Nano Res

1

Group 14 element based noncentrosymmetric quantum

spin Hall insulators with large bulk gap

Yandong Ma1 (), Liangzhi Kou2, Aijun Du3, and Thomas Heine1 ()

Nano Res., Just Accepted Manuscript • DOI 10.1007/s12274-015-0842-7

http://www.thenanoresearch.com on June 19, 2015

© Tsinghua University Press 2015

Just Accepted

This is a “Just Accepted” manuscript, which has been examined by the peer-review process and has been

accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance,

which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP)

provides “Just Accepted” as an optional and free service which allows authors to make their results available

to the research community as soon as possible after acceptance. After a manuscript has been technically

edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP

article. Please note that technical editing may introduce minor changes to the manuscript text and/or

graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event

shall TUP be held responsible for errors or consequences arising from the use of any information contained

in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI®),

which is identical for all formats of publication.

Nano Research

DOI 10.1007/s12274-015-0842-7

www.theNanoResearch.com∣www.Springer.com/journal/12274 | Nano Research

TABLE OF CONTENTS (TOC)

Group 14 element based noncentrosymmetric quantum

spin Hall insulators with large bulk gap

Yandong Ma1*, Liangzhi Kou2, Aijun Du3, and Thomas

Heine1*

1Jacobs University Bremen, Germany

2University of New South Wales, Australia

3Queensland University of Technology, Australia

Based on first-principles calculations, we predict a new family of 2D

inversion asymmetric TIs with sizeable bulk gaps in X2-GeSn (X=H,

F, Cl, Br, and I) monolayers.

Provide the authors’ webside if possible.

Author 3, http://staff.qut.edu.au/staff/du9/

Author 4, https://www.jacobs-university.de/ses/theine

| www.editorialmanager.com/nare/default.asp

2 Nano Res.

Group 14 element based noncentrosymmetric quantum

spin Hall insulators with large bulk gap

Yandong Ma1 (), Liangzhi Kou2, Aijun Du3, and Thomas Heine1 ()

Received: day month year

Revised: day month year

Accepted: day month year

(automatically inserted by

the publisher)

© Tsinghua University Press

and Springer-Verlag Berlin

Heidelberg 2014

KEYWORDS

Two-dimensional crystal,

Topological insulators,

Dirac states, Band

inversion, Strain

engineering, Group 14

honeycomb lattice.

ABSTRACT

To date, a number of two-dimensional (2D) topological insulators (TIs) have

been realized in Group 14 elemental honeycomb lattice, but all are inversion

symmetric. Here, based on first-principles calculations, we predict a new family

of 2D inversion asymmetric TIs with sizeable bulk gaps from 105 meV to 284

meV, in X2-GeSn (X=H, F, Cl, Br, and I) monolayers, making them in principle

suitable for room-temperature applications. The nontrivial topological

characteristics of inverted band orders are identified in pristine X2-GeSn with

X=(F, Cl, Br, I), while for H2-GeSn, it undergoes a nontrivial band inversion at

8% lattice expansion. Topologically protected edge states are identified in

X2-GeSn with X=(F, Cl, Br, I) as well as in strained H2-GeSn. More importantly,

the edges of these systems, which exhibit single-Dirac-cone characteristics

located exactly in the middle of their bulk band gaps, are ideal for

dissipationless transport. Thus, Group 14 elemental honeycomb lattices make a

fascinating playground for manipulation of quantum states.

1 Introduction

Topological insulators (TIs) represent a new state of

quantum matter that has generated great interest

within the condensed matter physics community

[1-6]. A TI is characterized by an insulating energy

band gap in the bulk and gapless boundary states. In

two-dimensional (2D) TIs, also known as quantum

spin Hall (QSH) insulators, the conducting edge

states exhibit dissipationless, spin-polarized

conduction channels which are immune to

nonmagnetic scattering [7, 8]. Such properties make

Nano Research

DOI (automatically inserted by the publisher)

Research Article

Address correspondence to Y. Ma, myd1987@gmail.com; T. Heine, t.heine@jacobs-university.de

| www.editorialmanager.com/nare/default.asp

Nano Res.

2D TIs better suited for low-power-consumption

electronics and error-tolerant quantum computing as

compared to three-dimensional (3D) TIs. Although

quite a few compounds, such as Bi2Se3, Bi2Te3, and

Sb2Te3, are well-established to be 3D TIs

experimentally [3, 9, 10], up to now there are only

two systems, namely the HgTe/CdTe [8] and

InAs/GaSb [11] quantum wells, that are

demonstrated to be 2D TIs in experiments. Even

worse is that the QSH effect in such two 2D TIs can

only be observed at ultralow temperature due to the

small bulk band gap of the order of meV. The need

for searching new QSH insulators with large bulk

band gaps is thus clear.

To date, extensive effort has been devoted to the

search for new QSH insulators with large bulk band

gap and stable structure. Several families of QSH

insulators, such as Bi/Sb honeycomb lattices [12-14],

bilayers of Group 13 elements with Bi [15],

ZrTe5/HfTe5 [16], 2D transition metal dichalcogenides

[17], and Group 14 honeycomb lattices [18-23], have

been proposed theoretically. Particularly, the Group

14 honeycomb lattice based QSH insulators are

expected to be more practical and promising. This is

largely thanks to their easy integration of TI states in

conventional electronic devices resulting from their

similarity with conventional semiconductors in

structures and chemical composition, as well as their

high thermal stability and their fascinating and

tunable electronic properties. Examples include

graphene [24], silicene [19], germanenen [19], stanene

[22], and their chemically modified counterparts [13,

14, 18, 20, 21, 23]. The Group 14 honeycomb lattices

could in principle provide a common host for many

topological phenomena and potential topological

applications. However, one obstacle is that the

realization of QSH insulator materials made of

Group 14 honeycomb lattices is limited to inversion

symmetric TIs, and for this materials class no

inversion asymmetric QSH insulator has ever been

observed or predicted so far. For TIs with inversion

asymmetry, they could not only preserve many

nontrivial intriguing phenomena (i.e.,

crystalline-surface-dependent topological electronic

states [25, 26] and pyroelectricity [27]), but also offer

ideal platforms for realizing topological

magneto-electric effects [28, 29]. Therefore, one key

step toward future applications is to realize inversion

asymmetric TIs, especially those that are

electronically stable at room temperature.

Implementing those features in Group 14

honeycomb lattices would offer their integration

within the same honeycomb framework in Group 14

materials, such as germanene or stannene, and thus

potentially avoid contact resistance and other issues

of traditional device concepts.

Recently, Arguilla et al. [30] demonstrated that Sn

can be incorporated onto the 2D hydrogenated

germanene (germanane): they successfully

synthesized 2D Ge1−xSnxH1−x(OH)x graphane

analogue from the topochemical deintercalation of

CaGe2–2xSn2x. Inspired by this experimental work,

here, we provide a systematical investigation on the

electronic and topological properties of free-standing

2D Group 14 honeycomb GeSn halide and GeSn

hydride (X2-GeSn, X=H, F, Cl, Br, and I) monolayers

(MLs) based on ab initio calculations. We predict that

X2-GeSn MLs with X=(F, Cl, Br, I) are large-gap 2D

TIs, presenting protected Dirac edge states that are

spin locked to momentum, and thus forming QSH

systems. On the other hand, H2-GeSn ML displays

normal band order but can be transformed into a

nontrivial topological phase with large energy gap

via appropriate strain engineering. Notably, the QSH

effect can be observed in an experimentally

accessible temperature regime in all these systems,

making them suitable for applications at

room-temperature. The nontrivial topological states

in these MLs are firmly established by the

identification of band inversion and the existence of

the topologically nontrivial edge states. Meanwhile,

all these 2D TIs reported here preserve inversion

asymmetry, making them unprecedented inversion

asymmetric polar QSH insulator candidates. The

present work not only expands the catalog of Group

14 honeycomb lattice based QSH insulators, but also

provides ideal platforms for realizing novel

topological phenomena.

2 Computational methods

First principles calculations are performed within the

density functional theory (DFT) using the projector

augmented wave method [31] as implemented in the

Vienna ab initio simulation package (VASP) [32, 33].

We employ the Heyd-Scuseria-Ernzerhof hybrid

www.theNanoResearch.com∣www.Springer.com/journal/12274 | Nano Research

Nano Res.

functional (HSE06) [34], which is well-known to

correctly predict the electronic structure. This

functional is computationally more involved than the

generalized gradient approximation (GGA).

Therefore, for the calculation of edge states, being

computationally very involved, we have employed

the GGA, i.e. the Perdew−Burke−Ernzerhof (PBE)

functional [35]. For the interested theorist, a

comprehensive comparison between the results

obtained by PBE and HSE06 is presented in the

Supplementary Material. In short, while the PBE

electronic structure is generally in excellent

agreement with HSE06, as common in GGA the

conduction bands are shifted to lower energies and

consequently band inversions are predicted for

lattice elongations of 6% and higher. Strain is

simulated by changing the in-plane lattice constant a.

After applying strain, the atomic structure is

reoptimized. The magnitude of biaxial strain is

defined as ε = (a-a0)/a, where the lattice constant of

the strained and unstrained systems is equal to a and

a0, respectively. The plane-wave-cutoff energy is set

to 500 eV and the atoms are allowed to fully relax

until the force acting on each atom is less than 0.01

eV/Å . A vacuum space of no less than 18 Å between

neighboring systems is used. The Monkhorst and

Pack scheme [36] of k-point sampling is used for

integration over the first Brillouin zone. A 17×17×1

grid for k-point sampling is used for both geometry

optimization and self-consistent calculations.

3 Results and discussion

H2-GeSn ML is a strict graphane analogue, as

displayed in Fig. 1(a), where Ge and Sn atoms

exhibit sp3 hybridization which gives rise to the

buckled geometry as formed by the carbon atoms in

graphane [37]. The H-Ge bond is a little shorter than

that of H-Sn, which is rationalized by the different

atomic radii of the Group 14 elements and by the

difference in electronegativity. Fig. 1(b) shows the

variation of the total energy of H2-GeSn ML as a

function of the in-plane lattice constant a, where the

lattice constant a is varied to identify the structural

ground state. And the atomic positions are fully

relaxed at each fixed lattice constant. We observe two

energy minimums for H2-GeSn: At a=3.16 Å , a

strongly corrugated (S) minimum occurs, while a

second minimum with weaker corrugation (W) is

observed for a=4.41 Å . Such double-well energy

curve was also found in almost all of the previously

reported graphene-like systems [15, 38, 39]. The W

structure of H2-GeSn is more stable by 1.26 eV per

H2-GeSn formula unit. Therefore, in the remainder

we will focus on the more stable W structure. The

energy difference between H2-GeSn ML and its

homogeneous counterparts stannane and germanane,

defined as EH2-GeSn– 0.5(EH2-GeGe+EH2-SnSn), is only 32

meV per formula unit, indicating that H2-GeSn ML

could be stable. The stability of H2-GeSn ML is

further confirmed by the calculation of phonon

dispersion curves which are shown in Fig. 1(c) with

all vibrational modes having real frequencies.

Figure 1 (a) Structural model (top and side views) of X2-GeSn

ML; the violet, green, and dark yellow balls indicate Ge, Sn, and

X=(H, F, Cl, Br, and I) atoms, respectively. (b) Energy versus

hexagonal lattice constant of X2-GeSn ML. (c) Phonon

dispersion curves for W H2-GeSn ML.

The electronic band structure of H2-GeSn ML

without spin-orbit coupling (SOC) is depicted in Fig.

2(a). A direct band gap of 1.155 eV is predicted at the

Γ point. Away from Γ point, the conduction and

valence bands are well separated, we therefore only

focus on the bands around Γ point. By projecting the

bands onto different atomic orbitals we observe that

the conduction band minimum and the valence band

maximum at Γ point are mainly composed of one s

and two p orbitals, respectively, see Fig. 2(a). Here,

the two p orbitals are energy-degenerated. In trivial

insulators, such as graphane, the s orbital is typically

located above the two p orbitals in energy.

Consequently, H2-GeSn ML shows a semiconducting

nature with normal band order. When SOC is

| www.editorialmanager.com/nare/default.asp

Nano Res.

switched on, as shown in Fig. 2(f), the degeneracy of

p orbitals is lifted but the energy gap is maintained

although the gap size is reduced (0.977 eV). By

including SOC, no band inversion can be observed,

suggesting H2-GeSn ML is a normal insulator.

Figure 2 Energy band structure without (upper panels)

and with (lower panels) SOC for H2-GeSn ML with (a and

f) 0%, (b and g) 2%, (c and h) 4%, (d and i) 6%, and (e and j)

8% lattice expansion. Zero of energy is set at the Fermi

level. Insert: the main projection of the bands near the

Fermi level at Γ point.

External mechanical strain can reduce the band

gap size, which in turn, might introduce band

inversion even in systems with relatively weak SOC.

It can be seen clearly from Fig. 2 that the band

structure of H2-GeSn ML is indeed sensitive to the

lattice expansion and the gap values versus lattice

expansion are plotted in Fig. 3. From Fig. 2(a)-(e) and

Fig. 3 we can observe that, for H2-GeSn ML without

SOC, by increasing lattice expansion the conduction

band minimum at Γ point (that is the s state, as

labeled in Fig. 2) is gradually lowered in energy. This

yields a significant reduction of the global band gap

as well as the energy difference (Es-p) between the s

state and the upper p state at Γ point just around the

Fermi level. Without SOC, we do not observe a band

inversion in the band structure of H2-GeSn ML for

lattice expansions of up 8% [see Fig. 2(a)-(e)]. Thus,

the band inversion cannot be induced solely by

lattice expansion. Our phonon calculations suggest

that H2-SnGe ML can maintain its stability within

the strain range of 8% (see Fig. S1). By introducing

SOC, when the lattice expansion changes from 0% to

6%, the two p states still appear below the s state at

the Γ point, as shown in Fig. 2, indicating the

topologically trivial phase in H2-GeSn ML is still

unchanged. When the lattice expansion researches

8%, remarkably, one of the p orbitals shifted above

the s orbital. This suggests that the inversion of two

bands, which is a strong indication for the formation

of nontrivial topological states in H2-GeSn ML,

implying that H2-GeSn ML with 8% is a 2D TI.

Further proof, edge state calculations, will be shown

below. More importantly, the magnitude of the

nontrivial topological bulk band gap is 105 meV,

which is significantly larger than thermal

perturbation kBT at room temperature (26 meV). We

can therefore conclude that the QSH effect may be

measured in strained H2-GeSn ML at room

temperature.

Although the electronic and topological properties

of H2-GeSn ML are strongly sensitive to the lattice

expansion as well as to the choice of functional (see

Figure S2), the SOC-induced energy splitting (ESOC)

between the two p orbitals at Γ point around Fermi

level is not. This can be clearly seen in Fig. 3(a) and

(b) that ESOC remains unaffected with increasing

lattice expansion and is also irrespective of the choice

of PBE or HSE06 functional. These may be

understood by the fact that SOC strength is an

intrinsic property of the material and is hard to be

affected. Another interesting feature we can observe

is that ESOC based on PBE is almost similar to that

based on HSE06, see Fig. 3(a) and (b). This origin of

the similarity derives from that the ESOC is created by

SOC between the bonding and antibonding states of

the p orbitals in H2-GeSn ML which exhibits

relatively weak correlation effect.

X2-GeSn ML with X=(F, Cl, Br, I) shares a similar

geometric structure as H2-GeSn ML. As shown in Fig.

1(b), the variation of the total energy of X2-GeSn ML

with X=(F, Cl, Br, I) as a function of the hexagonal

lattice constant a also exhibits a double-well energy

curve, corresponding to S and W configurations.

And also for these MLs, the W structure is more

stable in energy and thus will be discussed in the

following. The energy difference between X2-GeSn

ML and its homogeneous counterparts, stannane and

germanane, is only 29, 22, 15, and 2 meV per formula

unit, respectively, indicating that X2-GeSn ML could

also be stable. From Fig. 1(b), we can observe that the

www.theNanoResearch.com∣www.Springer.com/journal/12274 | Nano Research

Nano Res.

lattice constant of X2-GeSn ML gradually decreases

with moving X from F to I; however, all of them are

significantly larger than that of the H2-GeSn ML. The

energy band structures of X2-GeSn ML with X=(F, Cl,

Br, I) are depicted in Fig. 4. In the case without SOC,

X2-GeSn ML with X=(F, Br, I) are semimetalic with

the valence band maximum and conduction band

minimum touching at the Γ point just at the Fermi

level, which indicates different electronic properties

from those of H2-GeSn ML. For all these four

systems, the states around the touching point are

dominated by the degenerated p orbitals.

Noteworthy, the s orbital at Γ point around the Fermi

level, which is normally located above the two p

orbitals, shifts downwards and lies below the two p

orbitals, implying the existence of nontrivial band

Figure 3 Global energy gaps with and without SOC, energy difference (Es-p) between the s and upper p orbitals at Γ point with and

without SOC, and the SOC strength (ESOC) as a function of lattice expansion for H2-GeSn ML calculated by (a) PBE and (b) HSE06

functional. (c) Global energy gaps of X2-GeSn ML with X=(F, Cl, Br, I). Insert in (a) and (c) plot the dipole moment of H2-GeSn versus

lattice expansion and the dipole moment of X2-GeSn versus X=(F, Cl, Br, I), respectively.

Figure 4 Energy band structure without (upper panels) and with

(lower panels) SOC for X2-GeSn ML with X=(F, Cl, Br, I). Zero

of energy is set at the Fermi level. Insert: the main projection of

the bands near the Fermi level at Γ point.

order at Γ point even without considering SOC.

However, for Cl2-GeSn ML, it preserves normal

band order, with the s orbital locating above the p

orbitals, instead of the nontrivial band order. The

band gap in Cl2-GeSn ML is so small that the band

order at Γ point for Cl2-GeSn ML can be inverted by

turning on SOC, leading to a nontrivial band order in

Cl2-GeSn ML. From Fig. 4, we can find that, after

turning on SOC, X2-GeSn MLs with X=(F, Cl, Br, I)

are in insulating phases with nontrivial band orders

at Γ point, which strongly suggests that X2-GeSn

MLs with X=(F, Cl, Br, I) are 2D TIs. This indicates

that, in contract to the case of H2-GeSn ML, X2-GeSn

ML with X=(F, Cl, Br, I) is a 2D TI without applying

any external strain. In fact, concerning the relation

between the lattice constant and the band structure,

we can find that X2-GeSn ML with X=(F, Cl, Br, I)

behaves like a tensile strained H2-GeSn ML.

Moreover, as indicated in Fig. 3(c), the inclusion of

SOC produces a topologically nontrivial band gap of

187, 124, 174, and 284 meV, respectively, for X2-GeSn

ML with X=(F, Cl, Br, I). Such large nontrivial band

| www.editorialmanager.com/nare/default.asp

Nano Res.

gaps are capable of stabilizing the boundary current

against the influence of thermally activated bulk

carriers, and thus are beneficial for high-temperature

applications.

Figure 5 The calculated edge states for (a) strained H2-GeSn ML

and (c) F2-GeSn ML. (b) The zigzag nanoribbon used in the

edge calculations. Zero of energy is set at the Fermi level.

The topologically nontrivial insulating nature in

X2-GeSn ML should support an odd number of

Dirac-like topologically protected edge states

connecting the valence and conduction bands. In

order to further confirm the topological phases of

these MLs, we calculate the edge states of X2-GeSn

ML by constructing a zigzag nanoribbon structure

based on a slab model (a 8% lattice expansion is

employed for H2-GeSn ML). Here, all the dangling

bonds at edge sites are passivated by hydrogen

atoms. Such a nanoribbon structure is asymmetric

with GeH and SnH chains terminated at each side.

(see Fig. 5(b)). The nanoribbon widths exceed 10 nm

to avoid the interaction between two edges. The

calculated electronic structures, for computational

reasons only at the less expensive PBE level, of

X2-GeSn MLs are presented in Fig. 5 and Fig. S5. It

can be seen clearly that two sets of conducting edge

states in the energy gap crossing linearly at Γ point,

reflecting the two opposite edges of the nanoribbon.

The edge states marked with red and blue lines

correspond to the top and bottom edges, respectively.

The appearance of such gapless helical edge states

inside the bulk band gap is consistent with the band

inversion identification, which further prove that

X2-GeSn ML with X=(F, Cl, Br, I) and the H2-GeSn

ML with 8% strain are indeed QSH insulators. It is

worth noting that each edge is supposed to possess

edge states with different band dispersions due to

their asymmetric nanoribbon structures. However,

there is no significant difference between the two

edge states in each X2-GeSn ML and the two Dirac

points in each system are all located exactly at the

Fermi level. Considering the large nontrivial bulk

energy gaps, such X2-GeSn ML might be ideal

platforms for realizing QSH effect and are highly

desirable for the applications of topological edge

states in electronic and spintronic devices.

Apart from the interesting topological properties

demonstrated in these MLs, remarkably, the valence

band maximum also experience a significant band

splitting and a slight shift off the Γ point as shown in

Fig. 4. It is well known that in systems with inversion

symmetry, all the energy states are spin-degenerated

as long as the time-reversal symmetry is held.

Breaking inversion symmetry lifts such degeneracy

and leaves the energy states being spin-splitted at

generic k points. Such characteristics in X2-GeSn ML

originate from the local dipole field which is induced

by its inversion asymmetric structure. In X2-GeSn

ML, the X, Ge, Sn and X layers stack alternatingly,

giving rise to the polarity along the stacking axis.

The corresponding dipole moments of X2-GeSn ML

are listed in the insert of Fig. 3. The existence of

dipole moments in X2-GeSn ML with X=(F, Cl, Br, I)

as well as H2-GeSn ML with 8% strain strongly

indicates that all these systems are inversion

asymmetric QSH insulators. It should be noted that

up to now, only strained HgTe has been

experimentally realized and proved to be a 2D TI

with inversion asymmetry, but displays a rather

small energy gap (~20 meV) [40]. While for all the

previously reported Group 14 honeycomb lattice

based TIs, they are all inversion symmetric, severely

limiting their realistic applications. With the

advancement in experiment techniques, several

possible routes reported in recent works [15, 41] are

expected to be viable for synthesizing GeSn ML.

With synthesized GeSn ML, X2-GeSn ML can be

manufactured by employing the method for

preparing hydrogenated graphene [42]. Furthermore,

for actual applications, one critical concern is the

interface effect on the topological properties. To this

end, one should look for a substrate with minimal

www.theNanoResearch.com∣www.Springer.com/journal/12274 | Nano Research

Nano Res.

interfacial interaction with X2-GeSn ML (such as the

passivated substrates), and a more comprehensive

study concerning these problems should be carried

out in further works.

4 Conclusions

In conclusion, we have investigated the electronic

and topological properties of X2-GeSn ML by means

of ab initio calculations. We find that X2-GeSn MLs

with X=(F, Cl, Br, I) are QSH insulators, while for

H2-GeSn ML a topological phase transition can be

found at a 8% lattice expansion. Remarkably, all

these systems display large nontrivial topological

band gaps, which potentially can support their

applications under room temperature. More

interestingly, X2-GeSn ML with X=(F, Cl, Br, I) and

H2-GeSn ML with 8% strain are all in inversion

asymmetric topological insulator phases, making

them ideal candidates for realizing new topological

phenomena. The artificial honeycomb lattices

reported here can be prototypes for future

exploration of new inversion asymmetric QSH

insulators with large nontrivial band gaps.

Acknowledgments

Financial support by the European Research Council

(ERC, StG 256962) is gratefully acknowledged.

Electronic Supplementary Material: Phonon

dispersion curves for strained H2-GeSn ML, energy

band structure for H2-GeSn ML with different lattice

expansions calculated with PBE, phonon dispersion

curves for X2-GeSn ML with X=(F, Cl, Br, I), energy

band structure for X2-GeSn ML with X=(F, Cl, Br, I)

calculated with PBE, and calculated edge states for

Cl2-GeSn, Br2-GeSn, and I2-GeSn MLs are available

in the online version of this article at

http://dx.doi.org/10.1007/s12274-***-****-*

References [1] Moore, J. E. The birth of topological insulators. Nature 2013,

464, 194-198.

[2] Hasan, M. Z.; Kane, C. L. Colloquium: Topological

insulators. Rev. Mod. Phys. 2010, 82, 3045.

[3] Zhang, H. J.; Liu, C.-X.; Qi, X.-L.; Dai, X.; Fang, Z.; Zhang,

S.-C. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3

with a single Dirac cone on the surface. Nat. Phys. 2009, 5,

438-442.

[4] Yan, B. H.; Jansen, M.; Felser, C. A large-energy-gap oxide

topological insulator based on the superconductor BaBiO3.

Nature Phys. 2013, 9, 709-711.

[5] Kou, L. Z.; Wu, S.-C.; Felser, C.; Frauenheim, T.; Chen, C.

F.; Yan, B. H. Robust 2D topological insulators in van der

Waals heterostructures. ACS Nano 2014, 8(10),

10448-10454.

[6] Ma, Y. D.; Dai, Y.; Guo, M.; Niu, C. W.; Huang, B. B.

Intriguing behavior of halogenated two-dimensional tin. J.

Phys. Chem. C 2012, 116, 12977–12981.

[7] Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C. Quantum spin

Hall effect and topological phase transition in HgTe

quantum wells. Science 2006, 314, 1757-1761.

[8] König, M.; Wiedmann, S.; Brüne, C.; Roth, A.; Buhmann, H.;

Molenkamp, L. W.; Qi, X.-L.; Zhang, S.-C. Quantum spin

Hall insulator state in HgTe quantum wells. Science 2007,

318, 766-770.

[9] Chen, Y. L.; Analytis, J. G.; Chu, J.-H.; Liu, Z. K.; Mo, S.-K.;

Qi, X. L.; Zhang, H. J.; Lu, D. H.; Dai, X.; Fang, Z.; Zhang,

S. C.; Fisher, I. R.; Hussain, Z.; Shen, Z.-X. Experimental

realization of a three-dimensional topological insulator,

Bi2Te3. Science 2009, 325, 178-181.

[10] Xia, Y.; Qian, D.; Hsieh, D.; Wray, L.; Pal, A.; Lin, H.;

Bansil, A.; Grauer, D.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z.

Observation of a large-gap topological-insulator class with a

single Dirac cone on the surface. Nat. Phys. 2009, 5,

398-402.

[11] Knez, I.; Du, R.-R.; Sullivan, G. Evidence for helical edge

modes in inverted InAs/GaSb quantum wells. Phys. Rev.

Lett. 2011, 107, 136603.

[12] Murakami, S. Quantum spin Hall effect and enhanced

magnetic response by spin-orbit coupling. Phys. Rev. Lett.

2006, 97, 236805.

[13] Ma, Y. D.; Dai, Y.; Kou, L. Z.; Frauenheim, T.; Heine, T.

Robust two-dimensional topological insulators in

methyl-functionalized bismuth, antimony, and lead bilayer

films. Nano Lett. 2005, 15, 1083-1089.

[14] Liu, C.-C.; Guan, S.; Song, Z.; Yang, S. A.; Yang, J.; Yao,

Y. Quantum spin Hall insulators and quantum valley Hall

insulators of BiX/SbX (X=H, F, Cl and Br) monolayers

with a record bulk band gap. NPG Asia Mater. 2014, 6, 147.

[15] Chuang, F.-C.; Yao, L.-Z.; Huang, Z.-Q.; Liu, Y.-T.; Hsu,

C.-H.; Das, T.; Lin, H.; Bansil, A. Prediction of large-gap

two-dimensional topological insulators consisting of

bilayers of group III elements with Bi. Nano Lett. 2014, 14,

2505-2508.

[16] Weng, H.; Dai, X.; Fang, Z. Transition-metal pentatelluride

ZrTe5 and HfTe5: A paradigm for large-gap quantum spin

Hall insulators. Phys. Rev. X 2014, 4, 011002.

[17] Qian, X. F.; Liu, J. W.; Fu, L.; Li, J. Quantum spin Hall

effect in two-dimensional transition metal dichalcogenides.

Science, 2014, 346, 1344-1347.

[18] Xu, Y.; Yan, B. H.; Zhang, H.-J.; Wang, J.; Xu, G.; Tang, P.;

Duan, W. H.; Zhang, S.-C. Large-gap quantum spin Hall

insulators in tin films. Phys. Rev. Lett. 2013, 111, 136804.

(19) Liu, C.-C.; Feng, W. X.; Yao, Y. G. Quantum spin Hall

effect in silicene and two-dimensional germanium. Phys.

Rev. Lett. 2011, 107, 076802.

(20) Ma, Y. D.; Dai, Y.; Wei, W.; Huang, B. B.; Whangbo, M.-H.

Strain-induced quantum spin Hall effect in

| www.editorialmanager.com/nare/default.asp

Nano Res.

methyl-substituted germanane GeCH3. Sci. Rep. 2014, 4,

7297.

(21) Ma, Y. D.; Dai, Y.; Niu, C. W.; Huang, B. B. Halogenated

two-dimensional germanium: Candidate materials for being

of quantum spin Hall state. J. Mater. Chem. 2012, 22,

12587-12591.

(22) Liu, C.-C.; Jiang, H.; Yao, Y. G. Low-energy effective

Hamiltonian involving spin-orbit coupling in silicene and

two-dimensional germanium and tin. Phys. Rev. B 2011, 84,

195430.

(23) Si, C.; Liu, J. W.; Xu, Y.; Wu, J.; Gu, B.-L.; Duan, W. H.

Functionalized germanene as a prototype of large-gap

two-dimensional topological insulators. Phys. Rev. B 2014,

89, 115429.

(24) Kane, C. L.; Mele, E. J. Quantum spin Hall effect in

graphene. Phys. Rev. Lett. 2005, 95, 226801.

(25) Chen, Y. L.; Kanou, M.; Liu, Z. K.; Zhang, H. J.; Sobota, J.

A.; Leuenberger, D.; Mo, S. K.; Zhou, B.; Yang, S.-L.;

Kirchmann, P. S.; Lu, D. H.; Moore, R. G.; Hussain, Z.;

Shen, Z. X.; Qi, X. L.; Sasagawa, T. Discovery of a single

topological Dirac fermion in the strong inversion

asymmetric compound BiTeCl. Nat. Phys. 2013, 9,

704-708.

(26) Bahramy, M. S.; Yang, B.-J.; Arita. R.; Nagaosa, N.

Emergence of non-centrosymmetric topological insulating

phase in BiTeI under pressure. Nature Comm. 2012, 3, 679.

(27) Wan, X.; Turner, A. M.; Vishwanath, A.; Savrasov, S. Y.

Topological semimetal and Fermi-arc surface states in the

electronic structure of pyrochlore iridates. Phys. Rev. B

2011, 83, 205101.

(28) Brüne, C.; Liu, C. X.; Novik, E. G.; Hankiewicz, E. M.;

Buhmann, H.; Chen, Y. L.; Qi, X. L.; Shen, Z. X.; Zhang, S.

C.; Molenkamp. L. W. Quantum Hall effect from the

topological surface states of strained bulk HgTe. Phys. Rev.

Lett. 2011, 106, 126803.

(29) Kuroda, K.; Ye, M.; Kimura, A.; Eremeev, S. V.;

Krasovskii, E. E.; Chulkov, E. V.; Ueda, Y.; Miyamoto, K.;

Okuda, T.; Shimada, K.; Namatame, H.; Taniguchi, M.

Experimental realization of a three-dimensional topological

insulator phase in ternary chalcogenide TlBiSe2. Phys. Rev.

Lett. 2010, 105, 146801.

(30) Arguilla, M. Q.; Jiang, S. S.; Chitara, B.; Goldberger, J. E.

Synthesis and stability of two-dimensional Ge/Sn graphane

alloys. Chem. Mater. 2014, 26, 6941-6946.

(31) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to

the projector augmented-wave method. Phys. Rev. B 1999,

59, 1758-1775.

(32) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total

energy calculations for metals and semiconductors using a

plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15-50.

(33) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab

initio total-energy calculations using a plane-wave basis set.

Phys. Rev. B 1996, 54, 11169-11186.

(34) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid functionals

based on a screened Coulomb potential. J. Chem. Phys.

2003, 118, 8207-8215.

(35) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized

gradient approximation made simple. Phys. Rev. Lett. 1996,

77, 3865-3868.

(36) Monkhorst, H. J.; Pack, J. D. Special points for

Brillouin-zone integrations. Phys. Rev. B 1976, 13,

5188-5192.

(37) Sofo, J. O.; Chaudhari, A. S.; Barber, G. D. Graphane: A

two-dimensional hydrocarbon. Phys. Rev. B 2007, 75,

153401.

(38) Cahangirov, S.; Topsakal, M.; Akturk, E.; Şahin, H.; Ciraci,

S. Two- and one-dimensional honeycomb structures of

silicon and germanium. Phys. Rev. Lett. 2009, 102, 236804.

(39) Şahin, H.; Cahangirov, S.; Topsakal, M.; Bekaroglu, E.;

Akturk, E.; Senger, R. T.; Ciraci, S. Monolayer honeycomb

structures of group-IV elements and III-V binary

compounds: First-principles calculations. Phys. Rev. B 2009,

80, 155453.

(40) Chen, Y. L.; Liu, Z. K.; Analytis, J. G.; Chu, J.-H.; Zhang,

H. J.; Yan, B. H.; Mo, S.-K.; Moore, R. G.; Lu, D. H.;

Fisher, I. R.; Zhang, S. C.; Hussain, Z.; Shen, Z.-X. Single

Dirac cone topological surface state and unusual

thermoelectric property of compounds from a new

topological insulator family. Phys. Rev. Lett. 2010, 105,

266401.

(41) Zhou, M.; Ming, W.; Liu, Z.; Wang, Z.; Li, P.; Liu, F.

Epitaxial growth of large-gap quantum spin Hall insulator

on semiconductor surface. PNAS 2014, 111, 14378-14381.

(42) Elias, D.; Nair, R. R.; Mohiuddin, T. M.; Morozov, S. V.;

Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.;

Katsnelson, M. I.; Geim, A. K.; Novoselov, K. S. Control of

graphene's properties by reversible hydrogenation: Evidence

for graphane. Science 2009, 323, 610-613.