Surface state dominated transport in topological insulator Bi2Te3nanowiresBacel Hamdou, Johannes Gooth, August Dorn, Eckhard Pippel, and Kornelius Nielsch Citation: Appl. Phys. Lett. 103, 193107 (2013); doi: 10.1063/1.4829748 View online: http://dx.doi.org/10.1063/1.4829748 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v103/i19 Published by the AIP Publishing LLC. 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

Surface state dominated transport in topological insulator Bi2Te3 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 19 September 2013; accepted 27 October 2013; published online 6 November 2013)

We report on low temperature magnetoresistance measurements on single-crystalline Bi2Te3

nanowires synthesized via catalytic growth and post-annealing in a Te-rich atmosphere. The

observation of Aharonov-Bohm oscillations indicates the presence of topological surface states.

Analyses of Subnikov-de Haas oscillations in perpendicular magnetoresistance yield extremely low

two-dimensional carrier concentrations and effective electron masses, and very high carrier

mobilities. All our findings are in excellent agreement with theoretical predictions of massless

Dirac fermions at the surfaces of topological insulators. VC 2013 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4829748]

Topological Insulators (TIs) have a bulk band gap and

gapless surface states that are protected by time reversal sym-

metry, induced by strong spin-orbit interaction. Since the sur-

face states behave like massless Dirac fermions, which carry

electrical as well as spin currents with extremely high mobil-

ity, TIs present an opportunity for novel information process-

ing devices. Therefore, electrical transport properties of TIs

are of considerable current interest. However, studying topo-

logical surface states via electrical transport measurements is

still very difficult due to large bulk contribution to conductiv-

ity originating from unintentional doping and the small bulk

band gaps, which are typical for TI materials. Various

approaches have been developed to suppress bulk conductiv-

ity, for example, by compensatory doping,1–3 increasing the

surface-to-volume ratio through nanostructuring,4–8 or by

electrical gating.2,8–10 Another apparently straight forward

approach is improving the stoichiometry to achieve ideal

intrinsic material. Bi2Te3, also well known as an excellent

thermoelectric material, is one of the common TI materials

and has been synthesized via different growth methods in var-

ious morphologies, e.g., Bi2Te3 bulk material,11 thin

films,12,13 nanoribbons,8 nanobelts or nanowires (NWs).5,14,15

However, up to now electrical transport properties of these

structures vary strongly. Small formation energies of antisite

defects exacerbate the control over structural and electronic

properties of Bi2Te3. Therefore, the reported Fermi surface

properties differ strongly from the theoretically expected val-

ues for massless Dirac fermions in topological surface

states.5,8

Here, we report on parallel and perpendicular magnetore-

sistance (MR) measurements at low temperatures on single-

crystalline Bi2Te3 NWs. We show that the electrical transport

in our NWs is dominated by topological surface states at low

temperatures, which is the result of excellent material quality.

In Ref. 15, we presented a facile way for achieving

single-crystalline, stoichiometric Bi2Te3 NWs with intrinsic

electrical transport properties at room temperature.

The NWs were synthesized via catalytic growth in a sin-

gle zone tube furnace (MTI, Inc., USA/OTF-1200X-25).

After 1 h synthesis, the NWs were post-annealed in a Te-rich

atmosphere at 250 �C for 100 h inside a sealed quartz tube.

The post-annealing step is key to obtaining good stoichiome-

try and minimizing the defect-concentration. Details of the

NW synthesis and post-annealing are described in Ref. 15.

The dimensions of the NWs were determined by atomic

force microscopy (AFM) and scanning electron microscopy

(SEM). In Fig. 1(a), a representative SEM image of the NW

growth substrate is shown. The morphology of the NWs is

either cylindrical or rectangular with thicknesses (smallest

length perpendicular to the NW axis) of 30–150 nm and

lengths up to 15 lm. High resolution transmission electron

microscopy (HR-TEM) imaging reveals a hexagonal crystal

structure and the growth direction along the (110) orienta-

tion, perpendicular to the c-axis (Fig. 1(b)). Before anneal-

ing, the as-grown NWs exhibit a Te depletion near the

NW surface, and an average chemical composition of

Bi46 6 5Te54 6 5. Post-annealing in a Te-rich atmosphere

results in stoichiometric, single-crystalline Bi2Te3 NWs with

a uniform chemical composition across the diameter of the

NWs of Bi41 6 3Te59 6 3. A corresponding HR-TEM image

shown in Fig. 1(b) demonstrates that the annealed Bi2Te3

NWs exhibit smooth surfaces and a thin oxide layer of about

2–3 nm. The observed differences in crystal structure and

chemical composition between as-grown and annealed NWs

are also reflected in their electrical transport properties. The

conductivity of the annealed NWs r¼ (1.9 6 0.3)� 104 X�1

m�1 at room temperature is more than one order of magni-

tude lower compared to the as-grown NWs and close to

r¼ 1.4� 104 X�1 m�1, which has been reported for the

purest bulk Bi2Te3 specimens.11,16 Further, the annealed

NWs show semiconducting temperature dependence in con-

ductivity, which has been measured between 300 K and

460 K.15 The intrinsic electrical transport of the annealed

Bi2Te3 NWs above room temperature suggests a very low

bulk carrier concentration, which makes them excellent can-

didates for investigations of topological surface states via

electrical transport measurements.

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

0003-6951/2013/103(19)/193107/5/$30.00 VC 2013 AIP Publishing LLC103, 193107-1

APPLIED PHYSICS LETTERS 103, 193107 (2013)

For electrical characterization, the annealed NWs were

mechanically transferred onto Si substrates with a 300 nm

SiO2 layer. Electrical contacts to the NWs were defined

using a laser-lithography system (Heidelberg Instruments

lPG 101). After development, in situ sputter etching with Ar

was used to remove any photoresist residues or surface oxide

prior to the sputter-deposition of Ti (5 nm) and Pt (80 nm),

followed by a standard lift-off process. In Fig. 1(c), a typical

device used for the electrical measurements is shown. Our

experiments were performed in a cryostat system (Quantum

Design Physical Property Measurement System) with a base

temperature of 2 K in helium atmosphere, equipped with a 9

T magnet. The resistance of the NWs was determined by

standard low frequency lock-in techniques. By comparing

two-terminal and four-terminal measurements on our Bi2Te3

NWs, contact resistances were found to be negligible, thus

modulations in the MR curves can be attributed to the NWs.

The linear IV-curves in Fig. 1(d) demonstrate that the electri-

cal contacts to the NWs are ohmic over the whole tempera-

ture range.

We present data for three annealed Bi2Te3 NWs with dif-

ferent rectangular cross sectional areas of NW 1: 161� 60 nm,

NW 2: 213� 150 nm, and NW 3: 321� 80 nm. The conduc-

tivity at T¼ 300 K for the three measured NWs is

r¼ (1.81 6 0.09)� 104 X�1 m�1 on average, which is in

excellent agreement with the values we measured for same

type of NWs in Ref. 15. All three NWs exhibit a similar tem-

perature dependent resistance. A typical resistance versus tem-

perature curve at zero magnetic field is shown in Fig. 1(d).

Between 300 K and 260 K, the resistance increases with

decreasing temperature. This is consistent with semiconducting

temperature dependence measured above 300 K, which has

been presented in Ref. 15. Below �260 K, the resistance

decreases for decreasing temperature and saturates at around

5 K, indicating a typical metallic behavior. A similar tempera-

ture dependent resistance has also been observed for our

single-crystalline Sb2Te3 NWs, reported in Ref. 6, and other

small band gap topological insulators, e.g., Bi2Se3 nanoribbons

and thin films, or Bi2Te3 crystals.7,17–19 On the other hand, for

single-crystalline chemically synthesized Bi2Te3 NWs and

nanoribbons, a semiconducting behavior at very low tempera-

tures has been reported, which is attributed to carrier

freeze-out of impurity band conduction.5,17 Further, the resid-

ual resistivity ratio (RRR) of R300 K/R4 K� 4 for our measured

NWs is considerably higher than in the previous reports on

Bi2Te3 NWs. For a TI material, electrical transport results

from a superposition of contributions from the semiconducting

bulk and from the metallic surface states. Therefore, the metal-

lic behavior at low temperatures and the high RRR of our

NWs indicate a dominant surface state contribution to electri-

cal conductivity at 2 K.

In Fig. 2, the MR of NW 1 is shown where the magnetic

field is applied parallel to the NW axis. The MR exhibits

three pronounced features. Around B¼ 0 T a sharp dip can

be seen, which is attributed to the weak antilocalization

(WAL) effect, consistent with the presence of strong spin-

orbit coupling.20 Further analysis of the WAL effect in our

Bi2Te3 NWs will be presented in the discussion of the per-

pendicular MR results. For higher fields up to 69 T

FIG. 1. Material characterization and device. (a) SEM image of the NW

growth substrate at an angle of �15� to the substrate plane. (b) HR-TEM

image of an annealed Bi2Te3 NW. The inset shows the corresponding selected

area electron diffraction (SAED) pattern, indicating the single-crystallinity of

the NW and the growth direction along the (110) orientation. (c) SEM image

of a typical micro device including two electrical contacts for current injection

and two for voltage detection across the NW. (d) Representative temperature

dependence of the resistance at zero magnetic field in the range of 2–300 K.

The inset shows linear IV-curves at different temperatures, indicating ohmic

contacts over the whole temperature range.

FIG. 2. Parallel magnetoresistance. (a) Magnetoresistance MR ¼ ðR Bð Þ�R 0ð ÞÞR 0ð Þ

versus parallel magnetic field of NW 1 at five different temperatures. The

AB oscillations are damped with increasing temperature. (b) AB oscillations

of NW 1 after subtraction of the smooth background at 2 K. The inset shows

the corresponding index plot, indicating a high degree of linearity.

193107-2 Hamdou et al. Appl. Phys. Lett. 103, 193107 (2013)

oscillations appear. A plot of the oscillations after subtract-

ing a trace recorded at 6 K ðDR ¼ R2K � R6KÞ is shown in

Fig. 2(b). The high degree of linearity in the corresponding

index plot indicates that the oscillation period remains constant

over the whole magnetic field range. We attribute these peri-

odic oscillations to the Aharonov-Bohm (AB) effect,21 which

is predicted when charge carriers remain phase coherent

around the NW’s perimeter and thus enclose a magnetic flux

U0¼ h/e, where h is Planck’s constant and e is the unit

charge.4,7,8 The enclosed area A is associated with the period

of DB¼U0/A. The excellent agreement between the area

extracted from the AB oscillation period (9.96 6 0.06)� 10�15

m2 and the measured cross-sectional area of the NW

(9.66 6 0.57)� 10�15 m2 indicates the presence of surface

states. Both, the WAL resistance dip and the AB oscillations

are symmetric around zero field and smear out with increasing

temperature.

The third dominant feature in the parallel MR curve is

the resistance drop above B¼66 T at 2 K. The MR

decreases strongly and becomes negative at around 68 T.

For higher temperature the MR drop is shifted to lower mag-

netic fields.

In the following, we will discuss the results of MR

measurements for all three NWs, where the magnetic field is

applied perpendicular to the current along the axis of the rec-

tangular NWs. In Fig. 3(a), the representative perpendicular

MR of NW 1 in the low magnetic field range is shown. All

three NWs showed similar perpendicular MR. We observe

two prominent features. As in parallel MR, there is a sharp

dip around zero field, which we attribute to the WAL effect.

In the 2D case the correction factor to conductivity Dr can

be described by the Hikami-Larkin-Nagaoka formula20

Dr Bð Þ ¼ ae2

p hw

�h

4eBLU2þ 1

2

� �� ln

�h

4eBLU2

� �� �; (1)

where LU is the phase coherence length and w(x) is the

digamma function. It should be noted that the geometry of a

rectangular NW with surface states differs from a planar 2D

system. An analysis of the WAL effect by fitting the conduc-

tivity peak around zero field for all three measured NWs

with the Hikami-Larkin-Nagaoka formula is shown in Fig.

3(b). The resulting prefactor a yields information about the

scattering mechanism. A prefactor of a¼�1/2 is expected

for strong spin-orbit interaction and no magnetic scatter-

ing.20 In experiments a usually covers a wide range, because

the measured conductivity peak around zero magnetic field

displays a collective result from both the surface states and

the bulk.22,23 Thus, separating the bulk and surface contribu-

tions to the prefactor a is difficult. Our analysis for the three

measured NWs yields the following prefactors at 2 K: NW 1

(a¼�0.51 6 0.03), NW 2 (a¼�0.51 6 0.01), and NW 3

(a¼�0.43 6 0.03). These values indicate strong spin-orbit

coupling in our NWs, which is a prerequisite for topological

surface states. As expected, the prefactor a decreases with

increasing temperature, due to a decreasing phase coherence

FIG. 3. Perpendicular magnetoresistance. (a) Magnetoresistance MR ¼ ðR Bð Þ�R 0ð ÞÞR 0ð Þ versus perpendicular magnetic field of NW 1 at 2 K. The inset shows the re-

sistance after subtraction of the smooth background DR at 2 K. The 1/B-periodic oscillations are attributed to the Shubnikov-de Haas effect with the respective

Landau level n. (b) Conductance versus perpendicular magnetic field around zero field of NW 1 at three different temperatures. The conductance peak is attrib-

uted to the weak antilocalization effect. The solid lines are the related fits to Eq. (1). The inset shows the phase coherence lengths at 2 K for the three measured

NWs. (c) Landau level n versus 1/B for the three measured NWs. Besides the Landau level, which is defined as the minima of the resistance oscillations, the

maxima are additionally plotted. The linear fit intercepts the n-axis near the value c� 1=2 for all three NWs, indicative of Dirac fermions. (d) Conductance ver-

sus 1/B of NW 1 for three different temperatures. The lower inset shows the corresponding temperature dependence of the oscillation amplitude Dr(T)/Dr(0).

The solid line is a fit to v(T)/sinh(v(T)). The upper inset shows the Dingle plot log[(DRB sinh(v(T))] versus 1/B at 2 K. The solid line is a linear fit.

193107-3 Hamdou et al. Appl. Phys. Lett. 103, 193107 (2013)

length, shown in Fig. 3(b). Whereas a surface-to-volume ra-

tio dependence of a was not evident for the three measured

NWs. The corresponding phase coherence lengths at 2 K for

the three measured NWs are: NW 1 (LU¼ 167 6 9), NW 2

(LU¼ 165 6 1), and NW 3 (LU¼ 284 6 5).

For higher magnetic fields up to 61 T oscillations occur,

which are periodic in 1/B, as shown in the inset of Fig. 3(a),

where DR is plotted against 1/B. We attribute these oscilla-

tions to the Shubnikov-de Haas (SdH) effect. The Landau

index n is related to the Fermi surface by the following

equation:5,19,24

2p nþ cð Þ ¼SF�h

eB; (2)

where c¼ 0 or 1=2, e is the unit charge, �h is the reduced

Planck constant, and B is the magnetic flux density.

However, since SdH oscillations can arise from both bulk

carriers and surface states it is necessary to clarify the sur-

face state contribution. In Fig. 3(c), the Landau index n,

which is defined as the minima of the resistance oscillations,

is plotted against 1/B for all three NWs. For higher accuracy,

the resistance maxima are also plotted in the same diagram.

The linear extrapolation intercepts the n-axis at the values

NW 1: c¼ 0.65 6 0.09, NW 2: c¼ 0.55 6 0.14, NW 3:

c¼ 0.56 6 0.05, which are in good agreement with the pre-

dicted p-Berry phase (c¼ 1=2), expected for ideal 2D Dirac

fermions with a linear dispersion relation.19,24,25 In contrast,

for a regular 2D electron system the intercept would be zero.

From the slope of the Landau index plot the cross-sectional

Fermi surface area SF can be calculated. Using the equa-

tions5,19,24,25 kF ¼ffiffiffiffiffiffiffiffiffiffiSF=p

pand n2D ¼ kF

2=2p the Fermi

wavevector kF and the 2D carrier concentration n2D are esti-

mated to be kF¼ 0.01 A�1 and n2D¼ 1.7� 1011 cm�2 for

NW 1. The values for all three NWs are in the same range,

summarized in Table I. The 2D carrier concentration is very

low compared to the values reported for chemically synthe-

sized Bi2Te3 NWs n2D� 4.9� 1012 cm�2 and Bi2Te3 nano-

ribbons n2D� 1� 1012 cm�2.5,8 We also analysed the

temperature dependent damping of the SdH oscillations. The

amplitude of the oscillation is reduced due to disorder and

thermal smearing.24 The temperature dependence of the con-

ductivity amplitude can be described by Dr Tð ÞDr 0ð Þ ¼

vðTÞsinhðv Tð ÞÞ. The

thermal factor is given by v Tð Þ ¼ 2p2kBTmc

�heB , where mc is cyclo-

tron effective mass and kB is the Boltzmann constant. By fit-

ting the experimental data to this equation, shown in Fig.

3(d), cyclotron masses for the three measured NWs of

mc1¼ 0.04 m0, mc2¼ 0.03 m0, and mc3¼ 0.02 m0 can be

estimated, where m0 is the free electron mass. The corre-

sponding magnetic fields at which the SdH resonances were

analyzed are: NW 1 (B¼ 0.82 T), NW 2 (B¼ 0.88 T), and

NW 3 (B¼ 0.65). The very low cyclotron mass of

mc¼ (0.03 6 0.01) m0 on average is consistent with the theo-

retical prediction of massless Dirac fermions.

For NW 1 the carrier mobility l of the surface states can

be calculated by finding the Dingle damping factor from dis-

order RD ¼ e�p=sxc ,24,26 where s is the scattering time and

xc is the cyclotron frequency. The resistance amplitude of

the SdH oscillations is proportional to ½ v Tð Þsinh v Tð Þð Þ�e

�p=lB with

l ¼ sxc=B. If we plot log½DRBsinh v Tð Þ� �

� against 1/B, the

carrier mobility can be subtracted out of the slope in the log-

arithmic plot,5,8,19 which is shown in Fig. 3(d). We estimated

a carrier mobility of l¼ 21 000 cm2 V�1 s�1. By comparing

the surface conductivity Gs ¼ e2=h� �

kFl with the total con-

ductivity Gtotal,8 we estimated a surface contribution of

GS=Gtotal ¼ 70%. This confirms that the electrical transport

is dominated by the surface states. For NW 2 and NW 3, the

Dingle damping factor could not be determined because of

too small oscillation amplitudes.

For higher magnetic fields, the MR shows a linear

increase, which also has been observed for Bi2Se3 thin films27

and nanoribbons,28 Bi2Te3 crystals19 and thin films.12,29 The

corresponding authors argue that the unusual nonsaturating

linear MR at high magnetic fields could be attributed to

Abrikosov’s “quantum linear magnetoresistance” mecha-

nism,30 which is predicted for a system in the quantum limit

with a gapless linear dispersion relation.12,19,27,28 The quan-

tum limit requires a magnetic field that is high enough that the

degeneracy of each Landau level is very high and all the car-

riers are condensed in the lowest Landau level.30 Recent ex-

perimental investigations revealed that quantum linear MR

could also appear at even lower magnetic fields, with a few

populated Landau levels.31 In our case the lowest Landau lev-

els are in the magnetic field range of the expected quantum

limit where the nonsaturating linear MR begins.

In summary, MR measurements were performed with

the magnetic field parallel and perpendicular to the NW axis

at temperatures down to 2 K for three single-crystalline

Bi2Te3 NWs. We showed that the observed quantum effects

in MR characterize different aspects of the topological sur-

face states in our Bi2Te3 NWs. AB oscillations in parallel

MR indicate the presence of surface states. Weak antilocali-

zation suggests strong spin-orbit coupling, which is a prereq-

uisite for topological surface states. SdH oscillations in

perpendicular MR exhibit a p-Berry phase, as expected for

2D Dirac fermions. Further, extremely low 2D carrier

TABLE I. Estimated parameters from the SdH oscillations at 2 K. The data of Xiu et al. and Tian et al. were obtained for individual chemically synthesized

Bi2Te3 nanoribbons and cylindrical NWs, respectively.

NW Cross-section (nm) fSdH (T�1) kf (A�1) n2D (1011 cm�2) mc (m0) l (cm2 V�1 s�1) Gs/Gtotal (%) References

1 161� 60 0.28 0.01 1.7 0.04 21 000 70

2 213� 150 0.28 0.01 1.8 0.03 … … This work

3 321� 80 0.4 0.009 1.2 0.02 … …

185� 30 �0.025 �0.04 �10 �0.1 �5000 30–50 Xiu et al. (see Ref. 8)

p(40/2)2 0.036 0.055 49 … 3300 … Tian et al. (see Ref. 5)

193107-4 Hamdou et al. Appl. Phys. Lett. 103, 193107 (2013)

concentrations and cyclotron masses on the order of

n2D¼ 1.6� 1011 cm�2 and mc¼ 0.03 m0, respectively, and

extremely high carrier mobilities around l¼ 21 000 cm2 V�1

s�1 were determined, consistent with the theoretical predic-

tion of massless Dirac fermions. These findings demonstrate

that electrical transport at low temperatures in our Bi2Te3

NWs is dominated by topological surface states as a result of

optimized material quality that we achieved by a combina-

tion of catalytic growth and post-annealing in a Te-rich

atmosphere.

This work was supported by the German science founda-

tion (DFG) via the German priority program SPP 1386

“Nanostructured Thermoelectrics” and SPP 1666 “Topological

Insulators,” as well as within the Graduiertenkolleg 1286

“Functional Metal-Semiconductor Hybrid Systems.” We thank

L. Akinsinde and R. Meißner for technical support.

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