Surface state dominated transport in topological insulator Bi2Te3 nanowires Bacel 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
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Surface state dominated transport in topological insulator ...3 NWs, reported in Ref. 6, and other small band gap topological insulators, e.g., Bi 2Se 3 nanoribbons and thin films,
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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-
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-
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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