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)bhamdou@physnet.uni-hamburg.deb)knielsch@physnet.uni-hamburg.de

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.

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