low‐dimensional topological crystalline insulators...low-dimensional topological crystalline...

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Insulators

Low-Dimensional Topological Crystalline Insulators Qisheng Wang , Feng Wang , Jie Li , Zhenxing Wang , Xueying Zhan , and Jun He *

Topological crystalline insulators (TCIs) are recently discovered topological phase with robust surface states residing on high-symmetry crystal surfaces. Different from conventional topological insulators (TIs), protection of surface states on TCIs comes from point-group symmetry instead of time-reversal symmetry in TIs. The distinct properties of TCIs make them promising candidates for the use in novel spintronics, low-dissipation quantum computation, tunable pressure sensor, mid-infrared detector, and thermoelectric conversion. However, similar to the situation in TIs, the surface states are always suppressed by bulk carriers, impeding the exploitation of topology-induced quantum phenomenon. One effective way to solve this problem is to grow low-dimensional TCIs which possess large surface-to-volume ratio, and thus profoundly increase the carrier contribution from topological surface states. Indeed, through persistent effort, researchers have obtained unique quantum transport phenomenon, originating from topological surface states, based on controllable growth of low-dimensional TCIs. This article gives a comprehensive review on the recent progress of controllable synthesis and topological surface transport of low-dimensional TCIs. The possible future direction about low-dimensional TCIs is also briefl y discussed at the end of this paper.

1. Introduction ............................................. 2

2. Fundamentals of TCIs ................................ 2

3. Controllable Growth of Low-Dimensional TCIs ............................... 4

4. Surface Electronic Transport of Low-Dimensional TCIs ............................... 7

5. Prospects ............................................... 10

6. Conclusion ............................................. 11

From the Contents

small 2015, DOI: 10.1002/smll.201501381

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DOI: 10.1002/smll.201501381

Q. Wang, F. Wang, J. Li, Prof. Z. Wang, X. Zhan, Prof. J. He National Center for Nanoscience and Technology Beijing 100190 , P. R. China E-mail: [email protected]

1. Introduction

Thermal dissipation, due to the scattering of carriers during

transport process, is a common problem in current silicon-

based electronic devices. The emerging topological insulators

(TIs), a new quantum phase whose surface is conductive but

interior is insulating, open up a hopeful route to solve this

issue. [ 1–3 ] Owing to the relativistic effect (spin–orbit coupling)

and topological protection from time-reversal symmetry,

spin-locked current on the surface/edge of TIs is immune to

any nonmagnetic impurities, which endows them with great

application potential in low-dissipation electronic devices

and quantum information processing. The exciting discovery

and novel properties of TIs motivate scientists to search for

new topological phase classifi ed by other invariants. Topo-

logical crystalline insulators (TCIs), protected by point-group

symmetry, are such kind of topological phase. [ 4,5 ] So far, the

experimentally confi rmed TCIs are SnTe and its related alloy

Pb 1− x Sn x Te(Se) that possess high-symmetry rock-salt crystal

structure. Each high-symmetry surface of TCIs accommo-

dates four Dirac states. Interestingly, through controlling the

crystal symmetry, the topological nature of TCIs can be trans-

formed from nontrivial to trivial phase by strain and electrical

fi eld. Meanwhile, surface states properties of TCIs are highly

tunable by composition and temperature. All above features

indicate TCIs are promising for exploiting tunable electronic

and spintronic devices. However, similar to TIs, surface states

transport of TCIs is usually overwhelmed by bulk carrier. [ 6–8 ]

In order to resolve this problem, researchers dedicated to

growing low-dimensional TCIs since huge surface-to-volume

ratio of low-dimensional TCIs can signifi cantly enhance con-

tribution of carrier transport from surface states. Especially,

as topological nature varies from one high-symmetry facet

to another, controlling the crystal planes orientation of TCIs

nanostructures is crucial for probing unique surface states.

Furthermore, based on low-dimensional TCIs, researchers

successfully observed quantum transport phenomenon from

surface states. It is worth noting that, although it is a short

time after the fi rst theoretical prediction of TCIs by Fu et

al. in 2011, [ 4,5 ] researchers have achieved great success on

growth and surface states transport of low-dimensional

TCIs. This paper comprehensively reviews the recent pro-

gress in both synthesis and surface topological transport of

low-dimensional TCIs. We fi rst introduce the basic principle

of TCIs. Then, we summarize and analyze the newest results

about synthesis and quantum transport of low-dimensional

TCIs. The possible future directions about low-dimensional

TCIs are also proposed in the end.

2. Fundamentals of TCIs

2.1. From TIs to TCIs

One of the big breakthroughs in condensed matter physics is

the discovery of quantum Hall effect (QHE) in the 1980s. [ 9 ]

QHE occurs in 2D electrons system when an intense and per-

pendicular magnetic fi eld is applied to drive the electrons to

circulate in quantized orbits. As a result, the edge of samples

is characterized by dissipationless current fl ows while the

interior becomes inert. QHE is considered to be the fi rst TIs

because Hall conductivity σ xy equals integral multiples ( n )

of quantum conductance e 2 / h and n is the topological invar-

iant. [ 10 ] However, the requirements of low-temperature and

strong magnetic fi eld for generating QHE strictly limit its

practical application in electronic devices.

In the year of 2006, Zhang et al. [ 1,2 ] theoretically predi-

cated quantum spin Hall effect (QSHE) in 2D HgTe quantum

well, in which strong spin–orbital coupling replaces the role

of external magnetic fi eld to force the current to move in one

direction without back scattering. Such new TIs belong to a

novel topological classifi cation of a Z 2 index. Time-reversal

invariant property protects the surface spin-polarized elec-

tron fl ow from the scattering of nonmagnetic impurities.

This predication was subsequently verifi ed by experiments in

2007. [ 3 ] Channel conductivity σ xx was observed to be quan-

tized to 2 e 2 / h in zero magnetic fi eld, proving the existence of

gapless edges states in CdTe/HgTe/CdTe quantum well. This

encouraging discovery profoundly boosts the research of TIs.

Soon 3D TIs such as Bi 1− x Sb x , Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 with

2D surface gapless states are validated by both theory [ 11 ]

and experiments. [ 12,13 ] It is worth emphasizing that Bi 2 Se 3 ,

Bi 2 Te 3 , and Sb 2 Te 3 are ideal building blocks for the study of

topological surface states when we take account of the fol-

lowing aspects: [ 6,8,14 ] (1) they have simple chemical stoichio-

metric ratio, (2) they are of layered crystal structure that

each covalently bonded quintuple layer interacts with each

other by weak van der Waals forces, enabling the synthesis

of few-layer nanoplates by conventional vapor deposition or

mechanically exfoliated methods, and (3) their surface is ter-

minated by a single Dirac cone with a relatively large bulk

bandgap (≈0.2–0.3 eV) which makes it accessible to surface

states even at room temperature.

Inspired by the TIs, theorists are committing themselves

to fi nd new type of TIs by other symmetry. Fu et al. [ 4 ] fi rst

proposed that insulators with mirror symmetry, namely

TCIs, could also obtain robust surfaces states. They subse-

quently present defi nite materials of TCIs that are SnTe and

its related alloy Pb 1− x Sn x Te(Se). [ 5 ] The theoretical predi-

cation was immediately confi rmed by three groups who

detected the linear Dirac dispersion on mirror-symmetry

surfaces of TCIs by angle-resolved photoemission spectros-

copy (ARPES). [ 15–17 ] The discovery of TCIs considerably

extends the family of TIs. In starkly contrast to TIs, TCIs

show differences in the aspects of (1) they are of highly

symmetry crystal structures, (2) gapless metallic states only

reside on those mirror-symmetry surfaces such as (100),

(111), and (110), (3) Dirac cones on TCIs surface can be

opened up by breaking symmetry, manipulating tempera-

ture, and tailoring compositions. Basic information about

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http://doi.wiley.com/10.1002/smll.201501381



TIs and TCIs is listed in Table 1 from which we can clearly

see peculiar characteristics of TCIs. Take Pb 1− x Sn x Te as a

representative example, it crystallizes in the form of cubic

crystal structures. And it undergoes a band inversion and

obtains topological protection when Sn content ( x ) reaches

0.38 at 9 K. [ 15 ] Temperature also drives the conversion of

Pb 1− x Sn x Te from topological nontrivial insulator to trivial

insulator when it exceeds the critical temperature ( T c ).

Intriguingly, external physical disturbs such as strain and

electric fi eld can open up the surface gapless Dirac states by

destroying the crystal symmetry. These peculiar characteris-

tics make TCIs a promising materials system in the applica-

tions of tunable spintronic devices.

2.2. Surface Electronics of TCIs

TCIs harbor four Dirac cones on each high-symmetry sur-

face. Figure 1 a presents the electronic structure of (100) sur-

face in bulk SnTe. [ 5 ] Two surface bands with opposite mirror

eigenvalues cross each other and form a Dirac point along

TX . Four Dirac points can be found on the four equivalent

TX as shown in Figure 1 b. The surface Dirac states show a

Lifshitz transition that the Fermi surface fi rst exhibits two

disconnected hole pockets outside X . [ 18 ] And they then close

to each other with the decrease of Fermi energy and touch

each other. A large electron pocket with a hole inside is

formed fi nally (Figure 1 c). Another important feature of TCIs

lies in the tunability of topological surface states through

composition and temperature. [ 17,19–21 ] Figure 1 d shows the

ARPES of Pb 1− x Sn x Se (001) surface at various tempera-

tures in the vicinity of X . It obviously presents that surface

state is gapped above 100 K at which bottom of conduction

band connects to top of valence band with the formation of

a Dirac node. [ 15 ] Composition dependence of topological sur-

face states is also proved by Chen et al. in Pb 1− x Sn x Te (111)

fi lms. [ 22 ] Madhavan et al. [ 23,24 ] further pointed out that the

nontopological regime also host surface states. However, the

weight of Dirac surface states decreases when Sn content ( x )

approaches the trivial phase, imparting the mass to the mass-

less Dirac electrons. Zero-mass Dirac fermions protected by

crystal symmetry were found to coexist with massive Dirac

small 2015, DOI: 10.1002/smll.201501381

Table 1. Fundamental information of TIs and TCIs. Insets: a) quantum Hall effect in 2D electron system with dissipationless edge states. b) Back scattering from nonmagnetic impurities in TIs surface is prohibited. Reproduced with permission. [ 60 ] Copyright 2011, Nature Publishing Group. c) 2D helical surface states of 3D TIs. d) Energy dispersion of spin nondegenerate surface states on 3D TIs. Reproduced with permission. [ 61 ]

Copyright 2013, The Physical Society of Japan. e) Dirac-cone surface states on two different surface planes of (001) [ 16,28 ] and (111). [ 18 ] Reproduced with permission. [ 18 ] Copyright 2013, The American Physical Society.

Quantum Hall effect Quantum spin Hall effect

2D TIs 3D TIs 2D TCIs [65] 3D TCIs

Materials 2D electron system CdTe/HgTe/CdTe, AlSb/

InAs/GaSb/AlSb, Bi bilayer

Bi 1− x Sb x , Sb, Bi 2 Se 3 ,

Bi 2 Te 3 , Sb 2 Te 3 ,

Ag 2 Te, Bi 2 (Se 1− x Te x ) 3 ,

(Bi 1− x Sb x ) 2 Te 3

(001) monolayers of rock-

salt IV–VI semiconductors

XY (X = Ge, Sn, Pb, and

Y = S, Se, Te

SnTe, Pb 1– x Sn x Te,

Pb 1− x Sn x Se

Crystal structure – Layered rhombohedral crystal structure except 2D

quantum well

Cubic structure

bandgap – <30 meV except Bi

bilayer (0.1 eV)

≈0.3 eV except Sb

(semimetal)

0.26 eV for

monolayer PbTe

≈0–0.3 eV, invert with

temperature ( T ) and

composition ( x )

Protection TKKN invariant Time-reversal invariant (Z2 topology) Point-group symmetry (Mirror Chern number)

Surface states – Single Dirac cone Four Dirac cones on each surface

Characteristics Requirement of strong

magnetic fi eld

Strong spin–orbital coupling, simple chemical

stoichiometric ratio, large bandgap

Strong spin–orbital coupling, high crystal symmetry,

tunability by stain and composition, large bandgap

Schematic diagram



electrons due to the symmetry-breaking distortion on the

surface. And the magnitude of the symmetry-breaking dis-

tortion nearly keeps unchanged in the both topological and

nontopological regimes.

Since metallic surface states of TCIs are protected by

crystal symmetries instead of time-reversal symmetries, low-

dissipation logic devices and pressure sensors can be devel-

oped based on topological surface states by breaking the

crystal symmetry. Fu et al. fi rst theoretically demonstrated

topological transistor devices of TCIs thin fi lm grown along

the (001) direction. [ 25,26 ] They proposed the surface states of

an 11-layer SnTe thin fi lm will be gaped when applying a ver-

tical electrical fi led. Figure 1 e shows the surfaces electronic

structures of SnTe (001) surface without application of elec-

tric fi led. After a 0.1 V bias is applied across the thin fi lm, the

surface band opens up (Figure 1 f). They further revealed that

the ferroelectric-type structural distortion opened some or all

of Dirac points, whereas strain moves the Dirac points to the

Brillouin zone. And the perpendicular magnetic fi eld gener-

ates the discrete Landau levels while in-plane magnetic fi eld

causes asymmetry between Dirac points. [ 27 ]

3. Controllable Growth of Low-Dimensional TCIs

Achieving controllable growth is always a very important

step as well as a big challenge for any “new” material. This

is especially true for TCIs in which fragile surface states

may become undetected under the perturbation of defects

and bulk state. [ 17 ] To avoid the disturbance of defects, high

quality TCIs prepared by thermodynamic equilibrium syn-

thesis method, like modifi ed Bridgeman [ 28 ] and self-selecting

vapor growth methods, [ 17 ] are used in the initial experimental

studies. However, as we mentioned before, TCIs are topo-

logical insulators in which the gapless surface states are pro-

tected by mirror symmetry of the crystal. [ 16 ] In another word,

possessing objects with large area of surfaces (surface states)

of specifi c crystalline planes (mirror symmetry) is prerequi-

site if one wants to implement better experimental obser-

vation of possible topology-related phenomena. Taking this

into consideration, synthesizing low-dimensional TCIs is one

of the best choices. After its theoretical prediction in 2011, [ 4 ]

many ways, such as molecular beam epitaxy (MBE) and

vapor deposition method, have been employed to synthesize

low-dimensional TCIs. In the following part, we will give a

review on this rising fi eld. We note that there are still other

ways, [ 29–31 ] such as solution-phase synthesis method, to grow

low-dimensional TCIs. But the products either are too small

for device fabrication or have too bad crystalline quality for

probing surface state. Hence, they will not be discussed in

this section.

3.1. MBE for Thin Film

The fi rst TCI proved by experiment is SnTe. [ 16 ] However,

due to intrinsic Sn vacancies (usually p-type doped state),

small 2015, DOI: 10.1002/smll.201501381

Figure 1. a) Band structure and b) Fermi surface of SnTe (001) surface. c) A set of Fermi surface at different energy with a Lifshit transition. Reproduced with permission. [ 5 ] Copyright 2012, Nature Publishing Group. d) Temperature-dependent ARPES spectra in the vicinity of X . Reproduced with permission. [ 15 ] Copyright 2012, Nature Publishing Group. e) Gapless edge states of an 11-layer SnTe thin fi lm. f) The edge state opens up when applying a perpendicular electrical fi eld. Reproduced with permission. [ 26 ] Copyright 2014, Nature Publishing Group.



observing surface state of SnTe has been a challenge. [ 16 ] As

a result, synthesizing high-quality SnTe with few defects

is the fi rst task. MBE, by precisely controlling the deposi-

tion rate and compositions, is a promising candidate. In

2013, Yan et al. grow high-quality SnTe thin fi lm on Si(111)

substrates by MBE for the fi rst time. [ 32 ] Relying on the

good controllability of MBE, thickness- and Pb doping-

dependent properties of SnTe thin fi lm are studied. Soon

after, Assaf et al. synthesized SnTe fi lm by MBE on BaF 2

(001) substrates. [ 33 ] They found that high-quality fi lm, then

an increased Hall mobility and decreased carrier concentra-

tion, could be achieved through using higher growth tem-

perature. To take a step further, Taskin et al. grow SnTe fi lm

using Bi 2 Te 3 , which has a lower lattice mismatch with SnTe,

as substrates. [ 34 ] Beyond this binary TCI, its ternary com-

pound Pb 1− x Sn x Te is also an interesting material because

its topological nature can be tailored by Sn content ( x ). [ 16 ]

According to this idea, Yan et al. synthesized Pb 1− x Sn x Te

fi lm with variable Sn content and found that there is a topo-

logical phase transition from trivial to nontrivial state while

increasing Sn content. [ 22 ]

3.2. Vapor Deposition Method

The thickness and composition of fi lms grown by MBE are

precisely controlled. However, it is expensive and time con-

suming. As compared with MBE, vapor deposition method

is easier, cheaper and considered one of the most promising

routes to productively synthesize nanostructured materials.

For TCIs, the fi rst trial is on SnTe. In 2013, through adjusting

the temperature of substrates, Li et al. successfully synthe-

sized SnTe nanomaterials with different morphologies by

chemical vapor deposition (CVD). [ 35 ] Combining with ab

initio calculation, they found that it is the energy difference

of crystalline planes that determines the morphologies (see

Figure 2 a). Specifi cally, when the substrates were placed in

the relative higher temperature (here 645–675 °C), the Te

poor condition, (100) planes have the lowest surface energy

(left side of Figure 2 a). As a consequence, SnTe microcubes

(without Au catalyst, VS growth mode) and nanowires (with

Au catalyst, VLS and VS growth mode) with (100) exposed

planes were obtained. While on the occasion of lower tem-

perature (525–625 °C), the Te in rich condition, (100) and

(111) planes have a similar surface energy (right side of

Figure 2 a). As a result, complicated SnTe microcrystals

(without Au catalyst, VS growth mode) and zigzag nanowires

(with Au catalyst, VLS and VS growth mode) which exposed

both (100) and (111) planes were grown. Figure 2 b,c shows

the respective results. Almost at the same time, by controlling

the experimental conditions in the CVD process, our group

reported the synthesis of high-quality SnTe nanocrystals and

nanowires with highly symmetry facets. [ 36,37 ] Without the uti-

lization of Au catalyst, the surface orientation and crystal

shapes of SnTe micronanocrystals mainly depend on the

growth temperature which decides the surface energy of SnTe

micronanocrystals. However, when using Au nanoparticles as

the catalyst, the 1D anisotropic growth is excited due to the

induction of catalyst. Combining the effect of temperature,

we obtained octahedron-attached SnTe nanowires and trun-

cated octahedron-assisted SnTe nanowires. More recently,

catalyst composition is found to have a strong impact on the

morphologies of SnTe nanostructure. [ 38 ] Zou et al. pointed

out that liquid An–Sn catalyst with high Sn content induced

the thermally dynamic growth of SnTe triangular nanoplates

with dominant {100} surfaces at high growth temperature

region (500 °C). While SnTe nanowires with dominant {100}

side surfaces were formed in the low-temperature region

(450 °C) under the control of solid or quasisolid Au 5 Sn cat-

alysts. In addition to the infl uence from surface energy of

different crystal planes at given conditions, catalyst composi-

tion played the critical role in deciding the morphologies of

SnTe nanostructures by affecting interface lattice match and

chemical potential of Sn content. Compared with 3D bulks,

1D nanowire are favorable for probing surface state of TCIs

due to their high surface-to-volume ratio. [ 39 ] However, for a

better performance, nanoplates with large top and bottom

surfaces are more preferred. Having this idea in mind, Cha

et al. grew SnTe nanoplates via the CVD method recently. [ 40 ]

Figure 2 d–n gives their results. In detail, SnTe nanoplates

with (100) or (111) planes as top and bottom surfaces were

achieved when grown in a relative low temperature (around

300 °C). While in higher temperatures (350–450 °C), nanorib-

bons and nanowires would appear.

In the conventional vapor deposition method, sub-

strates with dangling bonds, like SiO x /Si, are usually used.

And vertical nanostructures with a variety of morphologies

have been synthesized. But for 2D nanomaterials parallel

to substrates, it turns out to be diffi cult because, as a result

of the strong bonds, the adatoms become hard to diffuse on

the top of substrates. [ 40 ] Thanks to van der Waals epitaxy

(vdWE) method, in which atomically smooth substrates

(such as mica) are used as substrates, many nanomaterials

with 2D morphologies have been synthesized success-

fully. [ 40–42 ] For example, Li et al. prepared single-crystal

topological insulators (Bi 2 Se 3 and Bi 2 Te 3 ) nanoplates

arrays using mica as substrates. [ 40 ] However, previous works

focused on growing 2D layered materials which have strong

intrinsic driving force of 2D anisotropic growth due to their

planar crystal structure. In the year of 2014, our group fi rst

proposed the growth of 2D nonlayered Te hexagonal nano-

plates by vdWE on mica substrate. [ 43 ] vdWE is advantaged

in that (1) it allows large lattice mismatching between the

target product and substrates, (2) excessive strain in the

heterointerface is relaxed due to weak van der Waals inter-

action in the interface, and (3) van der Waals substrates

facilitates the migration of adatoms and thus promotes the

lateral growth of nanoplates. By performing the synthesis of

SnTe and Pb 1− x Sn x Se nanostructures on mica substrates, we

further put forward the general strategy for van der Waals

epitaxial growth of 2D nonlayered semiconductor. [ 44 ] Two

conditions are required for the growth of 2D nonlayered

materials by vdWE: (1) the nonlayered materials should

have the driving force for the 2D anisotropic growth, which

can be excited by optimizing the experimental conditions in

CVD process, and (2) van der Waals materials such as mica

and BN need to be used as the growth substrates. Figure 3

shows representative examples of van der Waals epitaxial

small 2015, DOI: 10.1002/smll.201501381



2D nonlayered material. [ 45 ] Ultrathin 2D Pb 1− x Sn x Se nano-

plates with thickness ranging from 15 to 50 nm have been

successfully synthesized on the surface of mica. Two growth

conditions, in the CVD process, are thought to be the crit-

ical factors that affect the anisotropic growth of 2D TCIs.

One is the substrates temperature that mainly determines

the chemical activity of different crystal planes. In the case

of our previous work about vdWE of 2D Pb 1− x Sn x Se nano-

plates on mica, {110} surfaces of Pb 1− x Sn x Se showed higher

activation at growth temperature of 550 °C compared

with other facets, which leads to 2D anisotropic growth of

Pb 1− x Sn x Se nanoplates. The other important growth param-

eter is substrate surface chemistry property that infl uences

the nucleation, migration of adatoms, interface stability,

and thus the morphology of fi nal products. Our previous

work showed that, when we replaced layered mica with Si

substrate, Pb 1− x Sn x Se preferred to form microplates rather

than nanoplates under the same experimental parameters

as that on mica. This would be understood by the fact

that (1) dangling bonds on surface of 3D bonded Si cause

strong interaction between substrate and adatoms and thus

increase the migration energy barriers of adatoms, (2) large

lattice mismatch between Si (100) surface and Pb 1− x Sn x Se

(≈10.4%) makes it unstable assuming Pb 1− x Sn x Se epitaxi-

ally grows along surface of Si with planar geometry. Even

anisotropic growth of layered materials such as MoS 2 is

strongly affected by surface electronic properties of growth

substrate. A recent work showed MoS 2 tended to form 1D

nanobelt structure on Si instead of 2D nanoplates on SiO 2 .

The higher surface energy of Si (100 meV Å −1 ) compared

with SiO 2 (2.5 meV Å −1 ) explains the occurrence of this

growth behavior. [ 46 ]

small 2015, DOI: 10.1002/smll.201501381

Figure 2. a) The free energies of the (100), (110), (111): Sn and (111): Te surfaces as functions of the relative Te chemical potential Δ µ Te . Wulff constructions of the thermodynamic equilibrium SnTe crystals under the Te-lean and Te-rich conditions are shown in the inset. Wulff constructions b) and SEM images c) of SnTe nanostructures when Te is not in rich. Wulff constructions d) and SEM images e) of SnTe nanostructures when Te is in rich. The scale bars in bottom of (e) are 200 nm. Reproduced with permission. [ 35 ] Copyright 2013, American Chemical Society. f) CVD growth schematic of SnTe nanoplates with SiO 2 /Si used as substrates. g) SnTe unit cell. h) (100) cubic crystals, grown without Au catalyst. i,j) (100) nanoplates. k) (100) nanoribbon. l–n) Nanowires with <100> growth direction. o) (111) nanoplate and p) (111) nanoribbon. Reproduced with permission. [ 50 ] Copyright 2014, American Chemical Society.



4. Surface Electronic Transport of Low-Dimensional TCIs

As mentioned before that, because their huge surface-to-

volume ratio notably magnifi es the transport of carriers from

surface sates, low-dimensional TCIs are better candidate for

detecting topological surface states by electrical transport. [ 47 ]

More intriguingly, it is easier to observe quantum interference

phenomenon in TCIs nanostructures, which could be under-

stood by the fact that (1) topological surface states have consid-

erable mobility and (2) physical size of low-dimensional TCIs

is comparable to phase coherent length of surface states. [ 48,49 ]

This section surveys the recent research results about topology-

related electronic transport on low-dimensional TCIs.

4.1. Quantum Coherence Transport of Topological Surface States

It is reasonable to deduce that, compared with bulk coun-

terpart, the wave nature of topological surface states in low-

dimensional TCIs is more remarkable. In 2013, our group fi rst

discovered Aharonov–Bohm (AB) interference of surface

Dirac electrons in SnTe nanowires. [ 36 ] AB interference is the

result of quantum interference of two partial electron waves

along edge of nanowires which encircle certain magnetic fl ux.

It was fi rst used to characterize topological surface states of

TIs nanostructures by Peng et al. in 2010. [ 7 ] In our work, we

additionally detected Altshuler–Aronov–Spival (AAS) effect

which arises from quantum interference of two interfering

electron waves encircling the magnetic fl ux once ( Figure 4 a).

Both AB and AAS effects deteriorate with the increase of

temperature because of the disturbing from thermal excita-

tion. We further found SnTe nanowire exhibits pronounced

Shubnikov–de Haas (SdH) oscillations under the exposure

of vertical magnetic fi eld (Figure 4 b). SdH oscillations are

ascribed to the successive emptying of Landau levels with

the increase of the magnetic fi eld. The LL fan diagram gives

the intercept of 0.42, indicating the SdH oscillations are of

2D nature. The mobility of surface states is estimated to be

4866 cm 2 V −1 s −1 which is comparable to that of conventional

TIs. This work is the fi rst evidence of topological surface

states in TCIs nanostructures by magneto-transport. Almost

simultaneously, topological surface states transport was

confi rmed in SnTe thin fi lm by Ando et al. [ 34 ] In this work

p-type SnTe thin fi lm was grown on n-type Bi 2 Te 3 thin fi lm

small 2015, DOI: 10.1002/smll.201501381

Figure 3. a,b) Schematic illustrations of van der Waals epitaxial ultrathin nonlayered materials, c) optical microscope, d–f) SEM, and h,i) AFM images of van der Waals epitaxial ultrathin 2D Pb 1− x Sn x Se nanoplates. g) Histogram of Pb 1− x Sn x Se nanoplates thickness, smooth curve is the Gaussian fi t of the thickness distribution. Reproduced with permission. [ 45 ] Copyright 2013, American Chemical Society.



by MBE. They observed SdH oscillation of Dirac fermions

residing on the SnTe (111) surfaces due to a downward band

bending on the free SnTe surface (Figure 4 c). Based on SnTe

nanoplates, Cha et al. reported a structural phase transition

of SnTe that it transforms from rock salt at high temperature

to rhombohedral structure at low temperature. [ 50 ] However,

the work has not presented the weak antilocalization (WAL)

effect of topological surface sates, which would be because

the SnTe nanoplates are too thick to enhance transport of

surface states.

Multiple Dirac nodes on each high-symmetry surface

bring more complexity to surface transport of TCIs nano-

structures. In addition to the coupling between bulk and sur-

face states, the hybrid of different Dirac states strongly affects

the numbers of the transport channels. Heiman et al. [ 33 ] care-

fully investigate the valley coupling of degenerate TCIs sur-

face in SnTe thin fi lm. As shown in Figure 4 d, the numbers of

carrier valleys (2 α ) extracted from the HLN model change

with Fermi level ( E F ). At low E F , no bulk sates are involved

in the charge transport and the Fermi surface contains four

small 2015, DOI: 10.1002/smll.201501381

Figure 4. a) AB and AAS interferences of topological surface states in SnTe nanowire. b) SdH oscillation of SnTe nanowire. Reproduced with permission. [ 36 ] Copyright 2013, American Chemical Society. c) Angle-dependent SdH oscillation of SnTe thin fi lm. Reproduced with permission. [ 34 ] Copyright 2013, American Physical Society. d) Numbers of transport channels as the function of Fermi level. e) Plot of phase coherence length versus numbers of transport channels. Reproduced with permission. [ 33 ] Copyright 2014, American Physical Society.



Dirac surface valleys. 2 α = 8 is expected to obtain in this case.

As the Fermi level increases to the point of Lifshitz transi-

tion ( E F = 0.05 eV), pairs of Dirac surface cones merge into

four pairs of concentric constant energy contours. Below

this point, the inner Dirac cone and the outer Dirac cone

host opposite chirality, which makes the quantum coherent

transport in this case extremely complicated. In addition,

the contribution of bulk sates to transport becomes more

and more important, the trivial bulk states swallow the inner

Dirac cone, thus reducing the 2 α to smaller than 2. As the

E F decrease to 0.2–0.5 eV, surface and bulk states coexist

and a maximum of 2 α = 4 can be obtained. With Fermi level

exceeding 0.5 eV, the 2 α sharply decreases which would be

due to the fact that the shape of the surface valleys changes

again in the deep Fermi level. Figure 4 e further shows that

the numbers of transport channel linearly decrease with the

increase of phase coherence length ( L ). The smaller experi-

mental 2 α means the stronger valley coupling and thus

results in a larger coherence length. The valley coupling may

result from the scattering between top and bottom surfaces

of SnTe thin fi lm. And, given the valley degeneracy of SnTe,

the coupling also likely comes from the scattering between

two Dirac states on the same surface. The coupling between

bulk and surface states has also been observed by Kuroda

et al. [ 51 ] who reported that both the numbers of transport

channel and phase coherence length decrease with increase

of temperature. This is because that thermal excited carriers

take part in the transport and interact with the surface states

at higher temperature. The above two works are crucial for

understating the mechanism of surface states transport.

4.2. Surface Transport Modulation

Unique properties of TCIs provide more degree to control

the surface states of low-dimensional TCIs. First, the Sn con-

tent ( x ) of Pb 1− x Sn x Te(Se) has a strong impact on the surface

electronic structure. For Pb 1− x Sn x Te, when Sn content goes

beyond 0.38 at 9 K, it undergoes a topological phase transi-

tion from trivial to nontrivial. Our group fi rst demonstrated

this characteristic in Pb 1− x Sn x Te nanowires by electric trans-

port. [ 52 ] By conducting the magneto-transport of Pb 1− x Sn x Te

nanowires, we observed the weak localization (WL) effect

in PbTe nanowires while WAL effects in Pb 0.5 Sn 0.5 Te and

Pb 0.2 Sn 0.8 Te nanowires. The PbTe nanowire exhibits the

semiconductive behavior of electrical transport. The thermal

activation energy ( E a ), extracted from R eE k T/c B≈ at high

temperature (260–133 K), is about 8.2 meV, where k B is the

Boltzmann constant. The change of magneto-conductance

at 2 K displays a sharp downward cusp near zero magnetic

fi eld, which is a signature of WL effect ( Figure 5 a). How-

ever, the Pb 0.5 Sn 0.5 Te shows metallic transport behavior and

WAL effect that the curve of Δ G versus magnetic fi eld B

shows upward cusp around zero magnetic fi eld (Figure 5 b).

The angle-traced magneto-transport confi rms that the WAL

effects originate from the 2D surface states. The topological

phase transition by composition engineering has also been

realized by Xiu et al. [ 53 ] in Pb 1− x Sn x Se thin fi lms. They also

found that strong electron–electron interaction caused the

large resistance of Pb 0.75 Sn 0.25 Se thin fi lms. Except the com-

position, surface states of TCIs can be modulated by thick-

ness and gate voltage. As the thickness of TCIs thin fi lm

reaches the critical value at which top surface and bottom

surface couple with each other, the resistance of thin fi lm

will dramatically increase due to the absence of topological

surface states in this case. Xiu et al. further pointed out the

critical value for Pb 1− x Sn x Se thin fi lm is 10 nm. The resistance

of 10 nm Pb 1− x Sn x Se thin fi lm is about one order of magni-

tude larger than that of 16 nm Pb 1− x Sn x Se thin fi lm. They

further performed the gate voltage modulation in the surface

states of 16 nm Pb 0.93 Sn 0.07 Se thin fi lms at 2 K. As shown in

Figure 5 c, the p-type Pb 0.93 Sn 0.07 Se thin fi lms shows WAL

effects by applying negative bias. The Berry phase ϕ is related

to the Fermi level by

[1 ( / (2 ))]FEϕ π= − Δ (1)

where Δ is the gap size. The Fermi level moves toward valence

band as the gate voltage decreases from positive value to

negative value. And thus E F becomes larger and Berry

phase approaches π . Interestingly, the competition between

quantum interference ( σ qi ) and the electron–electron interac-

tion ( σ ee ) also leads to the transition from WAL to WL effect.

As shown in Figure 5 d, at low temperature, the σ qi serves as

the dominant role and thus leads to the WL behavior due

to the trivial Berry phase of surface states. However, σ ee

becomes the main factor that affects the conduction correc-

tion at high temperature, giving rise to the WAL effect.

If introducing the exotic elements, TCIs nanostructures

will exhibit new electronic properties. In-doped SnTe has

been confi rmed to topological superconductor which hosts

Majorana fermions. [ 54 ] Majorana fermions are charge-neutral

particles whose antiparticles are themselves. They are attrac-

tive because of their great potential for using as a qubit of

fault-tolerant topological quantum computing. [ 55 ] Super-

conductor Cu x Bi 2 Se 3 was found to present unconventional

superconductivity in its point-contact spectra. Sn 1− x In x Te also

holds signatures of unconventional superconductivity which

are important for fi nding massless Majorana fermions. [ 56 ]

Superconductivity of Sn 1− x In x Te has recently been confi rmed

by the Cha group [ 57 ] and the Ando group [ 58 ] individually by

synthesizing Sn 1− x In x Te nanoplates and fabricating their Hall

devices. Cha et al. further pointed out In doping will pro-

foundly enhance the surface states of Sn 1− x In x Te nanoplates

since In doping deceases the bulk mobility. [ 57 ]

At the end of this section, we want to briefl y discuss the

thermoelectric conversion properties of TCIs. Although it is

still unclear whether topological surface properties of TCIs

have relation with their thermoelectric nature, we noticed

that almost all TCIs as well as TIs are excellent thermoelec-

tricity materials. [ 54 ] In this regard, Zhang et al. fi rst demon-

strated diameter dependence of thermoelectric properties of

individual SnTe nanowires. [ 59 ] They found the thermopower

enhances a magnitude of two orders with the decrease of

diameter from ≈913 to ≈218 nm, while, due to the increasing

boundary scattering and phonon-defect scattering, the

thermal conductivity is notably reduced with the decrease of

small 2015, DOI: 10.1002/smll.201501381


10 www.small-journal.com © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim small 2015, DOI: 10.1002/smll.201501381

nanowire diameter. As a result, the simultaneous increase of

thermopower and suppression of thermal conductivity results

in an improved fi gure of merit ZT.

5. Prospects

Despite great progress in synthesis and surface transport

of TCIs nanostructures, the depth and width of research on

low-dimensional TCIs are far less than that on conventional

TIs nanostructures. Previous research on conventional TIs

nanostructures supplies a paradigm for us to exploit novel

quantum behavior and potential applications of TCIs nano-

structures. Like TIs, high-speed and low-dissipation elec-

tronic devices are thought to be one of the most promising

applications for TCIs nanostructures. [ 60 ] Considering the

ultrahigh surface mobility of TCIs, [ 34,36 ] ultrafast logic devices

with low-thermal dissipation would be developed based on

top gate and back gate modulation.

What is more, since crystal symmetry warrants the sur-

face states of TCIs, new type of logic device can be realized

by applying vertical electrical fi eld in a dual-gated fi eld-

effect transistor. The strong vertical electrical fi eld breaks

the crystal symmetry and thus opens up the surface Dirac

cones. Furthermore, since crystal symmetry of TCIs can also

be destroyed by strain, highly sensitive pressure sensors are

expected to achieve in TCIs nanostructures. However, the

above two applications rely on ultrathin TCIs nanoplates

with high quality, which is an important opportunity as well

as a big challenge for materials scientist.

In order to realize surface states-based electronic devices,

one must lower the bulk carrier density. One way is to syn-

thesize the low-dimensional TCIs. [ 61 ] Among various nano-

structures, due to the dominant top and bottom surfaces, 2D

nanoarchitectures with distinct mirror-symmetry facets are the

best construction for exploring surface states. However, TCIs

are different from conventional TIs with layered structures

and time-reversal symmetry. TCIs are cubic crystal structure

and the surface states only reside on high symmetry surfaces.

Few-layer conventional TIs such as Bi 2 Se 3 and Bi 2 Te 3 have

been successfully grown by CVD due to its strong intrinsic

driving force for 2D anisotropic growth. However, it is diffi -

cult to do this for TCIs as a result of its nonlayered crystal

structures. Meanwhile, one needs to tailor the surface of TCIs

nanostructures to high symmetry crystal planes. Although our

group have grown Pb 1− x Sn x Se nanoplates with distinct (100)

surfaces by vdWE, ultrathin SnTe and Pb 1− x Sn x Te nanoplates

are not yet reported. Meanwhile, formation of impurities in

the TCIs nanostructures is inevitable during the growth and

device fabrication process. For example, Pb 1− x Sn x Se thin fi lm

and nanoplates are usually p-type doping caused by cation

vacancies. Cations compensation may minimize the density

of cation vacancies. One can further tune the mole ratio of

Pb to Sn in ternary TCIs such as Pb 1− x Sn x Se(Te). Similar to

the work on (Bi − Sb 1− x ) 2 Te 3 nanoplates, this way can push the

Fermi level to the middle of bandgap and thus profoundly

decrease the bulk states. Hybrid structure based on TCIs is

also attractive for chemist and material scientist. [ 62,63 ] Inter-

facing TCIs nanostructures with superconductor, ferromag-

netic insulator, and insulator will bring exotic properties. [ 64 ]

Figure 5. a) Dominated WL effect of PbTe nanowire at 2 K, inset is the SEM image of four-terminal device with scale bar of 2 µm. b) Temperature-dependent magnetoconductance of Pb 0.5 Sn 0.5 Te nanowire. Reproduced with permission. [ 52 ] Copyright 2015, American Chemical Society. c) Gate voltage-modulated surface transport of 16 nm Pb 0.93 Sn 0.07 Se thin fi lm at 2 K. d) Change of magnetoconductance of 16 nm Pb 0.93 Sn 0.07 Se thin fi lm at various temperatures. Reproduced with permission. [ 53 ] Copyright 2015, American Chemical Society.


11© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.small-journal.comsmall 2015, DOI: 10.1002/smll.201501381

For example, interface between superconductor and TCIs is

predicted to generate Majorana fermions.

6. Conclusion

TCIs have been the star materials in condensed matter

physics. The marvelous topological surface states, guaran-

teed by crystal symmetry, render scientists an opportunity

for developing fundamental physics as well as low-dissipa-

tion electronic devices. Compared with the bulk counterpart,

low-dimensional TCIs, due to their large surface to volume

ratio, are more ideal system for exploiting surface states.

This paper comprehensively summarizes the recent progress

in controllable growth of low-dimensional TCIs. The device

applications based on TCIs nanostructures are also carefully

reviewed. Although this paper covers only the very tip of

the iceberg, the intriguing properties of TCIs will excite the

interest of a broad research community. It is worth noting,

compared with TIs, much work on TCIs nanostructures has

been left to do. For example, it has not yet elucidated that

how strain controls surface states transport. The unique elec-

tronic properties of TCIs nanostructures such as multiple

surface states have not been very well documented either.

We believe low-dimensional TCIs will bring us more exciting

breakthroughs in the near future.

Acknowledgements

This work at National Center for Nanoscience and Technology was supported by 973 Program of the Ministry of Science and Tech-nology of China (No. 2012CB934103), the 100-Talents Program of the Chinese Academy of Sciences (No. Y1172911ZX), the National Natural Science Foundation of China (No. 21373065 and No. 61474033), and Beijing Natural Science Foundation (No. 2144059).

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