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Communication
Gate-Variable Mid-Infrared Optical Transitions
in a (Bi
1-x
Sb
x
)
2
Te
3
Topological Insulator
William S. Whitney, Victor Watson Brar, Yunbo Ou, Yinming Shao, Artur
R. Davoyan, Dimitri N. Basov, Ke He, Qi-Kun Xue, and Harry A Atwater
Nano Lett.
,
Just Accepted Manuscript
• DOI: 10.1021/acs.nanolett.6b03992
• Publication Date (Web): 12 Dec 2016
Downloaded from http://pubs.acs.org on December 13, 2016
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1
Gate-Variable Mid-Infrared Optical Transitions in a
(Bi
1-x
Sb
x
)
2
Te
3
Topological Insulator
1
William S. Whitney,
2,3
Victor W. Brar,
4
Yunbo Ou,
5,6
Yinming Shao,
2
Artur R. Davoyan,
5,6
D.
N. Basov,
7
Ke He,
7
Qi)Kun Xue and
2
Harry A. Atwater
1
Department of Physics, California Institute of Tech
nology, Pasadena, CA 91125, USA
2
Thomas J. Watson Laboratory of Applied Physics, Cal
ifornia Institute of Technology, Pasadena,
CA 91125, USA
3
Kavli Nanoscience Institute, California Institute o
f Technology, Pasadena, CA 91125, USA
4
Beijing National Laboratory for Condensed Matter Ph
ysics, Institute of Physics, The Chinese
Academy of Sciences, Beijing 100190, China
5
Department of Physics, University of California)San
Diego, La Jolla, CA 92093, USA
6
Department of Physics, Columbia University, New Yor
k, NY
7
State Key Laboratory of Low)Dimensional Quantum Phy
sics, Department of Physics, Tsinghua
University, Beijing 100084, China
*Corresponding author: Harry A. Atwater (
haa@caltech.edu
)
Abstract:
We report mid)infrared spectroscopy measurements of
ultrathin, electrostatically gated (Bi
1)
x
Sb
x
)
2
Te
3
topological insulator films, in which we observe s
everal percent modulation of
transmittance and reflectance as gating shifts the
Fermi level. Infrared transmittance
measurements of gated films were enabled by use of
an epitaxial lift)off method for large)area
transfer of topological insulator films from infrar
ed)absorbing SrTiO
3
growth substrates to
thermal oxidized silicon substrates. We combine th
ese optical experiments with transport
measurements and angle)resolved photoemission spect
roscopy to identify the observed spectral
modulation as a gate)driven transfer of spectral we
ight between both bulk and 2D topological
surface channels and interband and intraband channe
ls. We develop a model for the complex
permittivity of gated (Bi
1)x
Sb
x
)
2
Te
3
, and find a good match to our experimental data.
These
results open the path for layered topological insul
ator materials as a new candidate for tunable,
ultrathin infrared optics and highlight the possibi
lity of switching topological optoelectronic
phenomena between bulk and spin)polarized surface r
egimes.
Keywords:
Bismuth antimony telluride, topological insulator,
tunable optical properties, mid)
infrared, Burstein)Moss shift, optical modulator
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Topological insulators – narrow band)gap semiconduc
tors that exhibit both an insulating
bulk and metallic Dirac surface states – have been
found experimentally in the past several years
to display a remarkable range of new electronic phe
nomena.
1)4
In addition, these Dirac surface
states have been predicted to host unique and techn
ologically compelling optical and
optoelectronic behavior. Some of these effects hav
e been experimentally demonstrated – giant
magneto)optical effects, helicity)dependent photocu
rrents and more – but many others, including
gapless infrared photodetection, gate)tunable, long
)lived Dirac plasmons and hybrid spin)
plasmon modes, remain elusive.
5)16
One of the most fascinating features of topological
insulator systems is the coexistence
and interplay of massless Dirac electrons and massi
ve bulk carriers. While systems like the
bismuth telluride family of materials are strong to
pological insulators, they are also structurally
two)dimensional, layered Van der Waals semiconducto
rs.
17, 18
For technologies like tunable
optics, for which the graphene Dirac system is prom
ising, excitations of both Dirac electrons and
these low effective mass bulk carriers are equally
compelling.
19)22
The low density of states of
both of these classes of carriers and availability
of ultrathin, gate)tunable films by Van der Waals
epitaxy indicate the possibility of highly tunable
infrared absorption.
23, 24
Furthermore, by tuning
the Fermi level of these materials it may be possib
le to switch dynamically between
optoelectronic regimes dominated by spin)polarized
topological surface physics and by bulk
semiconductor physics.
In this paper, we report a measurement of the infra
red reflectance and transmittance of
ultrathin (Bi
1)x
Sb
x
)
2
Te
3
(x = 0.94) topological insulator (TI) films while
applying a gate voltage
to modulate the Fermi level. To allow gated transm
ittance measurements, we developed an
epitaxial lift)off method for large)area transfer o
f TI films from the infrared)absorbing SrTiO
3
growth substrates to thermal oxidized silicon subst
rates.
25, 26
We combine these optical
experiments with gated transport measurements and a
ngle)resolved photoemission spectroscopy
to identify the mechanism of the observed spectral
modulation. This behavior consists of a gate)
driven transfer of spectral weight between both bul
k and 2D topological surface channels and
interband and intraband channels. We propose that
the physical bases for these phenomena are
Pauli)blocking of bulk interband transitions, for h
igher photon energies, and modulation of the
plasma edge with varying topological surface and bu
lk carrier densities, for lower photon
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energies. We develop a model for the complex permi
ttivity of gated (Bi
1)x
Sb
x
)
2
Te
3
, and find a
good match to our experimental data.
Our experimental optical setup and device structure
are shown in Fig. 1. The topological
insulator film sits atop a thermally oxidized silic
on substrate, allowing control of its Fermi level
by applying a voltage between electrodes on the fil
m and the doped silicon to accumulate or
deplete carriers by the field effect.
27
As depicted in Fig. 1, the topological surface st
ate is
thought to occupy a 1 – 2 nm region at the top and
bottom interfaces of the (Bi
1)x
Sb
x
)
2
Te
3
film.
28
An optical microscope image and AFM cross)cut are s
hown for a (Bi
1)x
Sb
x
)
2
Te
3
film transferred
from its growth substrate to thermally oxidized sil
icon and patterned into an electrically isolated
device.
The primary result of this work is the observation
of gate)control of inter and intra)band
optical transitions in transmittance and reflectanc
e (Fig. 2a,b). Infrared transmittance and
reflectance are probed using an infrared microscope
coupled to an FTIR spectrometer, while the
gate bias is varied. Modulation of transmittance a
nd reflectance of several percent is observed,
with respect to their values at zero)bias applied t
o the silicon gate. In transmittance, two major
features are seen. At lower photon energies, trans
mittance is increased as the Fermi level is
increased. At higher photon energies, transmittanc
e is decreased as the Fermi level is increased.
Between these features – labelled A and B, respecti
vely, in Fig. 2b – is an isosbestic point that
sees no modulation, suggesting a cross)over between
two competing effects.
To locate the Fermi level in our films, we measured
the sheet)resistance as functions of
gate voltage and temperature (Fig. 3a)c). With neg
ative gate bias, sheet resistance is seen to
increase as p)type carriers are depleted by the fie
ld effect and the Fermi level of our film is
increased. At large negative bias, the resistance
appears to approach a peak that, while not
visible in our range of gate voltages, we speculate
may be the Dirac point. Likewise, with
positive bias, sheet resistance is seen to decrease
as p)type carriers are accumulated and the
Fermi level is decreased. In measurements of sheet
resistance versus temperature, a transition
from metallic to insulating character is seen as th
e gate bias passes )40 V – indicating that the
Fermi level has crossed the bulk valence band edge.
29
Angle)resolved photoemission
spectroscopy (Fig. 3c) is used to map the band stru
cture of (Bi
1)x
Sb
x
)
2
Te
3
in this region. We note
that these photoemission spectroscopy results only
approximate the band structure in our
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transferred films, which will vary due to modified
doping. The total carrier density in the film at
zero bias, n
2D
= 2.5G10
13
cm
)2
, is obtained from Hall measurements.
From transport measurements, we conclude that unbia
sed (Bi
1)x
Sb
x
)
2
Te
3
films are hole)
doped, with a Fermi level position slightly below t
he bulk valence band edge. The modulation of
sheet resistance seen with gating indicates that th
e Fermi level of the entire film is modified by
the gate. However, band bending is expected and th
e effect of gating is thus stronger near the
oxide interface, as shown in Fig. 4.
8, 23
We estimate the screening length in the (Bi
1)x
Sb
x
)
2
Te
3
film to be of order 10 nm, as is discussed in the S
upporting Information. The observed
modulation further suggests that electrostatic gati
ng is forcing the film between regimes where
topological surface carriers and bulk carriers are
expected to dominate the conductivity,
respectively. The R
sh
on)off ratio is much lower than that seen in films
of other layered materials
with a similar thickness and band gap, such as blac
k phosphorus, consistent with the presence of
a conductive topological surface state that shorts
the insulating ‘off’ state of the field effect
device.
30
Given the identified Fermi level position of the fi
lm, we suggest that feature A in the
optical response at higher photon energies is drive
n by gate)modulation of interband transitions
via population of bulk valence band states with hol
es. As shown in Fig. 2c, a doped
semiconductor has a characteristic effective bandga
p defined – for hole)doped samples – by the
distance from the Fermi level to the conduction ban
d. In the (Bi
1)x
Sb
x
)
2
Te
3
system investigated
here, this Fermi level shifts with V
g
, altering the allowed and forbidden optical transi
tions and
hence its band edge optical constants. Similar beh
avior is seen for electrostatic doping in
graphene, and for chemical doping in narrow)band)ga
p semiconductor materials, in which it is
known as the Burstein)Moss effect.
24, 31)33
This behavior is seen only in thin films of mater
ials
with a low density of states, and indicates possibl
e technological applications for narrow)gap TI
materials as optoelectronic modulators. The observ
ed modulation persists at room temperature,
albeit with a lower strength. At a temperature of
5 K, as discussed in the Supporting
Information, the band)edge modulation is stronger a
nd sharper – indicative of a narrower Fermi
distribution – and an additional feature appears.
The resulting change in the optical band gap can
be approximated as follows, where H(E
BVB
) E
F
, T) is a Heaviside step)function with a
temperature)dependent broadening that accounts for
the width of the Fermi)Dirac distribution.
34
∆
= 2∆
−
−
,
1
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We propose that feature B in the optical response a
t lower photon energies is
characterized by a change in the intraband absorpti
on associated with both topological surface
states and bulk states. While depressing the Fermi
level into the bulk valence band will decrease
the band)edge interband transition rate – increasin
g transmittance near the band edge – it
simultaneously transfers spectral weight to intraba
nd channels, increasing absorption and
decreasing transmittance at lower energies. We sug
gest that the physical mechanism of this
change in intraband absorption is the modulation of
carrier density in the film – by as much as 27
percent – via electrostatics. This behavior indica
tes the possibility of extending the tunable, mid)
infrared Dirac plasmons seen in graphene to spin)po
larized topological insulator materials.
10, 35, 36
This conjecture is supported by our transport data,
which indicates that the Fermi level is shifting
back and forth across the bulk valence band edge, b
ut transmittance can also be modeled directly
using measured values and one free fitting paramete
r. A simple picture of the modulated bulk
interband absorption is provided by experimental me
asurements of the band edge dielectric
function, which was determined from infrared ellips
ometry measurements of an as)grown (Bi
1)
x
Sb
x
)
2
Te
3
film on sapphire. The change in the band edge diel
ectric function energy as a function
of gate voltage, is modeled by shifting the zero)bi
as dielectric function by an energy LE
S
,
proportional to the corresponding voltage, such tha
t the dielectric function as a function of gate
voltage can be described by a single free parameter
.
To model the optical response at small negative Fer
mi level positions, the topological
surface state and bulk carrier densities are first
parameterized as a function of gate voltage.
From our fit of the absorption)edge energy shifts,
a gate voltage of V
g
= +/)45V corresponds to a
shift of the Fermi level of approximately 28 meV.
The observed metal)insulator transition
occurs at V
g
≈ 40V, so the Fermi level at zero bias must be at
approximately (28 meV G 40 V /
45V) = 25 meV below the bulk valence band edge. Th
e bulk valence band is observed to be 150
meV below the Dirac point in angle)resolved photoem
ission measurements, indicating a Fermi
level of E
F
= )175 meV relative to the Dirac point.
17
The topological surface state carrier density
can be calculated from this Fermi level by assuming
the electronic structure is characterized by
the well)known topological surface state dispersion
relation.
17, 37
We find that
n
TSS
=k
F
2
4π
⁄
=
4G10
12
cm
)2
for each surface, where
=
ℏ
⁄
. Including both surfaces, our topological
surface state density / bulk carrier density ratio
is found to be approximately
n
2D,TSS
/
n
2D
= 30%.
As our films are deeply subwavelength in thickness,
we model the (Bi
1)x
Sb
x
)
2
Te
3
film as having
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a single effective dielectric function that include
s contributions from both of these types of
carriers, as well as interband absorption, as discu
ssed above. The intraband dielectric functions
for the topological surface state and bulk free car
riers were treated using Kubo and Drude
models, respectively.
38, 39
=
!"#$% &
,
,
+
!#%$% &, ())
*,+
,-,())
. +
!#%$% &, $/01
*,+
,-,$/01
.
=
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,
,
−
2
,
3ℏ4 +
5
6
7
4
+
,-,())
28
7
9
,
:
−
2
,
+
,-,$/01
3; 4 +
5
6
7
2
This dielectric function model is combined with a s
imple capacitor model that defines the
change in carrier concentration with gate voltage –
up to 27 percent at 90 V. The charge on each
plate is given by Q = V
g
C, where the capacitance C is calculated to be 12 n
F/cm
2
for the 285 nm
SiO
2
using a standard parallel plate geometry.
40
Combining these elements, we use the transfer
matrix method to calculate transmittance (Fig. 2d)
through the (Bi
1)x
Sb
x
)
2
Te
3
film and substrate
stack.
41
The modeled values for LT/T – based on experiment
al parameters and a single fitting
parameter – yield a close match to our experimental
results.
We note that band bending, as described in Fig. 4,
adds an additional degree of
complexity to this system, and that as the screenin
g length in the films is similar to their
thickness, transport and optical measurements will
not respond identically to gating.
8, 23, 42
Due
to these differences and any variation in band stru
cture between our samples and those
investigated by Zhang, et al., we present the above
analysis as an approximate model intended to
demonstrate qualitative agreement between our exper
imental results and our description of the
physical basis.
17
We further note two smaller features seen in FTIR
spectra. In Fig. 2a,b a small
dip in transmittance and reflectance modulation is
seen near 8 microns, which we attribute to
absorption in the silicon oxide due to the presence
of a phonon line. In Fig. 2b, a small peak in
transmittance modulation is seen near 3.8 microns.
We speculate that this peak may be due to a
defect state or subband, and add that it persists i
n room temperature measurements and is thus
unlikely to be excitonic in nature.
12, 43)45
Lastly, we acknowledge that interband transitions
between topological surface state bands should fall
within the energy range of our measurements.
We see no clear evidence of these transitions, whic
h are discussed further in the Supporting
Information.
In conclusion, we have experimentally investigated
the mid)infrared optical response of
(Bi
1)x
Sb
x
)
2
Te
3
films as the Fermi level position is varied by ele
ctrostatic gating. This response is
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characterized by a gate)driven transfer of spectral
weight between both bulk and 2D topological
surface channels and interband and intraband channe
ls. We associate the higher photon energy
behavior with Pauli)blocking of bulk interband opti
cal transitions, and the lower energy behavior
with modulation of the plasma edge with varying top
ological surface and bulk carrier densities.
These results present layered topological insulator
materials as a new candidate material for
ultrathin, tunable infrared photonics and illustrat
e the possibilities for switching topological
optoelectronic phenomena – tunable, mid)infrared Di
rac plasmons, hybrid spin)plasmons and
more – between bulk and spin)polarized surface regi
mes.
Methods:
Sample Preparation.
The 20 nm (Bi
1)x
Sb
x
)
2
Te
3
films are grown by molecular beam epitaxy on
heat)treated 500 Rm)thick SrTiO
3
(111) substrates, as previously reported.
17
A mixing ratio of
x=0.94 is used for this work. Epitaxial lift)off w
as used to transfer these films to thermal
oxidized silicon substrates, as described in the Su
pporting Information. Electron)beam
lithography (EBPG 5000+) and reactive ion etching (
SF
6
) are used to pattern the film into
electrically isolated squares, and Cr/Au contacts (
5 nm / 150 nm) are deposited via thermal
evaporation to allow gating and Van der Pauw transp
ort measurements.
Infrared Spectroscopy.
Infrared spectroscopy measurements are performed wi
th a Nicolet iS50
FTIR coupled to a Continuum microscope with a 50 Rm
spot size. Samples are wire)bonded and
mounted in a Linkam vacuum stage for temperature co
ntrol at 78 K and 300 K. The band)edge
optical constants of the (Bi
1)x
Sb
x
)
2
Te
3
are extracted with a J.A. Woollam IR)VASE infrared
ellipsometry system.
Transport.
Sheet resistance is measured using the Van der Pauw
method and a Janis ST)400
liquid helium cryostat for temperature control from
4.2 to 300 K. Carrier densities are measured
in an MMR Technologies Hall system.
Supporting Information:
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Supporting Information Available: Epitaxial lift)of
f methodology; 4K FTIR transmittance; room
temperature transmittance and reflectance; Thomas)F
ermi model of screening. This material is
available free of charge via the Internet at
http://pubs.acs.org
.
Acknowledgements:
The authors gratefully acknowledge support from the
Department of Energy, Office of Science
under Grant DE)FG02)07ER46405 and for facilities of
the DOE “Light)Material Interactions in
Energy Conversion” Energy Frontier Research Center
(DE)SC0001293). W.S.W. also
acknowledges support from an NDSEG Graduate Researc
h Fellowship. A.R.D acknowledges
fellowship support from the Resnick Institute and t
he Kavli Nanoscience Institute at Caltech. The
authors are grateful to Prof. George Rossman for he
lpful discussions and use of his FTIR
facilities.
Author Contributions:
W.S.W., V.W.B and H.A.A. conceived the ideas. Y.O.
grew the films and W.S.W. fabricated
the devices. W.S.W, Y.S. and Y.O. performed measure
ments. W.S.W and A.R.D calculated the
optical model. All authors contributed to writing
the paper. D.N.B, K.H., Q.K.X., and H.A.A.
supervised the project.
Notes:
The authors declare no competing financial interest
s.
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References:
1. Hasan, M. Z.; Kane, C. L.
Rev. Mod. Phys.
2010,
82, (4), 3045)3067.
2. Qi, X.)L.; Zhang, S.)C.
Rev. Mod. Phys.
2011,
83, (4), 1057)1110.
3. Chang, C.)Z.; Zhang, J.; Feng, X.; Shen, J.; Zha
ng, Z.; Guo, M.; Li, K.; Ou, Y.; Wei, P.;
Wang, L.)L.; Ji, Z.)Q.; Feng, Y.; Ji, S.; Chen, X.;
Jia, J.; Dai, X.; Fang, Z.; Zhang, S.)C.; He, K.;
Wang, Y.; Lu, L.; Ma, X.)C.; Xue, Q.)K.
Science
2013,
340, (6129), 167)170.
4. Pesin, D.; MacDonald, A. H.
Nat. Mater.
2012,
11, (5), 409)416.
5. Valdés Aguilar, R.; Stier, A. V.; Liu, W.; Bilbr
o, L. S.; George, D. K.; Bansal, N.; Wu,
L.; Cerne, J.; Markelz, A. G.; Oh, S.; Armitage, N.
P.
Phys. Rev. Lett.
2012,
108, (8), 087403.
6. McIver, J. W.; Hsieh, D.; Steinberg, H.; Jarillo
Herrero, P.; Gedik N.
Nat. Nanotechnol.
2012,
7, (2), 96)100.
7. Di Pietro, P.; Ortolani, M.; Limaj, O.; Di Gaspa
re, A.; Giliberti, V.; Giorgianni, F.;
Brahlek, M.; Bansal, N.; Koirala, N.; Oh, S.; Calva
ni, P.; Lupi, S.
Nat. Nanotechnol.
2013,
8, (8),
556)60.
8. Low, T.; Roldán, R.; Wang, H.; Xia, F.; Avouris,
P.; Moreno, L. M.; Guinea, F.
Phys.
Rev. Lett.
2014,
113, (10), 106802.
9. Lindner, N. H.; Farrell, A.; Lustig, E.; Refael,
G.; von Oppen, F., Lighting up topological
insulators: large surface photocurrents from magnet
ic superlattices. In
ArXiv e-prints
, 2014; Vol.
1403.
10. Raghu, S.; Chung, S. B.; Qi, X. L.; Zhang, S. C
.
Phys. Rev. Lett.
2010,
104, (11), 116401.
11. Jenkins, G. S.; Schmadel, D. C.; Sushkov, A. B.
; Drew, H. D.; Bichler, M.; Koblmueller,
G.; Brahlek, M.; Bansal, N.; Oh, S.
Phys. Rev. B
2013,
87, (15), 155126.
12. Post, K. W.; Chapler, B. C.; Liu, M. K.; Wu, J.
S.; Stinson, H. T.; Goldflam, M. D.;
Richardella, A. R.; Lee, J. S.; Reijnders, A. A.; B
urch, K. S.; Fogler, M. M.; Samarth, N.; Basov,
D. N.
Phys. Rev. Lett.
2015,
115, (11), 116804.
13. Wu, J.)S.; Basov, D. N.; Fogler, M. M.
Phys. Rev. B
2015,
92, (20), 205430.
14. Song, J. C. W.; Rudner, M. S.
Proc. Natl. Acad. Sci. U.S.A.
2016,
113, (17), 4658)4663.
15. Reijnders, A. A.; Tian, Y.; Sandilands, L. J.;
Pohl, G.; Kivlichan, I. D.; Zhao, S. Y. F.;
Jia, S.; Charles, M. E.; Cava, R. J.; Alidoust, N.;
Xu, S.; Neupane, M.; Hasan, M. Z.; Wang, X.;
Cheong, S. W.; Burch, K. S.
Phys. Rev. B
2014,
89, (7), 075138.
16. Jenkins, G. S.; Sushkov, A. B.; Schmadel, D. C.
; Butch, N. P.; Syers, P.; Paglione, J.;
Drew, H. D.
Phys. Rev. B
2010,
82, (12), 125120.
17. Zhang, J.; Chang, C. Z.; Zhang, Z.; Wen, J.; Fe
ng, X.; Li, K.; Liu, M.; He, K.; Wang, L.;
Chen, X.; Xue, Q. K.; Ma, X.; Wang, Y.
Nat. Commun.
2011,
2, 574.
18. Kong, D.; Cui, Y.
Nat. Chem.
2011,
3, (11), 845)849.
19. Grigorenko, A. N.; Polini, M.; Novoselov, K. S.
Nature Photon.
2012,
6, (11), 749)758.
20. Boltasseva, A.; Atwater, H. A.
Science
2011,
331, (6015), 290)291.
21. Low, T.; Rodin, A. S.; Carvalho, A.; Jiang, Y.;
Wang, H.; Xia, F.; Castro Neto, A. H.
Phys. Rev. B
2014,
90, (7), 075434.
22. Sun, Z.; Martinez, A.; Wang, F.
Nature Photon.
2016,
10, (4), 227)238.
23. Brahlek, M.; Koirala, N.; Bansal, N.; Oh, S.
Solid State Commun.
2015,
215–216, 54)62.
24. Burstein, E.
Phys. Rev.
1954,
93, (3), 632)633.
25. Bansal, N.; Cho, M. R.; Brahlek, M.; Koirala, N
.; Horibe, Y.; Chen, J.; Wu, W.; Park, Y.
D.; Oh, S.
Nano Lett.
2014,
14, (3), 1343)8.
26. Yang, F.; Taskin, A. A.; Sasaki, S.; Segawa, K.
; Ohno, Y.; Matsumoto, K.; Ando, Y.
ACS
Nano
2015,
9, (4), 4050)4055.
Page 9 of 15
ACS Paragon Plus Environment
Nano Letters
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
10
27. Chen, J.; Qin, H. J.; Yang, F.; Liu, J.; Guan,
T.; Qu, F. M.; Zhang, G. H.; Shi, J. R.; Xie,
X. C.; Yang, C. L.; Wu, K. H.; Li, Y. Q.; Lu, L.
Phys. Rev. Lett.
2010,
105, (17), 176602.
28. Zhang, W.; Yu, R.; Zhang, H.)J.; Dai, X.; Fang,
Z.
New J. Phys.
2010,
12, (6), 065013.
29. Rosenbaum, T. F.; Milligan, R. F.; Paalanen, M.
A.; Thomas, G. A.; Bhatt, R. N.; Lin, W.
Phys. Rev. B
1983,
27, (12), 7509)7523.
30. Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu,
H.; Feng, D.; Chen, X. H.; Zhang, Y.
Nat.
Nanotechnol.
2014,
9, (5), 372)377.
31. Li, Z. Q.; Henriksen, E. A.; Jiang, Z.; Hao, Z.
; Martin, M. C.; Kim, P.; Stormer, H. L.;
Basov, D. N.
Nat. Phys.
2008,
4, (7), 532)535.
32. Moss, T. S.
Proc. Phys. Soc. London, Sect. B
1954,
67, (10), 775.
33. Mak, K. F.; Ju, L.; Wang, F.; Heinz, T. F.
Solid State Commun.
2012,
152, (15), 1341)
1349.
34. Lin, C.; Grassi, R.; Low, T.; Helmy, A. S.
Nano Lett.
2016,
16, (3), 1683)1689.
35. Brar, V. W.; Jang, M. S.; Sherrott, M.; Lopez,
J. J.; Atwater, H. A.
Nano Lett.
2013,
13,
(6), 2541)2547.
36. Fei, Z.; Rodin, A. S.; Andreev, G. O.; Bao, W.;
McLeod, A. S.; Wagner, M.; Zhang, L.
M.; Zhao, Z.; Thiemens, M.; Dominguez, G.; Fogler,
M. M.; Neto, A. H. C.; Lau, C. N.;
Keilmann, F.; Basov, D. N.
Nature
2012,
487, (7405), 82)85.
37. Chen, Y. L.; Analytis, J. G.; Chu, J.)H.; Liu,
Z. K.; Mo, S.)K.; Qi, X. L.; Zhang, H. J.;
Lu, D. H.; Dai, X.; Fang, Z.; Zhang, S. C.; Fisher,
I. R.; Hussain, Z.; Shen, Z.)X.
Science
2009,
325, (5937), 178)181.
38. Falkovsky, L. A.
J. Phys.: Conf. Ser.
2008,
129, 012004.
39. Kittel, C.,
Introduction to Solid State Physics
. Wiley: 2004.
40. Schwierz, F.
Nat. Nanotechnol.
2010,
5, (7), 487)496.
41. Yeh, P.,
Optical Waves in Layered Media
. Wiley: 2005.
42. Fatemi, V.; Hunt, B.; Steinberg, H.; Eltinge, S
. L.; Mahmood, F.; Butch, N. P.;
Watanabe, K.; Taniguchi, T.; Gedik, N.; Ashoori, R.
C.; Jarillo)Herrero, P.
Phys. Rev. Lett.
2014,
113, (20), 206801.
43. Mak, K. F.; Shan, J.
Nature Photon.
2016,
10, (4), 216)226.
44. Seibel, C.; Bentmann, H.; Braun, J.; Minár, J.;
Maaß, H.; Sakamoto, K.; Arita, M.;
Shimada, K.; Ebert, H.; Reinert, F.
Phys. Rev. Lett.
2015,
114, (6), 066802.
45. Rönnlund, B.; Beckman, O.; Levy, H.
J. Phys. Chem. Solids
1965,
26, (8), 1281)1286.
46. Li, Z.; Carbotte, J. P.
Phys. Rev. B
2013,
87, (15), 155416.
Page 10 of 15
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Figure 1
: Schematic of experiment.
(a)
Schematic of setup. The sample structure consists
of a
10 nm a)Te layer atop a 20 nm (Bi
1)x
Sb
x
)
2
Te
3
(BST) film on 285 nm thermal oxide on silicon.
The metallic topological surface states in the BST
penetrate 1)2 nm into the insulating bulk. The
transmittance and reflectance of this stack are pro
bed by an FTIR spectrometer coupled to an
infrared microscope as the gate voltage is modulate
d. Inset: AFM cross)cut of transferred film,
showing 30 nm total height of a)Te and BST.
(b)
Schematic of observed behavior. The optical
response of the BST consists of contributions from
bulk and topological surface carriers.
46
With
changing gate voltage, spectral weight is transferr
ed between both bulk (blue) and topological
surface (green) channels and between interband (uns
haded region) and intraband (shaded region)
channels, as indicated by the arrow. Inset: Schema
tic band structure of BST, with bulk valence
and conduction bands, topological surface states an
d 0.3 eV band gap indicated.
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