![FIG. S2: Spin-resolved ARPES detection setup (a) Schematic of the spin-resolved ARPES spectrometer COPHEE (adapted from [32]). (b) The relative orientation of the sample (un-primed) to Mott (primed) coordinates. The polar angle ϑ is rotated during the measurement to access different values of k x. At normal emission (ϑ = 0 • ), the z and z axes are parallel and the y axis is rotated from the y axis by 45 •. The red axes are those along which the spin direction is measured. (c) The spin-averaged signal from the four pairs of detectors for a cut along the ¯ Γ-¯ M direction through the surface states of Bi 2 Te 3 at E B =-20 meV. An unpolarized background (green line) and Lorentzian lineshapes (red lines) yield a fit (black line) to the data. (d) The y component of the measured spin-polarization.](https://www.researchgate.net/profile/Dong-Qian-3/publication/26684629/figure/fig6/AS:667038372593664@1536045749055/FIG-S2-Spin-resolved-ARPES-detection-setup-a-Schematic-of-the-spin-resolved-ARPES_Q320.jpg)
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LETTERS
A tunable topological insulator in the spin helical
Dirac transport regime
D. Hsieh
1
, Y. Xia
1
, D. Qian
1,5
, L. Wray
1
, J. H. Dil
6,7
, F. Meier
6,7
, J. Osterwalder
7
, L. Patthey
6
, J. G. Checkelsky
1
,
N. P. Ong
1
, A. V. Fedorov
8
, H. Lin
9
, A. Bansil
9
, D. Grauer
2
, Y. S. Hor
2
, R. J. Cava
2
& M. Z. Hasan
1,3,4
Helical Dirac fermions—charge carriers that behave as massless
relativistic particles with an intrinsic angular momentum (spin)
locked to its translational momentum—are proposed to be the key
to realizing fundamentally new phenomena in condensed matter
physics
1–9
. Prominent examples include the anomalous quantiza-
tion of magneto-electric coupling
4–6
, half-fermion states that are
their own antiparticle
7,8
, and charge fractionalization in a Bose–
Einstein condensate
9
, all of which are not possible with conven-
tional Dirac fermions of the graphene variety
10
. Helical Dirac
fermions have so far remained elusive owing to the lack of
necessary spin-sensitive measurements and because such fermions
are forbidden to exist in conventional materials harbouring relati-
vistic electrons, such as graphene
10
or bismuth
11
. It has recently
been proposed that helical Dirac fermions may exist at the edges of
certain types of topologically ordered insulators
3,4,12
—materials
with a bulk insulating gap of spin–orbit origin and surface states
protected against scattering by time-reversal symmetry—and that
their peculiar properties may be accessed provided the insulator is
tuned into the so-called topological transport regime
3–9
. However,
helical Dirac fermions have not been observed in existing
topological insulators
13–18
. Here we report the realization and
characterization of a tunable topological insulator in a bismuth-
based class of material by combining spin-imaging and
momentum-resolved spectroscopies, bulk charge compensation,
Hall transport measurements and surface quantum control. Our
results reveal a spin-momentum locked Dirac cone carrying a non-
trivial Berry’s phase that is nearly 100 per cent spin-polarized,
which exhibits a tunable topological fermion density in the vici-
nity of the Kramers point and can be driven to the long-sought
topological spin transport regime. The observed topological nodal
state is shown to be protected even up to 300 K. Our demonstra-
tion of room-temperature topological order and non-trivial spin-
texture in stoichiometric Bi
2
Se
3
.M
x
(M
x
indicates surface doping
or gating control) paves the way for future graphene-like studies of
topological insulators, and applications of the observed spin-
polarized edge channels in spintronic and computing technologies
possibly at room temperature.
Unlike conventional Dirac fermions as in graphene, helical Dirac
fermions possess a net spin and are guaranteed to be conducting
because of time-reversal symmetry
2–5
, allowing the unique possibility
of carrying spin currents without heat dissipation. However, the
most important difference and a more exciting frontier lies in the
topological properties of helical Dirac fermion systems
3–5,12
, which
are expected to manifest in several ways, provided that the system can
be tuned to the topological transport regime where the charge density
vanishes (analogous to the charge neutrality point in graphene
10,19
).
These manifestations include an anomalous half-integer quantiza-
tion of Hall conductance
3–6
, a realization of Majorana fermions
(particles with anyon exchange statistics that differs from the con-
ventional Bose or Fermi–Dirac statistics)
7,8
, and generation of frac-
tionally charged quantum particles
9
. Helical fermions are believed to
exist on the edges of certain types of three-dimensional (3D) topo-
logical insulators
3,4,12
, with material candidates Bi
2
X
3
(X 5Se, Te)
15
recently proposed on the basis of observations
15,17
and models
15,20
.
However, these materials cannot be used to detect helical Dirac
fermion physics for three reasons. First, the helical properties of
the surface electrons are unknown and depend on the materials’ class.
Second, their electronic structure is not in the topological transport
regime, thus not allowing any of the interesting topological insulator
experiments to be performed to date. Third, unlike two-dimensional
(2D) quantum Hall Dirac systems such as graphene
10,19
, 3D topo-
logical insulators cannot be very easily tuned to this zero carrier
density regime through standard electrical gating, which has
prevented a revolution like that witnessed for graphene
10
from taking
place for topological insulators
2
.
To determine the key helical properties of the edge electrons near
the Fermi energy (E
F
) in our previously proposed candidate Bi
2
X
3
class
15
, we performed spin- and angle-resolved photoemission spec-
troscopy (spin-ARPES) scans using a double Mott detector set-up
21
,
which systematically measures all three components of the spin of the
electron as a function of its energy and momentum throughout the
Brillouin zone (Supplementary Information). Although the surface
electrons of both Bi
2
Se
3
and Bi
2
Te
3
exhibit a finite density of states
near E
F
(Fig. 1a–d), there is an additional contribution to the density
of states around momentum
CC from the spin-degenerate bulk con-
duction band in Bi
2
Se
3
. Therefore, the helical nature of the surface
electrons is most clearly resolved in Bi
2
Te
3
. We analysed the spin-
polarization of photoelectrons emitted at a binding energy
E
B
5220 meV along the k
x
(jj
CC{
MM) cut in Bi
2
Te
3
(Fig. 1e inset).
Because the surface state dispersion of Bi
2
X
3
exhibits a pronounced
time dependence after cleavage (Supplementary Information) related
to semiconductor band bending and topological charging effects
17
,
data collection times were only long enough to ensure a level of
statistics sufficient to measure the spin-polarized character of the
surface states.
Figure 1e and f shows the measured spin polarization spectra P
i
of the i5x,yand z(out-of-plane) components along the
CC{
MM
direction. In the xand zdirections, no clear signal can be discerned
within the margins of statistical error. In the ydirection on the other
hand, clear polarization signals of equal magnitude and opposite sign
are observed for surface-edge electrons of opposite momentum,
evidence that the spin and momentum directions are one-to-one
1
Joseph Henry Laboratories of Physics, Department of Physics,
2
Department of Chemistry,
3
Princeton Center for Complex Materials,
4
Princeton Institute for Science and Technology of
Materials, Princeton University, Princeton, New Jersey 08544, USA.
5
Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China.
6
Swiss Light Source, Paul
Scherrer Institute, CH-5232, Villigen, Switzerland.
7
Physik-Institute, Universitat Zurich-Irchel, 8057 Zurich, Switzerland.
8
Advanced Light Source, Lawrence Berkeley Laboratory,
Berkeley, California 94720, USA.
9
Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
Vol 460
|
27 August 2009
|
doi:10.1038/nature08234
1101
Macmillan Publishers Limited. All rights reserved
©2009
locked due to Z
2
topology. This is most clearly seen in the spin-
resolved spectra (I
y",#
; Fig. 1g), which are calculated from P
y
accord-
ing to I
y"
5I
tot
(1 1P
y
)/2 and I
y#
5I
tot
(1 2P
y
)/2, where I
tot
is the
spin-averaged intensity. To extract the spin polarization vectors of
the forward (1k
x
) and backward (2k
x
) moving electrons, we
performed a standard numerical fit (Supplementary Informa-
tion)
21
. The fit results yield 100(615)% polarized (Fig. 1h) spins that
point along the (k3z) direction, which is consistent with its topo-
logical spin–orbit coupling origin
14,21
. Spin-momentum locking is
the key to topological order in a topological insulator which cannot
be demonstrated without spin sensitive detection. Therefore the
existence of the topological insulator state was not established in
previous work on Bi
2
X
3
. Our combined observations of a spin–orbit
origin linear dispersion relation and a one-to-one locking of
momentum and spin directions allow us to conclude that the surface
electrons of Bi
2
X
3
(X5Se, Te) are helical Dirac fermions of Z
2
topological-order origin (Fig. 1).
To experimentally access these helical Dirac fermions for research-
device applications, the electronic structure must be in the topological
transport regime where there is zero charge fermion density
7–9
.
This regime occurs when E
F
lies in between the bulk valence band
maximum (VBM) and the bulk conduction band minimum (CBM),
and exactly at the surface or edge Dirac point, which should in turn lie
at a Kramers time-reversal invariant momentum
3,4
. This is clearly not
the case in either Bi
2
Te
3
,Bi
2
(Sn)Te
3
,Bi
2
Se
3
or graphene. Although
pure Bi
2
X
3
are expected to be undoped semiconductors
20,22,23
,
nominally stoichiometric samples are well known to be n- and p-type
semiconductors owing to excess carriers introduced via Se or Te site
defects, respectively
16,17
. To compensate for the unwanted defect
dopants, trace amounts of carriers of the opposite sign must be added
into the naturally occurring material, which may be easier to achieve
in Bi
2
Se
3
than in Bi
2
Te
3
because the former has a much larger
bandgap
15,24
(around 0.35 eV (ref. 25) compared to 0.18 eV (ref. 26),
respectively). To lower the E
F
of Bi
2
Se
3
into the bulk bandgap, we
substituted trace amounts of Ca
21
for Bi
31
in as-grown Bi
2
Se
3
,where
Ca has been previously shown
16
to act as a hole donor by scanning
tunnelling microscopy and thermoelectric transport studies
16
.
Figure 2a shows that as the Ca concentration increases from 0% to
0.5%, the low temperature resistivity sharply peaks at 0.25%, which
suggests that the system undergoes a metal to insulator to metal trans-
ition. The resistivity peak occurs at a Ca concentration where a change
in sign of the Hall carrier densityalso is observed (Fig. 2b),which shows
that for measured Ca concentrations below and above0.25%, electrical
conduction is supported by electron and hole carriers, respectively.
We performed systematic time-dependent ARPES measurements
to study the electronic structure evolution of Bi
22d
Ca
d
Se
3
as a func-
tion of Ca doping in order to gain insight into the trends observed in
transport (Fig. 2a and b). Early time ARPES energy dispersion maps
taken through the
CC point of the (111) surface Brillouin zone are
displayed in Fig. 2c–h for several Ca doping levels. In the as-grown
(d50) Bi
2
Se
3
samples, a single surface Dirac cone is observed with E
F
lying nearly 0.3 eV above the Dirac node forming an electron Fermi
surface. We also observe that E
F
intersects the electron-like bulk
conduction band. When a 0.25% concentration of Ca is introduced,
E
F
is dramatically lowered to lie near the Dirac node (Fig. 2d), which
is consistent with Ca acting as a highly effective hole donor. Because
the bulk CBM lies at a binding energy of approximately 20.1 eV for
d50 (Fig. 2c), a 0.3 eV shift in E
F
between d50 and d50.0025
suggests that for d50.0025, E
F
is located 0.2 eV below the CBM.
This is consistent with E
F
being in the bulk bandgap, because the
indirect energy gap between the CBM and the VBM is known from
both tunnelling
24
and optical
25
data and theory
22
to be nearly 0.35 eV.
As the Ca concentration is increased further, the position of E
F
continues a downward trend such that by d50.01, it is located
clearly below the Dirac node (Fig. 2) and intersects the hole-like bulk
valence band. The systematic lowering of E
F
with increasing din
Bi
22d
Ca
d
Se
3
observed in early time ARPES measurements
(Fig. 2i–k), which reflect the electronic structure of the sample bulk,
–0.2
0.0
0.2
4
3
2
–0.2
0.0
0.2
Spin polarization
Intensity (a.u.)
–0.2 –0.1 0.0 0.1 0.2 0.3
Py
Px
Pz
ef
EB = –20 meV EB = –20 meV
Iy
↑
Iy
↓
–0.2 –0.1 0.0 0.1 0.2 0.3
–0.2
–0.1
0.0
0.1
0.2
–0.2 –0.1 0.0 0.1 0.2
E
B
(eV)
–0.3
M
M
M
Low High
Bi2Te3
g
–0.2
–0.1
0.0
-0.2 -0.1 0.0 0.1 0.2
–0.1 0.0 0.1
–0.1 0.0 0.1
–0.1
0.0
0.1
–0.4
–0.2
0.0
kx (Å–1)
k
y
(Å
–1
)
d
Tuned Bi2–δCaδSe3
–0.2 –0.1 0.0 0.1 0.2 0.3
kx
ky
M
h
K
5° 86° 90°
5°
ab
c
kx (Å–1)
kx (Å–1)
kx (Å–1)kx (Å–1)
Figure 1
|
Detection of spin-momentum locking of spin-helical Dirac
electrons in Bi
2
Se
3
and Bi
2
Te
3
using spin-resolved ARPES. a,b, ARPES
intensity map at E
F
of the (111) surface of tuned stoichiometric Bi
22d
Ca
d
Se
3
(a; see text) and of Bi
2
Te
3
(b). Red arrows denote the direction of spin
projection around the Fermi surface. c,d, ARPES dispersion of tuned
Bi
22d
Ca
d
Se
3
(c) and Bi
2
Te
3
(d) along the k
x
cut. The dotted red lines are
guides to the eye. The shaded regions in cand dare our projections of the
bulk bands of pure Bi
2
Se
3
and Bi
2
Te
3
, respectively, onto the (111) surface.
e, Measured ycomponent of spin-polarization along the
CC{
MM direction at
E
B
5220 meV, which only cuts through the surface states. Inset, schematic
of the cut direction. f, Measured x(red triangles) and z(black circles)
components of spin-polarization along the
CC{
MM direction at
E
B
5220 meV. Error bars in eand fdenote the standard deviation of P
x,y,z
where typical detector counts reach 5 310
5
; solid lines are numerical fits
21
.
g, Spin-resolved spectra obtained from the ycomponent spin polarization
data. The non-Lorentzian lineshape of the I
y"
and I
y#
curves and their non-
exact merger at large
|
k
x
|
is due to the time evolution of the surface band
dispersion, which is the dominant source of statistical uncertainty. a.u.,
arbitrary units. h, Fitted values of the spin polarization vector P(S
x
,S
y
,S
z
) are
(sin90ucos295u, sin90usin295u, cos90u) for electrons with 1k
x
and
(sin86ucos85u, sin86usin85u, cos86u) for electrons with 2k
x
, which
demonstrates the topological helicity of the spin-Dirac cone. The angular
uncertainties are of the order of 610uand the magnitude uncertainty is of
the order of 60.15.
LETTERS NATURE
|
Vol 460
|
27 August 2009
1102
Macmillan Publishers Limited. All rights reserved
©2009
consistently explain the measured transport behaviour. However, we
observe that E
F
rises back up over time across all samples, such that all
spectra relax back to a d50 like spectrum on a typical timescale of
18 h (Fig. 2l). Such a slow upward shift of the surface Fermi level has
also been observed in Bi
2
Te
3
(ref. 17) and is due to a surface band
bending effect commonly observed in many semiconductors
(Supplementary Information). Therefore, although bulk Ca doping
succeeds in tuning E
F
between the bulk valence and conduction
bands, it does not change the position of E
F
relative to the surface
Dirac point in the ground state.
Because the surface Dirac point in the ground state of most insu-
lating compound studied, stoichiometric Bi
2
Se
3
or Bi
1.9975
Ca
0.0025
Se
3
,
lies ,0.3 eV below E
F
, its electronic structure is still not in the much
desired topological quantum transport regime. To bring the surface
Dirac point level with E
F
in Bi
22d
Ca
d
Se
3
, we demonstrate here that
hole carriers can be remarkably systematically introduced into the
surface of a large-gap topological insulator by dosing with NO
2
mole-
cules, which has been previously known to work in non-insulating
materials
27,28
. Figure 3 shows that with increasing surface hole donor
concentration, the binding energy of the surface Dirac point rises
monotonically towards E
F
. Starting from E
B
<20.3 eV at a dose of
0 Langmuir (0 L; refs 27, 28), it rises to 20.15 eV at 0.1 L where the
surface bent CBM has completely disappeared, and finally to the
charge neutrality point (E
B
50 eV) at 2 L. No further changes of
the chemical potential are observed with higher dosages. To quantify
the surface carrier density (n) dependence on surface hole donor
concentration, we mapped the surface state Fermi surface in
Fig. 3a–c and performed a Luttinger electron count (number density
on the surface) based on Fermi surface area, n5A
FS
/A
BZ
, where A
FS
is
the area of the Fermi surface and A
BZ
is the area of the surface Brillouin
zone. We find that 0.1 L of NO
2
removes approximately 0.0066 elec-
trons per surface unit cell of Bi
22d
Ca
d
Se
3
(111), and an excess of 2 L
reduces the Fermi surface to a single point within our experimental
resolution, which has an additional 0.005 electrons per unit cell
–0.3
–0.2
–0.1
0.0
0.1
0.2
0.3
0
5
10
15
20
25
δ = 0.005
Bi2–δCaδSe3
δ = 0
nHall (1020 e cm–3)
δ = 0.0025x = 0.03
ρ4K (mΩ cm)
EF
BCB
BVB
SS
0.10.0
–0.4
–0.2
0.0
k (Å–1)k (Å–1)k (Å–1)
EF
Low High
f hg
l
m
Bi2Se3+x
Bi0.9Sb0.1
Bi1.9933Sn0.0067Te3
a
b
Bi1.9975Ca0.0025Se3
CBM
VBM
z=0
E
B
(eV)
n
EB
Crystal Vac.
p-type
n-type
3D topological
insulator
–0.1 0.10.0–0.1 0.10.0–0.1 0.10.0–0.1
0.10.0–0.1 0.10.0–0.1 0.10.0–0.1 0.10.0–0.1
Intensity (a.u.)
ijk
cde
Char
g
e compensation
Ca 0% Ca 0.25% Ca 1%
Figure 2
|
Tuning the bulk Fermi level through systematic bulk charge
compensation monitored through systematic transport and ARPES
measurements. a, Resistivity at T54 K measured for samples of Bi
2
Se
3
(filled circles, no arrow labels) that are bulk electron doped due to varying
concentrations of Se vacancies
16
(x) or bulk hole doped through Ca/Bi
substitution (d). These are compared to analogous values for the topological
insulators Bi
0.9
Sb
0.1
(black square, arrowed; ref. 13) and Bi
1.9933
Sn
0.0067
Te
3
(purple triangle, arrowed). The stoichiometric Bi
2
Se
3
(Bi
1.9975
Ca
0.0025
Se
3
)is
found to be the most insulating of these topological insulators. In
Bi
2
(Ca)Se
3
, bulk resistivity in excess of 75 mVcm is possible, which will be
shown elsewhere. The bulk insulating state in Bi
0.9
Sb
0.1
(ref. 13) is intrinsic
and not due to disorder which will also be shown elsewhere.
Bi
1.9933
Sn
0.0067
Te
3
is known to be most metallic-like among the three classes
studied so far. b, Hall carrier density of the same samples determined using
Hall measurements. Symbols in aand bcoloured red (blue) represent n- (p-)
type behaviour. c–e, ARPES band dispersion images of Bi
22d
Ca
d
Se
3
(111)
through
CC collected within 20 min after cleavage for d50(
c), d50.0025
(d) and d50.01 (e). f–h, Corresponding momentum distribution curves.
Red lines are guides to the eye. i–k, Schematic downward evolution of E
F
with
increasing Ca content. The occupied bulk conduction band (BCB) and bulk
valence band (BVB) states are shaded dark, and the occupied surface states
(SS) are coloured red. l, Typical ARPES band dispersion image of c–etaken
around 18 h after cleavage, and m, its corresponding momentum
distribution curves. n, Schematic of the surface band bending process that is
responsible for the observed downward shift in energies over time. Vac.,
vacuum.
–0.2 0.0 0.2
–0.2
0.0
0.2
–0.2 0.0 0.2–0.2 0.0 0.2
k
y
(Å
–1
)
2 L
kx (Å–1)
0
–0.4
–0.2
–0.1 0.0 0.1 –0.1 0.0 0.1 –0.1 0.0 0.1
b
de f
c
Low
High
0 L 0.1 L
a
0
–0.4
–0.2
g h i
0 L 0.1 L0.01 L
0.5 L 1 L 2 L
E
B
(eV)E
B
(eV)
Kramers’
point
Figure 3
|
Tuning the density of helical Dirac electrons to the spin-
degenerate Kramers point and topological transport regime. a, A high
resolution ARPES mapping of the topological surface Fermi surface near
CC
of Bi
22d
Ca
d
Se
3
(111). The diffuse intensity within the ring originates from
the bulk-surface resonance state
15
.b, The Fermi surface after 0.1 L of NO
2
is
dosed, showing that the resonance state is removed. c, The Fermi surface
after a 2 L dosage, which achieves the Dirac charge neutrality point. d–i, High
resolution ARPES surface band dispersions through
CC after an NO
2
dosage
(L) of 0 (d), 0.01 (e), 0.1 (f), 0.5 (g), 1 (h) and 2 (i). The arrows denote the
topological spin polarization of the bands. We note that owing to an
increasing level of surface disorder with NO
2
adsorption, the measured
spectra become progressively more diffuse and the total photoemission
intensity from the buried Bi
22d
Ca
d
Se
3
surface is gradually reduced.
NATURE
|
Vol 460
|
27 August 2009 LETTERS
1103
Macmillan Publishers Limited. All rights reserved
©2009
removed. Because surface doping does not affect the carrier density in
the bulk (which thus remains insulating),the energy of the Dirac point
is lifted above the bulk VBM: a new time independent electronic
ground state is realized that lies in the topological transport regime
with E
F
intersecting the Dirac node.
In order to investigate the thermal stability and strength of topo-
logical order of this nodal Dirac ground state (Fig. 4e), temperature
dependent ARPES scans were collected on Bi
22d
Ca
d
Se
3
samples that
were first surface hole doped with NO
2
at a temperature T510 K.
Figure 4c and d illustrates that the charge neutral point-like Fermi
surface (Fig. 4a) is robust up to room temperature (T5300 K) over
measurement times of days. A density of states that decreases linearly
to zero at the Dirac point energy at 300 K (Fig. 4f) is further evidence
that the low energy properties of stoichiometric Bi
2
Se
3
.NO
2
or
Bi
1.9975
Ca
0.0025
Se
3
.NO
2
are dominated by a novel topological ground
state that features massless helical Dirac fermions with nearly 100%
spin polarization. This also confirms a non-trivial pBerry’s phase on
the surface due to the spin-momentum locking pattern that we
observed which is similar to the robust Berry’s phase previously
observed in the Bi-Sb system
14
(Fig. 1).
Helical nodal Dirac fermions are forbidden from acquiring a mass
through bandgap formation because they are located around time-
reversal invariant (Kramers’) momenta k
T
5
CC or
MM (Fig. 4h). This
makes them fundamentally different from chiral Dirac fermions such
as those found in graphene, which are located at
KK and not topo-
logically protected (Fig. 4g) and can develop an undesirable mass
while in contact with a substrate. The helical nodal Dirac fermion
on the surface of Bi
2
Se
3
owes its existence to a non-zero topological
number n
0
given by ({1)n0~P
kT
P
N
m~1j2m(kT), where j
2m
(k
T
) is the
parity eigenvalue of the bulk wavefunction at the 3D Kramers’ point
k
T
and Nis the number of occupied bulk bands
4
. Because Ca dopants
are present in only trace quantities in Bi
1.9975
Ca
0.0025
Se
3
.NO
2
, the
values of j
2m
(k
T
) do not deviate from those of Bi
2
Se
3
, as evidenced
by the persistence of a single gapless surface band in both naturally
grown Bi
2
Se
3
and Bi
1.9975
Ca
0.0025
Se
3
. Both Ca
21
and NO
2
2
are non-
magnetic and so do not break time-reversal symmetry, therefore the
same topological quantum number (n
0
51) applies in the Dirac
transport regime (Fig. 4) realized by our method shown here, which
is stable with both time and temperature. Our direct demonstration
of spin-polarized edge channels and room temperature operability of
chemically gated stoichiometric Bi
2
Se
3
or Bi
22d
Ca
d
Se
3
.NO
2
, not
achieved in purely 2D topological systems such as Hg(Cd)Te
quantum wells
29
, enables exciting future room temperature experi-
ments on surface helical Dirac fermions that carry non-trivial p
Berry’s phase.
Our demonstration of topological order at room temperature
opens up possibilities of using quantum Hall-like phenomena and
spin-polarized protected edge channels for spintronic or computing
device applications without the traditional requirements of high
magnetic fields and delicate cryogenics. A direct detection of sur-
face-edge states would be possible in stoichiometric Bi
2
Se
3
or
Bi
22d
Ca
d
Se
3
, using transport methods which will bear signatures of
weak anti-localization and thus exhibit anomalous magneto-
optic effects. Here we envisage a few sample experiments that could
be carried out by using surface doped or electrically gated
Bi
22d
Ca
d
Se
3
. By applying a weak time-reversal breaking perturbation
at the helical surface so as to lift the Kramers degeneracy at E
F
(a
method of gap opening on the surface is shown in Supplementary
Information), a half-integer quantized magneto-electric coupling
can be realized
3–6
, which could be measured by standard quantum
Hall probes. This would enable a variety of novel surface quantum
Hall physics to be realized. Another class of experiments would be
made possible by interfacing the helical topological surface with
magnetic and ordinary superconducting films. An interferometer
device could be built based on Bi
22d
Ca
d
Se
3
to create and detect
long-sought Majorana fermions
7,8
. These particles, which have never
been observed, possess only half the degrees of freedom of a conven-
tional fermion and constitute the key building block for topological
quantum computing that can operate in a fault-tolerant mode. Yet
another class of experiments would be made possible by sandwiching
a charge neutral topological insulator film made of Bi
22d
Ca
d
Se
3
within a charged capacitor. In this way, a microchip that supports
a topological electron–hole condensate with fractional vortices
9
could be fabricated, which offers the exciting opportunity to probe
EF
Intensity (a.u.)
–10
200 K
–20
300 K
10 K
0
BCB
BVB
Kramers’
point
NO2
0–1 1
0
–1
1
2
M
M
K
K
–0.2
0
–0.4
0 0.1–0.1
T = 10 K
T = 300 K
k
y
(Å
–1
)
E
B
(eV)
EB (eV)
a
c
be
Bi2–δCaδSe3.NO2kx
ky
kx
ky
kx (Å–1)kx (Å–1)
0 0.1–0.1
Chiral Dirac gound state
Kramers’ nodal
helical ground state
Kramers’ point
–0.2
0
–0.4
df
–0.15 –0.1
E–ED (eV)
–0.05
g
h
EDirac
Density of states (a.u.)
0
1
2
DOS
0.0
Background
½
300 K
300 K
Γ
Γ
Figure 4
|
Topological order of the nodal helical Dirac ground state at
300K. a, Typical ARPES intensity map of the Bi
2
(Se/Te)
3
class collected at
E
F
spanning several Brillouin zones. b, Energy distribution curves of the
valence bands of Bi
22d
Ca
d
Se
3
taken at T510 K, 200 K and 300 K. The peaks
around 24 eV and 27.5 eV come from NO
2
adsorption (Supplementary
Information). The intensity of these NO
2
core level peaks do not change over
this temperature range, indicating no measurable NO
2
desorption during
the heating process. c,d, ARPES intensity map of the surface state band
dispersion of Bi
22d
Ca
d
Se
3
(111) after a 2 L dosage of NO
2
is applied at
T510 K, which is taken at 300 K (c) and 10 K (d). e, Schematic of the surface
and bulk electronic structure of Bi
22d
Ca
d
Se
3
.NO
2
, tuned to the topological
transport regime. f, Angle-integrated intensity near
CC (red) shows a linear
trend. Inset, the expected density of states (DOS) of a helical Dirac cone,
which is 1/2 that of a graphene Dirac cone due to its single spin degeneracy.
g, Schematic of the chiral Dirac fermion ground state of graphene, which
exhibits spin-degenerate Dirac cones that intersect away from the Kramers’
points. h, Schematic of the helical Dirac fermion ground state of
Bi
22d
Ca
d
Se
3
.NO
2
, which exhibits a spin-polarized Dirac cone that intersects
at a Kramers’ point and guarantees a n
0
51 topological order quantum
number for the nodal Dirac ground state.
LETTERS NATURE
|
Vol 460
|
27 August 2009
1104
Macmillan Publishers Limited. All rights reserved
©2009
interactions between Dirac fermions of opposite helicity; this would
enable searching for exotic quantum phenomena beyond the
standard model of particle physics
30
.
METHODS SUMMARY
Spin-integrated ARPES data were taken at beamlines 12.0.1 and 7.0.1 of the
Advanced Light Source in Lawrence Berkeley National Laboratory with 29-eV
to 100-eV photons. Typical energyand momentum resolutions were 15 meV and
1% of the surface Brillouin zone (29-eV photons) and 50 meV and 2% of the
surface Brillouin zone (100-eV photons). Spin-resolved ARPES measurements
were performed at the SIS beamline at the Swiss Light Source using the COPHEE
spectrometer, which consists of two 40-kV classical Mott detectors that measure
all three spatial components of spin polarization. Spin-resolved measurements
were taken with 20-eV to 22-eV photons with energy andmomentum resolutions
of 80 meV and 3% of the surface Brillouin zone (all photons). Spin-integrated
data were collected on tunedBi
22d
Ca
d
Se
3
and tuned Bi
2
Te
3
single crystals cleaved
in ultrahigh vacuum (pressures better than 5 310
211
torr) and maintained at a
temperature of 10 K unless otherwise specified. Spin-resolved data were collected
at 50 K. Adsorption of NO
2
molecules on Bi
22d
Ca
d
Se
3
was achieved via controlled
exposures to NO
2
gas (Matheson, 99.5%). The adsorption effects were studied
under static flow mode by exposing the cleaved sample surface to the gas for a
certain time then taking data after the chamber was pumped down to the base
pressure. Spectra of the NO
2
adsorbed surfaces were taken within minutes of
opening the photon shutter to minimize photon exposure related effects. The
theoretical band calculations were performed with the LAPW method in slab
geometry using the WIEN2K package.
Full Methods and any associated references are available in the online version of
the paper at www.nature.com/nature.
Received 30 April; accepted 29 June 2009.
Published online 20 July 2009.
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Supplementary Information is linked to the online version of the paper at
www.nature.com/nature.
Acknowledgements We acknowledge the following people for discussions:
P. W. Anderson, B. Altshuler, L. Balents, M. R. Beasley, B. A. Bernevig, C. Callan,
J. C. Davis, H. Fertig, E. Fradkin, L. Fu, D. Gross, D. Haldane, K. Le Hur, B. I. Halperin,
D. A. Huse, C. L. Kane, C. Kallin, E. A. Kim, R. B. Laughlin, D.-H. Lee, P. A. Lee,
J. E. Moore, A. J. Millis, A. H. Castro Neto, J. Orenstein, P. Phillips, S. Sachdev, Dan
C. Tsui, A. Vishwanath, F. Wilczek, X.-G. Wen and A. Yazdani. The spin-resolved
and spin-integrated ARPES measurements using synchrotron X-ray facilities and
theoretical computations are supported by the Basic Energy Sciences of the US
Department of Energy (DE-FG-02-05ER46200, AC03-76SF00098 and
DE-FG02-07ER46352) and by the Swiss Light Source, Paul Scherrer Institute.
Materials growth and characterization are supported by the NSF through the
Princeton Center for Complex Materials (DMR-0819860) and Princeton
University. M.Z.H. acknowledges additional support from the A. P. Sloan
Foundation, an R. H. Dicke fellowship research grant and the Kavli Institute of
Theoretical Physics at Santa Barbara.
Author Contributions D.H., Y.X. and D.Q. contributed equally to the experiment
with the assistance of L.W. and M.Z.H.; D.G., Y.S.H. and R.J.C. provided critically
important high quality single crystal samples; J.G.C. and N.P.O. performed the
transport measurements; J.H.D., F.M., J.O., L.P. and A.V.F. provided beamline
assistance; H.L. and A.B. carried out the theoretical calculations; M.Z.H. conceived
the design to reach the topological transport regime and was responsible for the
overall project direction, planning, and integration among different research units.
Author Information Reprints and permissions information is available at
www.nature.com/reprints. Correspondence and requests for materials should be
addressed to M.Z.H. (mzhasan@Princeton.edu).
NATURE
|
Vol 460
|
27 August 2009 LETTERS
1105
Macmillan Publishers Limited. All rights reserved
©2009
METHODS
Spin-ARPES methods. Spin-integrated angle-resolved photoemission spectro-
scopy (ARPES
31
) measurements were performed with 29–100 eV linearly polar-
ized photons on beam lines 12.0.1 and 7.0.1 at the Advanced Light Source in
Lawrence Berkeley National Laboratory. All endstations were equipped with a
Scienta hemispherical electron analyser (see VG Scienta manufacturer website
(http://www.vgscienta.com/) for instrument specifications). Spin-resolved
ARPES measurements were performed at the SIS beam line at the Swiss Light
Source using the COPHEE spectrometer
32
with two 40-kV classical Mott detec-
tors and linearly polarized photons with energies of 20–22 eV. The COPHEE
spectrometer is capable of measuring all three spatial components of the spin
polarization vector for any point in reciprocal space, from which a spin-resolved
band structure is constructed. The typical energy and momentum resolution was
15 meV and 1% of the surface Brillouin zone respectively at beam line 12.0.1,
50 meV and 2% of the surface Brillouin zone respectively at beam line 7.0.1, and
80 meV and 3% of the surface Brillouin zone respectively at SIS using a pass
energy of 3 eV. Spin-integrated data were taken from single crystal Bi
22d
Ca
d
Se
3
and Bi
2
Te
3
cleaved along its (111) surface in ultrahigh vacuum at pressures better
than 5 310
211
torr and maintained at a temperature of 10 K unless otherwise
specified. Spin-resolved data were collected at 50 K. Adsorption of NO
2
mole-
cules on Bi
22d
Ca
d
Se
3
was achieved via controlled exposures to NO
2
gas
(Matheson, 99.5%). The adsorption effects were studied under static flow mode
by exposing the cleaved sample surface to the gas for a certain time then taking
data after the chamber was pumped down to the base pressure. Spectra of the
NO
2
adsorbed surfaces were taken within minutes of opening the photon shutter
to minimize potential photon induced charge transfer and desorption effects.
Crystal growth methods. To grow single crystals of Bi
22d
Ca
d
Se
3
, a mixture of
elemental Bi (99.999%) and Se (99.999%) was first melted at 800 uC in a quartz
tube for 16 h, then cooled to room temperature. Stoichiometric amounts of Ca
pieces (99.8%) were then added to the mixture and reheated to 400uC for 16 h.
After an additional day of heating at 800 uC, the crystalline sample was cooled to
550 uC in 24 h. The sample was then annealed for 3 days at 550uC followed by
furnace-cooling to room temperature. Scanning tunnelling microscopy data
16
has shown that Ca addition suppresses Se vacancies to a higher degree than the
addition of excess Se alone. Large single crystals of Bi
2
Te
3
were grown by melting
stoichiometric mixtures of elemental Bi (99.999%) and Te (99.999%) at 800 uC
overnight in a sealed vacuum quartz tube. The crystalline sample was cooled over
a period of two days to 550 uC, and maintained at the temperature for 5days. It
was then furnace cooled to room temperature.
Sample quality characterization. X-ray diffraction measurements were used to
check that the samples were single phase, and confirmed that the single crystals
presented in this paper have a rhombohedral crystal structure with space group
D5
3d(R
33m). The X-ray diffraction patterns of the cleaved crystals exhibit only the
(hhh) peaks showing that the naturally cleaved surface is oriented along the
trigonal (111) axis. Room temperature data were recorded on a Bruker D8
diffractometer using Cu Karadiation (l51.54 A
˚) and a diffracted beam mono-
chromator. The crystal structure of Bi
2
(Te/Se)
3
can be visualized as a stack of
hexagonal atomic layers, each consisting of only Bi or Te/Se. Five atomic layers
are stacked in a close-packed f.c.c. fashion along the [111] direction in order Te/
Se(1)-Bi-Te/Se(2)-Bi-Te/Se(1), in a quintuple layer, and cleavage takes place
naturally between such layers. The topmost layer after cleavage is the Te/Se(1)
layer as shown by scanning tunnelling microscopy data
24
. Our ARPES results
were reproducible over many different sample batches, although relaxation time
scales may vary by up to 10 min and the magnitude of band bending may vary up
to 50 meV. The in-plane crystal orientation was determined by Laue X-ray dif-
fraction before insertion into an ultrahigh vacuum environment. Cleaving these
samples in situ between 10 K and 300 K at chamber pressures less than
5310
211
torr resulted in shiny flat surfaces.
Bulk transport measurements. Resistivity and Hall effect measurements were
done in standard four-probe geometries with an AC applied current at 18 Hz.
Current was applied in the a–bplane and magnetic field along the c-axis ([111]
direction) for Hall effect measurements. Contacts were made with gold wire and
silver paint, with resulting contact resistance less than 1 V. Measurements were
done under vacuum pressures better than 10
26
torr.
Theoretical band calculation methods. The calculations were performed with
the LAPW method in slab geometry using the WIEN2K package
33
. Generalized
gradient approximations
34
were used to describe the exchange-correlation poten-
tial. Spin–orbit coupling was included as a second variational step using scalar-
relativistic eigenfunctions as basis. The surface was simulated by placing a slab of
six quintuple layers in vacuum using optimized lattice parameters
35
. A grid of
35 335 31 points were used in the calculations, equivalentto 120 k-points in the
irreducible Brillouin zone and 2,450 k-points in the first Brillouin zone.
31. Hufner, S. Photoelectron Spectroscopy (Springer, 1995).
32. Hoesch, M. Spin-polarized Fermi Surface Mapping. PhD thesis, Univ. Zurich (2002).
33. Blaha, P. et al. Computer Code WIEN2k (Vienna University of Technology, 2001).
34. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made
simple. Phys. Rev. Lett. 77, 3865
–
3868 (1996).
35. Wang, G. & Cagin, T. Electronic structure of the thermoelectric materials Bi
2
Te
3
and Sb
2
Te
3
from first-principles calculations. Phys. Rev. B 76, 075201 (2007).
doi:10.1038/nature08234
Macmillan Publishers Limited. All rights reserved
©2009
SUPPLEMENTARY INFORMATION
1
www.nature.com/nature
doi: 10.1038/nature08234
SI I. Diagrammatic summary of steps to achieve topological transport regime
-0.1 0. 0 0.1
-0.4
-0.2
0.0
-0.1 0.0 0.1
-0.1 0. 0 0.1
(a)����Ca�0% (c)��Ca�0.25%
Low High
E��(eV)
B
EF
BCB
BVB
SS
k(Å )
-1
0 0.1-0.1
-0.2
0
-0.4
k(Å )
-1
EF
CBM�(early)
VBM�(early)
z=0
EB
crystal vac
CBM�(late)
VBM�(late)
E��(eV)
B
(b) (d)
early late
(e)��Ca�0.25%
(f)
0.0
-0.2
-0.4
z=0
EB
crystal vac
(h)
E��(eV)
B
(g)
(1)�Pure�Bi��Se
is�electron�doped
23 (2)�Bulk�hole�dope�Bi��Se
with�Ca�to�reach�bulk�insulator.
But�stable�SS�Dirac�point�not�at�E
23
F
(3)�Surface�hole�dope
Bi����Ca��Se��with�NO
to�reach�topological
transport�regime
2- 2
FIG. S1: . Flowchart of steps required to reach topological transport regime (a) ARPES
dispersion spectrum of pure Bi2Se3, which reflects a bulk n-type behavior (b) where the bulk
valence band is completely filled while the bulk conduction band is only partially filled. (c) Early
time ARPES dispersion of Bi2−δCaδSe3, which is representative of the band structure prior to
band bending, corroborates our transport data (Fig. 2) that (d) the bulk material is an insulator.
(e) Late time ARPES dispersion of the same sample after band bending occurs, which shows a
surface spectrum shifted down in energy due to (f) the band bending effect near the surface. (g)
The surface states of bulk insulating Bi2−δCaδSe3after surface dosing with 2L of NO2gas. (h)
The bulk remains insulating in this system while the surface Dirac node now intersects the Fermi
level. This is finally the much desired topological transport regime.
SI II. Detailed analysis procedure of Spin-Resolved ARPES data
Here we present details of the spin-resolved ARPES analysis that show how we arrive at
the spin-resolved surface band dispersions presented in the main text. In the VUV incident
photon energy regime that we use, spin conserving photoemission processes (where the
electric field of light only acts on the orbital degree of freedom of the electron inside a solid)
2
2
www.nature.com/nature
doi: 10.1038/nature08234 SUPPLEMENTARY INFORMATION
-0.2 -0.1 0.0 0.1 0.2 0.3
7
6
5
4
3
Counts�( 10��)
5
z’ z’
y’ y’x’ x’
x
y
z
(a) (b)
Polarimeter�1 Polarimeter�2
(c)
Spin�polarization
k(��)
x-1
P
y
(d)
-0.2
0.0
0.2
-0.2 -0.1 0.0 0.1 0.2 0.3
k(��)
x-1
FIG. S2: Spin-resolved ARPES detection setup (a) Schematic of the spin-resolved ARPES
spectrometer COPHEE (adapted from [32]). (b) The relative orientation of the sample (un-primed)
to Mott (primed) coordinates. The polar angle ϑis rotated during the measurement to access
different values of kx. At normal emission (ϑ=0
◦), the zand zaxes are parallel and the yaxis is
rotated from the yaxis by 45◦. The red axes are those along which the spin direction is measured.
(c) The spin-averaged signal from the four pairs of detectors for a cut along the ¯
Γ- ¯
M direction
through the surface states of Bi2Te3at EB= -20 meV. An unpolarized background (green line)
and Lorentzian lineshapes (red lines) yield a fit (black line) to the data. (d) The ycomponent of
the measured spin-polarization.
dominate over spin non-conserving processes (which arise from coupling to the magnetic field
of light) [36]. Spin-resolution takes place at COPHEE using the principle of Mott scattering,
which is the asymmetry in left-right back scattering of spin-up or spin-down electrons from
a nucleus due to spin-orbit coupling [36], where spin-up or spin-down are defined to be
parallel and anti-parallel to the scattering plane normal respectively. A Mott polarimeter
consists of a gold foil target with silicon diode detectors positioned to its left (L), right (R),
3
3
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SUPPLEMENTARY INFORMATION
doi: 10.1038/nature08234
top (T) and bottom (B). Each detector pair LR or TB measures the component of spin
along the normal to its scattering plane defined by the photoelectron incidence direction on
the gold foil and the detector pair. In the COPHEE spectrometer, energy and momentum
analysis of the photoelectrons takes place using a hemispherical electrostatic analyzer as
in conventional ARPES (Fig. S2). Electrons at some selected energy and momentum are
then accelerated to high energy (typically around 40 keV) and are alternately deflected into
two Mott polarimeters that are mounted perpendicular to one another so that a total of
four (three independent x,yand z) components of spin are measured (Fig. S2(b)). The
asymmetry (Ay) in the intensities between a left detector (IL
y) and right detector (IR
y),
which measures the ycomponent for example, is given by Ay=(IL
y−IR
y)/(IL
y+IR
y), and is
related to the spin polarization Py= (1/Sef f )×Aythrough the effective Sherman function
Seff =0.07 [32]. Typical electron counts on the detector reach 5 ×105, which places an
error bar of approximately ±0.01 for each point on our polarization curves. However, the
main source of error originates from the time evolution of the spectrum. To account for
unequal sensitivities between a detector pair, we applied a small multiplicative factor to the
intensity from one detector to ensure that the unpolarized background intensity yields zero
polarization.
Figure S2(c) shows a spin averaged momentum distribution curve (MDC) along the
¯
Γ to ¯
M direction taken at EB= -20 meV, collected within a short period of time af-
ter cleavage to minimize the effects of spectrum time evolution. This MDC was ob-
tained by summing the signal coming from both LR and TB electron detectors in the
Mott polarimeter. Lorentzian lineshapes denoted Iiand a non-polarized background B
are fitted to this MDC, which are used as inputs to the two-step fitting routine devel-
oped by Meier et al. [21] in the following way. To begin with, a spin polarization vector
Pi
M=(Pi
x,Pi
y,Pi
z)=ci(cos θicos φi,cos θisin φi,sin θi) is assigned to each band, where ci
is the spin magnitude and θiand φiare referenced to the primed Mott coordinate frame.
A spin-resolved spectrum is then defined for each peak iusing Ii;↑,↓
α=Ii(1 ±Pi
α)/6, where
α=x,y
,z, and + and −correspond to the spin direction being parallel (↑) or antiparallel
(↓) to α. The full spin-resolved spectrum is then given by I↑,↓
α=iIi;↑,↓
α+B/6, from which
the spin polarization of each spatial component can be obtained as Pα=(I↑
α−I↓
α)/(I↑
α+I↓
α).
This latter expression is a function of the spin magnitude ciand spin orientation angles θi
and φi, which are varied to achieve the best fit to experimental data. The fitted curves
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shown in Fig.1 of the main text are consistent with the spins near the Fermi level being fully
polarized (ci= 1) and pointing in opposite directions on opposite sides of the Fermi surface.
The slight deviations of the fitted angles from ideality are due to the large noise level of the
data originating from the time dependence of the surface electronic structure. Even though
the measured polarization curves only reach a magnitude of less than ±0.2 (Fig. S2(d)), this
is similarly seen in studies of Bi1−xSbxalloys [14] and is due to the non-polarized background
and overlap of adjacent peaks with different spin polarization.
SI III. Complete time dependent ARPES data sets
High quality conventional semiconductors are well known to exhibit a band bending ef-
fect near the sample surface [31]. In this section, we demonstrate that slow band bending
dynamics after cleavage are also ubiquitous in high quality Bi2Se3samples, and that charac-
teristic relaxation time scales may be slowed by substituting impurity atoms such as Ca. We
then describe experiments that were performed to rule out extrinsic or instrumental factors
that may lead to the observed time dependence.
i. Time dependent surface states of Bi2−δCaδSe3
A slow surface band bending time scale is achieved in Bi2Se3through Ca/Bi substitution.
After cleaving the Ca-doped Bi2Se3sample in situ at 10K, the surface spectrum of the
samples gradually relaxes back to a δ= 0 -like spectrum. This behavior is observed at
all values of Ca doping concentration δ. Fig. S3 shows the time evolution of the surface
states for δ=0.5%. Immediately after cleavage (Fig. S3(a)), the Dirac point of the surface
state lies above the Fermi level. This spectrum is the most representative of the bulk (non-
bent) bands, as reflected in transport measurements that show bulk p-type behavior. Over
a period of 18 hours, the chemical potential gradually shifts upward as the Dirac point is
moved below EF. Shifts in the positions of the valence band peaks in the energy distribution
curve (EDC) at ¯
Γ (panel (f)) over an 18 hour time interval reveal a band bending magnitude
∆∼340 meV.
Such behavior has been attributed to a downward band bending near the surface that is
caused by the breaking of inter-quintuple layer van der Waals Te(1)-Te(1) bonds and the
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-2.0
-1.5
-1.0
-0.5
0.0 18 hr.
15 hr.
3 hr.
2 hr.
15 min.
-0.2 0.0 0.2
-0.6
-0.4
-0.2
0.0
-0.2 0.0 0.2
E (eV)
B
15�min
k(Å )
-1
19�eV 31�eV
-0.2 0.0 0.2
-0.2 0.0 0.2
-0.2 0.0 0.2
2�hours 3�hours 15�hours 18�hours
Low High
(a) (b) (c) (d) (e) (f)
FIG. S3: Time evolution of the surface states (a), Surface spectrum shortly after cleavage
reveals a Dirac point lying above EFin Bi2−δCaδSe3. (b-e), the spectrum gradually relaxes back
toaδ= 0 -like state as time elapses, with the Dirac point moving gradually to higher binding
energy. (f), EDCs through the ¯
Γ point suggest a shift of approximately 340 meV over this time
interval.
formation of Te(1)-Bi bonds [23, 24] upon crystal termination. It has been suggested that
the band bending process is slow because charge accumulation at the surface is coupled to
a much slower surface lattice relaxation [17]. Such slow surface structural dynamics have
been directly measured in GaAs using surface sensitive probes such as low energy electron
diffraction, scanning tunneling microscopy and photoelectron spectroscopy [37]. Therefore
system may be significantly delayed in achieving equilibrium by local lattice/charge density
fluctuations such as may arise from site defects, which are prominent in such materials [16,
24].
ii. Ruling out extrinsic factors that may lead to time dependence
Surface charging effects are commonly observed in ARPES in poorly electrically con-
ducting samples. This effect arises from the positive charging of the sample surface due to
photoelectrons being ejected and a lack of electron compensation from the system the sample
is in contact with. Because we observe an increase rather than a decrease in the Fermi level
position with time, such charging effects can be ruled out. In order to eliminate the role of
radiation dosage to the time dependence of the bands, we systematically delayed the time
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between cleaving the sample and exposing it to radiation, while keeping the measurement
commencement time fixed at 40 minutes after cleavage and the data collection time short
(∼1 minute). We find that the Dirac cone dispersion after 40 minutes is independent of ra-
diation dose received by the crystal, therefore the band evolution is independent of radiation
effects.
It will be shown that a small amount of iron deposited onto the surface of Bi2Se3(SI.
VI) can lead to a significant rise in the Fermi level, and it has been reported that less
than 0.1 monolayers of adatoms adsorbed on GaAs will result in significant band bending
[38]. Therefore it is possible that the gradual adsorption of residual gas onto the Bi2Te3or
Bi2−δCaδSe3surfaces in the UHV chamber can lead to the observed time dependence. In
order to eliminate this possibility, we measured the surface Dirac cone dispersion an hour
after cleavage at various temperatures, which correspond to vacuum pressures that differ by
an order of magnitude (∼10−11 torr to ∼10−10 torr). We find that there is no observable
change in the Fermi level from 15 K up to 260 K, which shows that the spectrum after an
hour is not affected by the concentration of residual gas in the environment.
SI IV. Signatures of NO2surface adsorption in core level spectroscopy
Fig. S4 presents the experimental valence bands with binding energies up to -12eV before
and after exposure to NO2. On the clean samples (Fig. S4(a)), dispersive Bi2−δCaδSe3valence
bands are clearly observed at binding energies from 0 to -5eV. There are additional weak
features with binding energies of -9 to -11eV. After exposure to NO2, two additional strong
features appear at binding energies of -4eV and -7.5 eV (Fig. S4(b)). These new features
are non-dispersive - indicating that they are due to photoelectrons from randomly adsorbed
molecules. The overall signal intensity from the underlying Bi2−δCaδSe3is weakened, due
to the additional layers of molecules deposited onto the surface [31]. As reported by studies
of NO2adsorption on graphene, extensive photon exposure can remove NO2molecules from
the doped sample surfaces [27]. A very different behavior is observed on the Bi2−δCaδSe3
(111) surface. In our experiment, we find that the NO2peaks do not change in magnitude
with photon exposure. Therefore, NO2adsorption is very stable against photon exposure.
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0.1
-0.1
0
0.1
-0.1
0
0-5-10
Binding�Energy�(eV)
k�(A )
-1
k�(A )
-1
Intensity�(arb�Units)Intensity�(arb�Units)
NO2
(a)�Before�NO absorption
2
(b) After�NO absorption
2
Bi Ca Se
2- 3� �
FIG. S4: Angle-resolved and angle-integrated valence band spectra before and after
NO2adsorption (a), Before NO2adsorption, the valence bands are sharp and dispersive. (b),
After exposing to NO2gas, two additional non-dispersive features appear at binding energies of
-4eV and -7.5eV. The total signal intensity from Bi2Se3is weakened.
SI V. Thermal stability of NO2adsorption at different dosage levels
Figures S5 (a)-(b) present the surface band spectra of samples dosed with 0.5L of NO2
at 10K and then imaged at 10K and 300K. The samples are warmed to room temperature
at a rate of approximately 5-10K per minute. The position of the Dirac point is nearly
identical (∼100meV below the Fermi level), suggesting that there is no significant NO2
thermal desorption affecting the hole doping on the Bi2−δCaδSe3surface, just as is the
case for 2L dosages (see text). This observation is further confirmed by the valence band
spectra at 10K and 300K (Figs S5(c)&(d)), which exhibit no changes of the -4 and -7.5eV
non-dispersive features attributed to the adsorbed NO2molecules.
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0 0.1-0.1
(b)�300K
-0.2
0
-0.4
Momentum�k�(A )
-1
(a)�10K
Binding�Energy�(eV)
0 0.1-0.1
Momentum�k�(A )
-1
-0.1
0.1
0
-0.1
0.1
0
-10 -5 0
Binding�Energy�(eV)
(d)�300K
(c)�10K
Bi Ca Se
2- 3��
FIG. S5: Thermal stability of the doped holes on Bi2−δCaδSe3(a), Surface bands after the
sample is exposed to 0.5L of NO2at 10K and slowly warmed to (b), 300K. The corresponding
valence bands at (c), 10K and (d), 300K.
SI VI. Effects of Fe adsorption onto the Bi2Se3surface
In this section we describe preliminary ARPES results on Bi2Se3(111) that has been
deposited with iron atoms. This is a possible method of introducing a weak time-reversal
symmetry breaking magnetic field at the surface of a topological insulator to lift the Kramers’
degeneracy, which is needed to observe the interesting topological physics described in the
text such as the half-integer surface quantum Hall effect and an interferometry based detec-
tion of Majorana fermions.
Figure S6 shows that when less than 1% of a monolayer of Fe is deposited on the Bi2Se3
surface, there are two effects. First, the Fermi level rises by around 200 meV relative to the
undoped sample (Figure 2(c) main text), which suggests that surface Fe atoms act as highly
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-0.2 -0.1 0.0 0.1 0.2
-0.8
-0.6
-0.4
-0.2
0.0
E���(eV)
B
k(��)
x-1
FIG. S6: Changes in the electronic structure of Bi2Se3(111) after Fe doping. (a), ARPES
spectrum of Bi2Se3obtained with 29 eV photons along the ¯
Γ- ¯
M direction after less than 1% of
a monolayer of Fe is deposited onto the sample in situ. (b), The corresponding EDCs. Dots are
guides to the eye.
effective electron donors. This rise in EFreveals a pair of spin-split parabolic bands inside
the bulk-surface resonance state, which are reminiscent of those observed in Sb(111) at ¯
Γ
[14]. Second, we observe a strong spectral weight suppression around EB= -0.5 eV, which
is very different from the undoped case where the signal intensity is highest at the Dirac
node. Furthermore, we observe a discontinuity near EB= -0.5 eV within the positive and
negative dispersing branches of the Dirac cone. These features are suggestive of an opening
of a small gap at the Dirac node. Further experiments are required to verify the magnetic
origin of this gap-like feature.
[36] Johnson, P. Spin-polarized photoemission. Rep. Prog. Phys. 60, 1217-1304 (1997).
[37] Deng, Z. W. et al. Time-resolved measurement of surface band bending of cleaved GaAs(110)
and InP(110) by high resolution XPS. App. Surf. Sci. 158, 58-63 (2000).
[38] Spicer, W. E. et al. The surface electronic structure of 35 compounds and the mechanism of
Fermi level pinning by oxygen (passivation) and metals (Schottky barriers). Surf. Sci. 86, 763
(1979).
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