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Aharonov-Bohm oscillations and weak antilocalization in topologicalinsulator Sb2Te3 nanowiresBacel Hamdou, Johannes Gooth, August Dorn, Eckhard Pippel, and Kornelius Nielsch Citation: Appl. Phys. Lett. 102, 223110 (2013); doi: 10.1063/1.4809826 View online: http://dx.doi.org/10.1063/1.4809826 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v102/i22 Published by the American Institute of Physics. Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors
Aharonov-Bohm oscillations and weak antilocalization in topologicalinsulator Sb2Te3 nanowires
Bacel Hamdou,1,a) Johannes Gooth,1 August Dorn,1 Eckhard Pippel,2
and Kornelius Nielsch1,b)
1Institute of Applied Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany2Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany
(Received 27 March 2013; accepted 23 May 2013; published online 6 June 2013)
Recently, it has been theoretically predicted that Sb2Te3 and related materials are 3D topological
insulators, a phase of matter that has a bulk bandgap and gapless electronic surface states protected
by time-reversal symmetry. We report on low temperature magnetoresistance measurements on
single crystalline Sb2Te3 nanowires with different cross sectional areas and high surface-to-volume
ratios, synthesized via catalytic growth. The observation of Aharonov-Bohm oscillations and weak
antilocalization indicates the presence of topological surface states. VC 2013 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4809826]
Topological insulators (TIs) represent a new state of
quantum matter with a bulk band gap and gapless surface
states that are protected against backscattering by time-
reversal symmetry induced by strong spin-orbit coupling.1
Theoretical predictions of materials such as Bi2Se3, Bi2Te3,
and Sb2Te3 being TIs1,2 have been experimentally confirmed
by angle resolved photoemission spectroscopy (ARPES)
measurements.2–4 Up to now, it has been difficult to observe
surface states in TIs via electronic transport measurements
because of the dominant bulk contribution to conductivity
arising from unintentional doping and the small bulk band
gaps typical for TI materials. However, low-dimensional sol-
ids such as nanowires (NWs) are expected to significantly
enhance the contribution of surface states to electrical trans-
port due to their large surface-to-volume ratios. Recently,
Aharonov-Bohm (AB) oscillations have been observed in
single crystalline Bi2Te3, Bi2Se3 nanoribbons, and b-Ag2Te3
NWs,5–7 which suggest the presence of topological surface
states. Furthermore, weak antilocalization (WAL) is an indi-
cation for strong spin-orbit coupling, which is a prerequisite
for the existence of topological surface states. By these
means, evidence for surface states in Bi2Se2Te crystals,8
Bi2Se3 and Sb2Te3 thin films,9,10 and Bi2Te3 microflakes11
has been found. Aharonov-Bohm oscillations and WAL have
not been observed in Sb2Te3 NWs so far. According to
Hsieh et al.,4 surface states are not favored in Sb2Te3
because the Fermi level is located in the valence band due to
a high level of intrinsic doping.
We report on magnetoresistance measurements on single
crystalline Sb2Te3 NWs at low temperatures, where the mag-
netic field is oriented parallel to the NW axis. The Sb2Te3
NWs were synthesized via catalytic growth in a single-heater
zone tube furnace (MTI, Inc., USA/OTF-1200X-25). Inside a
1 in. diameter quartz tube 3 mg of the source materials, Sb and
Te powder (99.999% purity) were thermally evaporated at
430 �C and 280 �C, respectively, at a heating rate of 16 �C min–1.
The growth substrate (Si with native oxide, covered with
30 nm gold nanoparticles purchased from Ted Pella, which
serve as catalysts for the growth of NWs) was located in a
temperature region of T � 390–400 �C. At a base pressure of
10 Torr, a constant flow of Ar carrier gas (80 sccm) was used
to transport the precursor vapors to the substrate where wire
growth took place.12 Before synthesis, the charged furnace
was evacuated to below 10 Torr and flushed several times
with Ar gas to obtain an inert atmosphere. After a reaction
time of 4 h, the heating power was switched off. Under con-
stant Ar flow and pressure, the furnace was returned to room
temperature by natural cooling.
The dimensions of the NWs were determined by atomic
force microscopy (AFM) and scanning electron microscopy
(SEM). Figures 1(c) and 1(d) show typical SEM images
of the as-grown Sb2Te3 NWs. The morphology of the NWs
is either cylindrical or rectangular with thicknesses of
52–135 nm, widths of 46–435 nm, and lengths of up to
15 lm. The presence of a gold nanoparticle at the top of each
NW is consistent with a catalytic unidirectional growth pro-
cess. High resolution transmission electron microscopy
(HRTEM) analysis reveals the single-crystallinity and a
growth direction along the [110] direction, perpendicular to
the c-axis. The surface is smooth to within a few atomic
layers and there is no indication of a native oxide layer.
TEM based energy dispersive X-ray spectroscopy (EDX)
shows a uniform chemical composition across the diameter
of the NW of Sb4261Te5861, which confirms the desired
Sb:Te¼ 2:3 phase (shown in Fig. 1(b)). Further, the EDX
results show that contrary to as-grown bismuth telluride
NWs recently synthesized via catalytic growth in the same
tube furnace,13 Sb2Te3 NWs exhibit no tellurium depletion
near the NW surface. The as-grown NWs were mechanically
transferred onto Si substrates with 300 nm SiO2. Electrical
contacts for current injection and voltage detection across
the NWs were defined using a laser-lithography system
(Heidelberg Instruments lPG 101). In order to remove any
photoresist residues or surface oxide, in-situ sputter etching
with Ar was used prior to the sputter-deposition of Ti (5 nm)
and Pt (80 nm), followed by a lift-off process. A typical de-
vice used for electrical measurements is shown in Fig. 1(e).
a)[email protected])[email protected]
0003-6951/2013/102(22)/223110/4/$30.00 VC 2013 AIP Publishing LLC102, 223110-1
APPLIED PHYSICS LETTERS 102, 223110 (2013)
By comparing two-terminal and four-terminal measurements
on our Sb2Te3 NWs, contact resistances were found to be
negligible. Thus, the modulations on top of the magnetore-
sistance curves result exclusively from the Sb2Te3 NWs. The
linear IV-curves confirm that the electrodes form Ohmic
contacts to the NWs over the whole temperature range,
which is shown in Fig. 2(a). All electrical measurements
were performed in a variable temperature cryostat system
(Quantum Design PPMS) with a base temperature of 2 K
in helium atmosphere, equipped with a 9 T magnet. The re-
sistance of the NWs was determined by standard lock-in
techniques.
We studied the transport properties of three individual
Sb2Te3 NWs with different rectangular cross sectional areas
of NW 1: 82� 52 nm, NW 2: 92� 63 nm, and NW 3:
133� 75 nm. The resistivity at T¼ 300 K for the three meas-
ured NWs is q¼ (1.15 6 0.07) � 10�5 Xm on average. This
value is considerably higher than the previously reported
resistivities for single crystalline Sb2Te3 NWs14 grown under
similar conditions,12 which are comparable to the bulk val-
ues for Sb2Te3 of q¼ 0.25� 10�5 Xm (Ref. 15) and
q¼ 0.21� 10�5 Xm.16 Minor differences in growth condi-
tions such as the gold colloid size, the amount of elemental
powders, and growth temperature therefore appear to have a
strong influence on the electronic properties of the resulting
NWs. Fig. 2(a) shows a typical resistance versus temperature
curve at zero magnetic field. In the temperature range of
5–300 K, the resistance decreases with decreasing tempera-
ture, indicating a metallic behaviour, in which inelastic pho-
non scattering dominates.5,6,13 Below around 30 K, the slope
changes noticeably until the resistance saturates at around
5 K, presumably due to the absence of inelastic phonon scat-
tering,6 so that transport is dominated by impurity scattering
of the charge carriers.17
The results of the magnetoresistance measurements are
presented in Figs. 2(b) and 2(c), exhibiting two dominant
features. Around B¼ 0 T, a sharp dip occurs, and for higher
fields up to 69 T, oscillations can be clearly seen, which are
periodic with magnetic field. Both features, the low magnetic
FIG. 1. Material characterization and device. (a) High resolution TEM
image of a Sb2Te3 NW. The inset shows the corresponding selected area
electron diffraction (SAED) pattern. The chemical composition (b) was
measured across the NW’s cross-section, using EDX spectroscopy. The inset
shows a high-angle annular dark-field scanning transmission electron mi-
croscopy (HAADF-STEM) image of the NW, indicating the EDX line-scan.
The SEM images (c) and (d) show typical transferred NWs with cylindrical
(c) and rectangular (d) cross section, respectively. (c) SEM image of a typi-
cal micro device including two electrical contacts for current injection and
two for voltage detection across the NW.
FIG. 2. Temperature dependent resistance
and magnetoresistance. (a) Resistance
versus temperature of NW 1 at zero mag-
netic field in the range of 2–300 K. The
insets show linear IV-curves at different
temperatures, indicating Ohmic contacts
and the saturating resistance in the low
temperature range, respectively. (b)
Resistance versus parallel magnetic field
at four different temperatures. The AB
oscillations are damped with increasing
temperature. (c) Resistance versus parallel
magnetic field for the three measured
NWs with different cross sectional areas
at 2 K and (d) AB oscillations and the
related index plots after subtraction of the
smooth background.
223110-2 Hamdou et al. Appl. Phys. Lett. 102, 223110 (2013)
field resistance dip and the oscillations, are symmetric
around zero field and smear out with increasing temperature.
In Figure 2(d), the magnetic field position of resistance min-
ima versus index n and the related magnetoresistance after
subtracting the smooth background are plotted for the three
measured NWs. The index plots show a high degree of line-
arity, indicating that the oscillation period remains constant
up to 69 T. We assume that these oscillations arise from the
Aharonov-Bohm effect,18 which is a consequence of quan-
tum interference when charge carriers encircle closed trajec-
tories. For NWs, such AB oscillations are predicted when
charge carriers retain phase coherence around the perimeter
of the NW and therefore enclose a magnetic flux U0¼ h/e,
where h is Planck’s constant and e is the unit charge.5–7 The
enclosed area A is associated with the period of DB¼U0/A.
The corresponding areas from the AB oscillation periods
(NW 1: (4.22 6 0.04) � 10�15 m2, NW 2: (5.97 6 0.07)
� 10�15 m2, and NW 3: (10.05 6 0.06) � 10�15 m2) are in
excellent agreement with the measured cross-sectional
areas of the NWs (NW 1: (4.26 6 0.36) � 10�15 m2, NW 2:
(5.80 6 0.42) � 10�15 m2, and NW 3: (9.98 6 0.76)
� 10�15 m2) to within measurement accuracy and therefore
indicate the presence of surface states. The AB oscillations,
which are pronounced at 2 K, are damped with increasing
temperature and vanish between 4 K and 6 K, as seen in Fig.
2(b). Thermo-cycling indicates that the samples are highly
robust. Even after three cycles, the AB oscillation period
remains the same (1 cycle � heating up to 300 K and cooling
down to 2 K). Furthermore, note that the surface states travel
along different interfaces (TI-vacuum, TI-substrate) on their
paths around the NWs. The AB oscillations are superim-
posed on a slowly varying background, as is clearly seen in
Figs. 2(b)–2(d). These background features in the magneto-
resistance could result from bulk states, Universal
Conductance Fluctuations (UCFs) or from the Shubnikov-
de-Haas (SdH) effect.19,20 In a simple two band model, the
magnetoresistance shows a parabolic increase for small mag-
netic fields.12 This behaviour has been observed in Sb2Te3
NWs, Sb2Te3 crystals and bulk Sb2Te3 for low magnetic
fields.12,21–23 Comparing the magnetoresistance background
of the three measured NWs (Fig. 2(c)) indicates a suppres-
sion of the parabolic bulk contribution for higher surface-to-
volume ratios (as seen for NW1 and NW2), thus the AB
oscillations are more pronounced.
The sharp dip in the magnetoresistance around B¼ 0 T
is attributed to the weak antilocalization effect, which is con-
sistent with the presence of strong spin-orbit coupling
reported in Sb2Te3 thin films, arising from TI surface
states.10 WAL is suppressed when time-reversal symmetry is
broken by a magnetic field. This leads to a correction factor
Dr to the conductivity, which can be described in the 2
dimensional case by the Hikami-Larkin-Nagaoka formula24
DrðBÞ ¼ ae2
p hw
�h
4eBLU2þ 1
2
� �� ln
�h
4eBLU2
� �� �; (1)
where w(x) is the digamma function and LU is the phase co-
herence length. The prefactor a results in the following val-
ues: a¼ 0 when magnetic scattering is strong, a¼ 1 when
spin-orbit interaction and magnetic scattering is weak or
absent, a¼�1/2 when spin-orbit interaction is strong and
there is no magnetic scattering.24 Since the surface states are
attributed to strong spin-orbit coupling and to a higher
charge carrier mobility as compared to bulk, one can classify
a single surface conducting channel by a¼�1/2.9–11,25–27
Usually, the prefactor a covers a wide range in experiments,
because the observed WAL is a collective result from both
the WAL of the surface channels and WL of the bulk chan-
nels.25 Therefore, a clear separation of bulk and surface con-
tribution to the prefactor a is difficult.
The WAL effect in the three measured NWs is analysed
by fitting the low-field magnetoconductivity with the
Hikami-Larkin-Nagaoka formula. However, it should be
noted that the geometry of a NW with surface states, corre-
sponding to a curved 2 dimensional electron system, differs
from a planar 2 dimensional system. The resulting prefactor
a of NW 1 (a¼�0.49) and NW 2 (a¼�0.49) support our
hypothesis of surface state dominated transport in these
NWs. Whereas for NW 3 with the lowest surface-to-volume
ratio a¼�0.42 slightly differs from �1/2, suggesting a
minor bulk contribution, which is consistent with the results
of the AB analyses. The extracted temperature dependence
of LU is plotted in Figure 3 for NW 1. The coherence length
LU increases from 77 nm to 413 nm as T is reduced from
20 K to 2 K. Indicated by the solid line in Fig. 3, LU is pro-
portional to T�1/2, which is expected for a 2-dimensional
electron system.10,28 Comparing LU with the perimeter of
NW 1 (u¼ 268 nm), it can be seen that between 4 K and 6 K
LU is in the range of the NW’s perimeter. In this temperature
range, the AB oscillations occur in the magnetoresistance
(Fig. 2(b)), which suggests the beginning of charge carrier
coherence around the NW’s perimeter. Similar behaviour
was observed for NW 2, whereas LU for NW 3 at 2 K is
approximately 16% lower than its perimeter, presumably due
to bulk contribution. The results of the Hikami-Larkin-
Nagaoka model are consistent with the AB analyses for NW
1 and NW 2 which also have high surface-to-volume ratios.
In summary, single crystalline Sb2Te3 NWs with high
surface-to-volume ratios were synthesized via catalytic
growth. Magnetoresistance measurements with the magnetic
field parallel to the NW axis were performed at temperatures
FIG. 3. Weak antilocalization analysis. Estimated phase coherence length
LU of NW 1 versus temperature. The solid line indicates a temperature de-
pendence of LU / T�1/2. The inset shows the conductance versus parallel
magnetic field of NW 1 at 2 K (open triangles) and 4 K (open circles) and
the related fits to Eq. (1).
223110-3 Hamdou et al. Appl. Phys. Lett. 102, 223110 (2013)
down to 2 K for three Sb2Te3 NWs. Periodic Aharonov-
Bohm oscillations in magnetoresistance up to 69 T were
observed. Areas extracted from the AB oscillations are in
excellent agreement with the geometrical cross sectional
areas of the respective NWs. The sharp dip in magnetoresist-
ance around zero magnetic field can be attributed to weak
antilocalization and is consistent with strong spin-orbit cou-
pling. These findings indicate the presence of topological
surface states. Interestingly, WAL and AB oscillations were
most pronounced in NWs with small cross-sectional areas,
which is consistent with the idea that the bulk contribution to
conductivity is strongly suppressed for large surface-to-vol-
ume ratios. This work provides a promising starting point for
further investigation of surface states in topological insulator
Sb2Te3 NWs.
This work was supported by the German science foun-
dation (DFG) via the German priority program SPP 1386,
“Nanostructured Thermoelectrics” as well as within the
Graduiertenkolleg 1286 “Functional Metal-Semiconductor
Hybrid Systems.” We thank L. Akinsinde, J. Kimling, and R.
Meißner for technical support.
1H. Zhang, C.-X. Liu, X.-L. Qi, Z. Fang, and S.-C. Zhang, Nat. Phys. 5,
438 (2009).2Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer,
Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nat. Phys. 5, 398 (2009).3Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J.
Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain,
and Z.-X. Shen, Science 325, 178 (2009).4D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L.
Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D.
Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature 460, 1101 (2009).5F. Xiu, L. He, Y. Wang, L. Cheng, L.-T. Chang, M. Lang, G. Huang, X.
Kou, Y. Zhou, X. Jiang, Z. Chen, J. Zou, A. Shailos, and K. L. Wang, Nat.
Nanotechnol. 6, 216 (2011).
6H. Peng, K. Lai, D. Kong, S. Meister, Y. Chen, X.-L. Qi, S.-C. Zhang,
Z.-X. Shen, and Y. Cui, Nature Mater. 9, 225 (2010).7S. Lee, J. In, Y. Yoo, Y. Jo, Y. C. Park, H.-J. Kim, H. C. Koo, J. Kim, B.
Kim, and K. L. Wang, Nano Lett. 12, 4194 (2012).8L. Bao, L. He, N. Meyer, X. Kou, P. Zhang, Z.-G. Chen, A. V. Fedorov, J.
Zou, T. M. Riedemann, T. A. Lograsso, K. L. Wang, G. Tuttle, and F. Xiu,
Sci. Rep. 2, 726 (2012).9G. Zhang, H. Qin, J. Chen, X. He, L. Lu, Y. Li, and K. Wu, Adv. Funct.
Mater. 21, 2351 (2011).10Y. Takagaki, A. Giussani, K. Perumal, R. Calarco, and K.-J. Friedland,
Phys. Rev. B 86, 125137 (2012).11S.-P. Chiu and J.-J. Lin, Phys. Rev. B 87, 035122 (2013).12J. S. Lee, S. Brittman, D. Yu, and H. Park, J. Am. Chem. Soc. 130, 6252
(2008).13B. Hamdou, J. Kimling, A. Dorn, E. Pippel, R. Rostek, P. Woias, and K.
Nielsch, Adv. Mater. 25, 239 (2013).14Y. M. Zuev, J. S. Lee, C. Galloy, H. Park, and P. Kim, Nano Lett. 10,
3037 (2010).15J. Jiang, L. Chen, S. Bai, Q. Qin Yao, and Q. Wang, J. Cryst. Growth 277,
258 (2005).16J. S. Dyck, P. Hajek, P. Lostak, and C. Uher, Phys. Rev. B 65, 115212 (2002).17E. Conwell and V. F. Weisskopf, Phys. Rev. 77, 388 (1950).18Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).19P. A. Lee and A. D. Stone, Phys. Rev. Lett. 55, 1622 (1985).20T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).21Z. J. Yue, C. B. Zhu, S. X. Dou, and X. L. Wang, Phys. Rev. B 86, 195120
(2012).22V. A. Kulbachinskii, Z. M. Dashevskii, M. Inoue, M. Sasaki, H. Negishi,
W. X. Gao, P. Lostak, J. Horak, and A. de Visser, Phys. Rev. B 52, 10915
(1995).23V. A. Kulbachinskii, A. Yu. Kaminskii, N. Miyajima, M. Sasaki, H.
Negishi, M. Inoue, and H. Kadomatsu, J. Exp. Theor. Phys. Lett. 70, 767
(1999).24S. Hikami, A. I. Larkin, and Y. Nagaoka, Prog. Theor. Phys. 63, 707
(1980).25H.-Z. Lu and S.-Q. Shen, Phys. Rev. B 84, 125138 (2011).26I. Garate and L. Glazman, Phys. Rev. B 86, 035422 (2012).27M. Lang, L. He, X. Kou, P. Upadhyaya, Y. Fan, H. Chu, Y. Jiang, J. H.
Bardarson, W. Jiang, E. S. Choi, Y. Wang, N.-C. Yeh, J. Moore, and K. L.
Wang, Nano Lett. 13, 48 (2013).28B. L. Altshuler, A. G. Aronov, and D. E. Khmelnitsky, J. Phys. C 15, 7367
(1982).
223110-4 Hamdou et al. Appl. Phys. Lett. 102, 223110 (2013)