPES) and theoretical [7,19] evi-
dence suggest that Bi2Se3is a large band gap (300 meV)
single-Dirac-cone topological insulator. In this Letter, we
report a bulk and surface ARPES investigation of single
crystals of Bi2Te3,Bi2xMnxTe3, and Sb2Te3. Remark-
ably, we find that their electronic structures are in close
agreement with our topological SOC calculations shown
here, and a single Dirac cone is realized on their (111) sur-
face. Although Sb2Te3is found to have stable gapless bulk
states, we show that the Fermi energy of Bi2Te3is time
dependent, which has also been observed with ARPES in
hole-doped Bi2Te3samples [20], and can be controlled via
Mn doping. Using a synchrotron light source with a vari-
able photon energy (h), we show that the bulklike states
of Bi2xMnxTe3(x¼0) are insulating with the valence
band maximum lying around 150 meV below EF, realizing
a large band gap topological insulator with tunable surface
dynamics that can be used for novel topological physics.
ARPES measurements were performed with 28–45 eV
linearly polarized photons on beam line 12.0.1 at the
Advanced Light Source in Lawrence Berkeley National
Laboratory. The typical energy and momentum resolution
was 15 meV and 1% of the surface Brillouin zone (BZ),
respectively. Single crystals of Bi2xMnxTe3were grown
by melting stoichiometric mixtures of elemental Bi
(99.999%), Te (99.999%), and Mn (99.95%) at 800 C
overnight in a sealed vacuum quartz tube. The crystalline
sample was cooled over a period of 2 days to 550 Cand
maintained at the temperature for 5 days. The same proce-
PRL 103, 146401 (2009) PHYSICAL REVIEW LETTERS week ending
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0031-9007=09=103(14)=146401(4) 146401-1 Ó2009 The American Physical Society
dure was carried out with Sb (99.999%) and Te (99.999%)
for Sb2Te3crystals. Our calculations were performed with
the linear augmented-plane-wave method in slab geometry
using the WIEN2K package [21]. The generalized gradient
approximation of Perdew, Burke, and Ernzerhof [22] was
used to describe the exchange-correlation potential. Spin-
orbit coupling was included as a second variational step
using scalar-relativistic eigenfunctions as a basis. The
surface was simulated by placing a slab of six quintuple
layers in vacuum using optimized lattice parameters from
Ref. [23]. A grid of 35 35 1points was used in the
calculations, equivalent to 120 kpoints in the irreducible
BZ and 2450 kpoints in the first BZ.
The most basic 3D topological insulator supports a
single Dirac cone on its surface [Fig. 1(a)], with the
Dirac node located at a momentum kTin the surface BZ,
where kTsatisfies kT¼kTþGand Gis a surface
reciprocal-lattice vector [2]. Our theoretical calculations
on Bi2Te3(111) show that it is a SOC-induced bulk band
insulator and that a single surface Dirac cone that encloses
kT¼
appears only when SOC is included [Fig. 1(b)]. To
determine whether single crystalline Bi2Te3is a topologi-
cal insulator as predicted, we first mapped its high energy
valence bands using ARPES. Figures 1(c) and 2show that
the measured bulk band structure is well described by SOC
calculations, suggesting that the electronic structure is
topologically nontrivial. A more direct probe of the topo-
logical properties of Bi2Te3, however, is to image its
FIG. 1 (color online). A single massless topological spin-Dirac
cone on the surface of Bi2xMnxTe3: (a) Schematic of the (111)
surface Brillouin zone with the four time-reversal-invariant
momenta (
,3
M) marked by blue circles. A single Fermi
surface enclosing
that arises from a Dirac cone is the signature
of the most basic topological insulator. Red arrows denote the
direction of spin [6] around the Fermi surface of a Dirac cone.
(b) Calculated band structure along the
K
Mcut of the
Bi2Te3ð111ÞBZ. Bulk band projections are represented by the
shaded areas. The band structure results with SOC are presented
in blue and that without SOC in green. The magnitude of the
bulk indirect gap is typically underestimated by ab initio calcu-
lations. No pure surface band is observed within the bulk band
gap without SOC (black lines). One pure gapless surface band
crossing EFis observed when SOC is included (red lines). The
inset shows an enlargement of the low energy region (shaded
box) near
. (c) ARPES second derivative image of the bulk
valence bands of Bi2Te3along
M. (d) ARPES intensity map
of the gapless surface state bands imaged 1 h after cleavage. The
blue dotted lines are guides to the eye. The spin directions are
marked based on calculations. (e) Energy distribution curves of
the data shown in (d). (f) Constant energy ARPES intensity map
collected at EFusing h ¼35 eV. Yellow dotted lines are
guides to the eye.
FIG. 2 (color online). Observation of insulating bulklike states
in stoichiometric Bi2Te3supporting a six-peak electronic struc-
ture: (a) bulk rhombohedral Brillouin zone of Bi2Te3. According
to local-density approximation band structure calculations
[24,25], six valence band maxima are located at the bpoints
that are related to one another by 60rotations about ^z. The red
lines show the momentum space trajectories of the ARPES scans
taken using h ¼31, 35, and 38 eV. The inset shows a schematic
of the indirect bulk band gap. (b) Calculated valence band
structure along cut 2 superimposed on the second derivative
image of a corresponding ARPES cut. The calculated band
energies have been shifted downwards to match the data. (c)–
(e) show ARPES intensity maps along the h ¼31, 35, and
38 eV trajectories, respectively, obtained 1 h after sample
cleavage. The in-plane momentum components of the band d
points are marked by black arrows, and the energy of the valence
band maximum relative to EF() is marked by a double-headed
arrow. Yellow arrows denote the direction of the spin of Dirac-
cone surface states. (f)–(h) show the energy distribution curves
corresponding to images (c)–(e), respectively.
PRL 103, 146401 (2009) PHYSICAL REVIEW LETTERS week ending
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surface states. Figures 1(d) and 1(e) show that the surface
states are metallic and are characterized by a single-Dirac-
cone crossing EF, in agreement with theory [Fig. 1(b)].
Moreover, the density of states at EFis distributed about a
single ring enclosing
[Fig. 1(f)], in accordance with
Bi2Te3being a topological insulator.
Our theoretical calculations show that stoichiometric
Bi2Te3is a bulk indirect gap insulator [Fig. 1(b)]. The
bulk valence band maximum (VBM) in Bi2Te3lies at the
bpoint in the ZL plane of the three-dimensional bulk BZ
[Fig. 2(b)], giving rise to a VBM in each of the six such
mirror planes in agreement with previous proposals
[24,25]. The VBM exhibits an indirect gap with the con-
duction band minimum (CBM) above EF, which is located
at the dpoint in the ZL plane. In order to establish
whether Bi2Te3is a bulk insulator as predicted, we per-
formed a series of ARPES scans along the cuts shown by
red lines in Fig. 2(a) (displaced along kzby varying h)
that traverse the locations of the VBM and CBM in the bulk
BZ. All h-dependent scans were taken more than an hour
after cleavage to allow the band structure to stabilize (see
Fig. 3). Figures 2(c)–2(h) show a series of ARPES band
dispersions along momentum cuts in the kxkzplane
taken using h ¼31, 35, and 38 eV, respectively. The
Dirac cone near EFshows no dispersion with h, support-
ing its surface state origin. In contrast, a strongly h
dispersive holelike band is observed near kx¼0:27
A1,
whose maximum rises to an energy closest to EF(¼
150 50 meV) when h ¼35 eV [Fig. 2(d)]. Using the
free electron final state approximation, the VBM is located
at ð0:27;0;0:27Þ
A1, in agreement with calculations.
ARPES scans taken in the vicinity of the dpoint
ð0:17;0;0:37Þ
A1, which is traversed directly when h ¼
38 eV, do not measure any signal from the CBM, showing
that EFlies in the bulk band gap. This is consistent with the
size of the indirect band gap (>150 meV) measured using
tunneling [26] and optical techniques [27]. We note that
because ARPES is sensitive only to the topmost quintuple
layer [Fig. 3(a)] at our sampled photon energies [28], the
measured energy of the bulk band edge may differ from
the true bulk value due to band bending effects that are
commonly observed in semiconductors.
In order to investigate the effects of semiconductor band
bending on the surface Dirac cone on Bi2Te3, we per-
formed time-dependent ARPES experiments. Our results
show that the binding energy of the Bi2Te3surface Dirac
node exhibits a pronounced time dependence, increasing
from EB100 meV 8 minutes after cleavage to EB
130 meV at 40 minutes [Figs. 3(c)–3(e)], in agreement
with a previous report [20]. Such behavior has been attrib-
uted to a downward band bending near the surface
[Fig. 3(b)] that is caused by the breaking of interquintuple
layer van der Waals Teð1Þ—Teð1Þbonds [Fig. 3(a)], which
creates a net electric field near the surface upon crystal
termination [25,26]. Unlike previous calculations [19], our
calculated position of the Dirac node lies in the bulk band
gap [Fig. 1(b)], which corroborates our experimental find-
ing that the intensity is strongest near the Dirac node and
drastically weakens away from
as the surface band
merges with the bulk bands and become short-lived
[5,6,28]. The slow dynamics of the band bending process
suggests that charge accumulation at the surface is coupled
to a much slower surface lattice relaxation [20]. The sys-
tem is likely to be significantly delayed in achieving equi-
librium by local lattice or charge density fluctuations such
as may arise from site defects, which are prominent in such
materials [8,26]. By systematically increasing the defect
concentration through Mn for Bi substitution, we demon-
strate here that band bending can be slowed by up to
tenfold [Figs. 3(f)–3(h)], allowing a wider range of the
intrinsic relaxation time scale to be accessed. ARPES
valence band spectra [Fig. 3(i)]ofBi1:95Mn0:05Te3taken
over a 15 h period show that the positions of the valence
band edges shift downward by a total energy of around
100 meV, which we take as a measure of the total magni-
tude of band bending .
FIG. 3 (color online). Slow dynamics of the surface Dirac-cone dispersion in Bi2xMnxTe3: (a) the crystal structure of Bi2Te3
viewed parallel to the quintuple layers. The Te(1) 5porbitals that form the interquintuple layer van der Waals bonds are shown in
yellow. (b) Schematic of the band bending of the bulk VBM near the cleaved surface. (c) ARPES spectra of Bi2Te3along the
-
M
direction taken with h ¼30 eV (c) 8, (d) 20, and (e) 40 min after cleavage in UHV. Analogous ARPES spectra for Bi1:95 Mn0:05Te3
(f) 15 min, (g) 4 h, and (h) 9 h after cleavage, showing a slower relaxation rate. Red lines are guides to the eye. (i) The energy
distribution curves of Bi1:95Mn0:05 Te3at
at various times after cleavage.
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Having identified a new topological insulator Bi2Te3,we
proceed to investigate whether similar topological effects
can take place in a non-bismuth-based compound. Fig-
ure 4(a) shows the calculated electronic structure of
Sb2Te3, which, like Bi2Te3, exhibits a bulk insulating band
structure that is strongly influenced by SOC and a single
Dirac cone on its (111) surface. By comparing our SOC
calculations with the experimentally measured bulk va-
lence bands, it is clear that there is good agreement along
both the kx[Fig. 4(d)] and ky[Fig. 4(e)] directions, show-
ing that the bulk electronic structure of Sb2Te3is consistent
with having topologically nontrivial bulk properties. How-
ever, due to a high level of intrinsic doping that is typical of
these compounds, the Fermi energy of naturally grown
Sb2Te3lies in the bulk valence band continuum and thus
does notcut through thesurface states. UnlikeBi2xMnxTe3,
no time dependence of the bands is observed. Recently, we
came across independent work [29] on a different
Bi2ðSnÞTe3series that finds a single Dirac cone.
In conclusion, our first-principles theoretical calcula-
tions and ARPES results show that Bi2Te3and Sb2Te3
possess bulk band structures where the insulating gap
originates from a large spin-orbit coupling term, and
such insulators support topologically nontrivial Z2surface
states. Our direct observation of single Dirac cones in these
materials and the systematic methods demonstrated to
control the Dirac fermion dynamics on these highly non-
trivial surfaces point to new opportunities for spintronic
and quantum-information materials research.
The use of synchrotron x rays and theoretical computa-
tions is supported by DOE/BES (No. DE-FG-02-
05ER46200, No. AC03-76SF00098, and No. DE-FG02-
07ER46352). Materials growth is supported by NSF
(No. DMR-0819860). M. Z. H. acknowledges the A. P.
Sloan Foundation.
*mzhasan@Princeton.edu
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FIG. 4 (color online). Evidence for a topologically nontrivial
band structure in Sb2Te3: (a) calculated band structure along the
K-
-
Mcut of the Sb2Te3ð111ÞBZ. Bulk band projections are
represented by the shaded areas. The bulk (surface) band struc-
ture results with SOC are presented in blue (red lines) and that
without SOC in green (black lines). (b) Schematic of the single
surface spin-Dirac cone in Sb2Te3based on calculations.
(c) Enlargement of low energy region [shaded box in (a)] near
. (d) Second derivative image of the bulk valence bands along
-
Mand (e)
-
Kat kz¼0:77 -Z. Corresponding bulk band
calculations are superimposed.
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