Strain-Induced Topological Insulator in Methyl-Decorated SiGe Films

Subscriber access provided by UNIV OF LOUISIANA

Article

Strain-Induced Topological Insulator in Methyl-Decorated SiGe Films Tamiru Teshome, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08485 • Publication Date (Web): 08 Oct 2018 Downloaded from http://pubs.acs.org on October 13, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Strain-Induced Topological Insulator in Methyl-Decorated SiGe Films Tamiru Teshome and Ayan Datta* School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A, and 2B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, West Bengal, India. Email: [email protected]

ABSTRACT: Since the discovery of topological insulators (TIs), there has been much research into prediction and experimentally discovering distinct classes of these materials, in which the bulk insulating but helical edge states are conducting in the absence of magnetic field. Herein, using first principle calculations along with tight-binding model, methyl decorated SiGe film is shown to undergo a topological phase transition under external tensile strain. The band gap can be tuned by the tensile strain, and at critical strain (ε = 8 %) at ᴦ-point opens a gap Eg = 0.35 eV due to band inversion. The nonzero topological invariant and helical edge states are further confirmed by topological invariant, Z2 = 1, for stretched SiGeCH3. Thus, a large energy gap induced by SOC and tensile strain indicates that methyl-decorated SiGe film is quite promising to design 2D TIs materials for practical application. Moreover, for design and fabrication of topological electronic devices, we propose a bilayer of h-BN as suitable substrate for supporting SiGeCH3 film without perturbing the nontrivial topology.

toxicity and incompatibility with silicon-based devices.

Introduction Topological insulators (TIs), have emerged as a new

Several graphene analogs of other carbon family

quantum state of matter, known as QSH insulators for

elements have a nontrivial topological phase, such as

which though the bulk has an insulating state yet it has

honeycomb lattices of silicene and germanene7, stanene8

conducting edge states which are topologically protected

and plumbene9 exhibit topological phase transition from

due to time-reversal symmetry (TRS) and spin-orbit

normal insulators (NIs) to TIs due to SOC and external

In 2005 Kane and Mele

pressure. Though silicene in native structure has been

proposed a new topological insulator state theoretically

synthesized,10-12 but it strongly interacts with the

based on calculations on graphene.3 Unfortunately, the

substrate. However, till now, no free-standing silicene

coupling (SOC)

interaction.1,2

SOC gap in graphene is very small

(~10-3

meV), which

have been synthesized experimentally, and its QSH

limits its observation experimentally. However, TIs have

insulator might be observed only at low temperature.13

been experimentally demonstrated in HgTe/CdTe4 and

To design 2D TIs for practical application in electronic

InAs/GaSb5 quantum wells at a very low temperature

device, two key points are essential: (1) the materials

(below 10 K) limited by their small band gap. Recently,

must have sizable large bulk gap to realize TI at room

bismuthene grown on a substrate-support of SiC for QSH

temperature, and (2) they must be compatible with the

at a high-temperature has been experimentally achieved

current silicon-based electronic technology device.

Unfortunately, the HgTe-

Closely related to silicon in terms of compatibility, the

CdTe quantum well and their predicted analogues have

search of 2D TIs has been extended to hydrogenated,

serious limitation including difficulty of fabrication,

halogenated and methyl-decorated of germanene, stanene

with a band gap of 0.8

eV.6

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 12

and plumbene which have been explored for nontrivial

applied in SCF for the calculation electronic

topological insulators with sizable energies gaps induced

properties. Additionally, the Hybrid Heyd-Scuseria-

by SOC. On other hand, a trivial to nontrivial phase

Ernzerhof (HSE06)28 functional is used to obtained

transition can be achieved by chemical doping or

more realistic estimate of the band gap. Phonon

alloying the

composition.14-16

Strain modification can

calculations is performed by using the PHONOPY29

also render in a TIs phase without any doping.17-21

code combined with density functional perturbation

Hence,

strain

theory (DFPT) method in VASP. Wannier Charge

circumvents the difficulty of unwanted inhomogeneity of

Center (WCC) were obtained from the WANNIER90

doping and defects.

package.30

physical

tuning

like

pressure

or

The

topological

invariant,

Z2

was

computed using the Z2pack. Chemical functionalization of monolayers is an effective channel to modify the electronic and topology of the 2D

Results and Discussion

materials. For example, GeCH3 and SnCH3 were

SiGeCH3 has a hexagonal structure with buckling where

Hence,

Si and Ge atoms are sandwiched between two sheets of

a NIs to TIs under strain can be interesting in 2D

CH3 groups. There are one Si, one Ge atom and two CH3

materials system for quantum devices. Furthermore, the

on alternating sides forming a rhombohedral unit cell as

stability of the material can also be modified by the

represented by the shaded region and dotted line as

removal of surface activity. Motivated by this point, we

shown in Fig. 1(a). The optimized structure has buckling

suggest methyl decorated SiGe film to be excellent

height (h), Si-Ge bond length (d), lattice constant and

candidates to achieve QSH insulator.

bond angle (θ) as 0.79 Å, 2.41 Å, 3.91 Å and 109.68˚,

predicted to produce a nontrivial TIs ε = 12

%.8,22

respectively. The bond angle is larger than the free standing of 2D SiGe monolayer.20Such significantly

Computational Details In this article, the first principle calculations were

buckled structure can result in higher tolerance towards

implemented by using the Vienna ab initio simulation

tensile strain modification and better stretching of 2D

package (VASP).23The projector-augmented-wave

material. Therefore, we utilize tensile strain as one of the

(PAW)24 potential, Perdew-Burke-Ernzerhof (PBE)

strategies to tune the electronic properties of chemical

exchange-correlation

functional.25,26

To avoid the

decorated 2D SiGe film. The variation of buckling

interaction between periodic images a vacuum space

height, Si-Ge bond length, buckling angle are defined as

to be set 25 Å. The kinetic-energy cutoff plane-wave

Δh = (h-ho)ho, Δl = (l-lo)lo and Δθ = (θ-θo)θo, respectively

expansion is set 500 eV. All the atoms in the unit

where h, l and θ are geometry parameters in strained

cell are fully relaxed until the forces on each atom is

SiGeCH3 monolayer as presented in Fig. 1(b). The bond

less than 0.001 eV/Å. Furthermore, the Brillouin

length and bond angle increase with higher tensile strain.

zone (BZ) was sampled by using 15 × 15 × 1

In contrast, increase in strain decreases the buckling

Gamma-centered

Tensile

height. Therefore, when a tensile strain is induced, Si-Ge

strained was expressed as 𝜀 = ∆𝑎/𝑎𝑜, where 𝑎𝑜 is the

bond is stretched and the lattices parameters are relaxed

equilibrium lattice and ∆𝑎 + 𝑎𝑜 is the strained

accordingly as shown in Table S1.

Monkhorst-Pack

grid.

modified lattice. The spin-orbital coupling27 were


Page 3 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: (a) Top and side views of a SiGeCH3 monolayer. The blue, pink, yellow and cyan balls denote Si, Ge, C and H atoms, respectively. The shaded region represents the unit-cell of SiGeCH3 monolayer. (b) Variation of buckling height (Å), Si-Ge bond length (Å), lattice parameter (Å), and angle (degrees), as a function of strain and (c) Phonon dispersion. The stability is estimated as the formation energy per unit cell, which can be evaluated as the following

The energies of the bands can be tuned by lowering the

expression

crystals symmetry for example by applying external

Ef = ESiGeCH3 ― [ESiGe + [2ECH3/CH3]]

strain to the lattice.8,17-22 The direct band gap at

Where ESiGeCH3the total energy of SiGeCH3 is film,

equilibrium structure obtained without the inclusion of

whereas 𝐸𝑆𝑖𝐺𝑒 and 𝐸𝐶𝐻3 is energies of SiGe monolayer

SOC is 1.40 eV (1.43 eV with SOC) as shown in Fig.

and chemical potential of CH3, respectively. The binding

2(a,e).

energy is -3.4 eV per unit cell, which are larger than

underestimates

those of the formation energy of GaBiCl2 (-2.90 eV)31

performed at the hybrid HSE06 functional resulting a

and TlSb(CH3)2 (-3.08 eV).32 Further the dynamical

band gap = 1.52 eV (Fig. S4). The valance band

stability of the SiGeCH3 was calculated by phonon

maximum (VBM) of SiGeCH3 is contributed by 𝑝𝑥,𝑦

spectra as shown in Fig. 1(c). The phonon spectra,

orbitals and the conduction band minimum (CBM) is

indicates absence of any imaginary frequency mode

mainly composed of s and 𝑝𝑧 orbitals as illustrated in Fig.

which confirms the dynamical stability of the material.

S1(a-c). The normal order of s and p orbitals suggests no

Considering


the

that band

the gap,

PBE

functional

calculations

were


Page 4 of 12

band inversion in the equilibrium (unstrained) of

shifts upwards leading to semi-metal at ε = 8 % without

SiGeCH3 film and even up to ε = 8 % without SOC as

SOC and hence, non-existence of the band inversion as

shown in Fig. S2(a-c). Furthermore, we have studied the

presented in Fig. 2(d) with the appearance of a Dirac

electronic structure and evolutions of band energies

cone like show at ᴦ-point (blue shaded area). The shifting

under tensile strain effect as shown in Fig. 2(a-d) in the

of CBM and VBM at ᴦ-point suggests that the SiGeCH3

absence of SOC interaction. For this, the tensile strain

turns into a semi-metal. As the tensile strain is increased

was applied by fixing the lattice parameter to series of

further, a band inversion (“m”-shape) occurs at ᴦ-point in

value longer than that of unstrained (equilibrium) state

presence of SOC and a non-trivial band gap is obtained,

and subsequently optimizing the atomic coordinate only.

Eg = 0.35 eV. Therefore, with the presence of SOC and ε

The variation of Si-Ge bond length, buckling height, and

= 8 %, one observes a phase transition for a NI to TI as

buckling angle as the function of strain is shown in Fig.

shown in Fig. 2(h). Under strain less than 8 %, the s and

1(b). Strain can be effectively tune the band inversion of

pz orbitals are typically present above px,y orbital in terms

s-p states and hence leads to topological phase transition

of energy as shown in Fig. S2(a). Furthermore, the Dirac

from normal insulator to nontrivial topology. As a result

cone like appears at the ᴦ-point when the strain is applied

of tensile strain effect, the CB progressively shifts

8 % without SOC as shown that in Fig. 2(d).

downward to the Fermi level. On the other hand, the VB

Figure 2: The band structures calculated without SOC for SiGeCH3 monolayer (a) ε = 0 %, (b) ε = 4 %, (c) ε = 6 % and (d) ε = 8 %. The band structures induced with SOC for SiGeCH3 monolayer (e) ε = 0 %, (f) ε = 4 %, (g) ε = 6 % and (h) ε = 8 %. The shaded regions shown in (d) represents the Dirac cone at ᴦ-point and (h) shows the band-gap opening at the Dirac cone like due to SOC interaction (band inversion zoomed-in view).


Page 5 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The band gap can be tuned by tensile strain as shown in

― 14.684 eV, εpSi = ― 8.081 eV, εsGe = ― 15.052 eV,

Fig. 3(a), which opens the Dirac cone like through SOC.

and εpGe = ― 7.815 eV.33 The values for SiGeCH3 are

The orbital contribution of Si and Ge atoms, which

Vssσ = ―1.868 eV, Vspσ = 2.455 eV, Vppσ = 4.322 eV

contribute major in the vicinity of ᴦ-point are shown in

and Vppπ = ― 1.081 eV, respectively. Furthermore, the

Fig. S1(a-c). In the absence of SOC, the conduction band

Si-Ge bond length changes only slightly at small strain.

minimum (CBM) consists of spz orbitals, whereas the

We started from the semiconductor with a direct band

valance band maximum (VBM) has px,y a character

gap of 1.4 eV without SOC which can be fitted by the

dominating in Fermi level as presented in Fig. S2(a-c).

TB Hamiltonian as shown in Fig. 3(b) and at critical

Upon inclusion of SOC, the degeneracy of conduction

strain (8 %) without SOC the TB also agrees with the

and valence bands get lifted resulting in a gap Eg = 0.35

PBE value well as presented in Fig. 3(c).

eV at the ᴦ-point for ε = 8 % (Fig. S3).

As the

buckling height decreased the order of the VB become inverted at ᴦ-point due to interchange of spz and px,y

To illustrate the mechanism of the band inversion, we introduce a tight-binding model of 𝑠, 𝑝𝑥,

orbitals character (Fig. S3). Hence, SiGeCH3 is

𝑝𝑦 and 𝑝𝑧

transformed from normal insulator into topological

atomic orbitals. The effective Hamiltonian is taken as: HTB =

∑

εαi cαi + cαi

i,α

+

∑

α+ tαβ ij (ci

cβj

insulator due to SOC induced into the TB Hamiltonian as shown in Fig. 3(d). The nontrivial phase transition in

+ h.c.)

〈i, j〉,α,β

SiGeCH3 film is confirmed by calculating the topological

Here, 𝜀𝛼𝑖, 𝑐𝛼𝑖 + and 𝑐𝛼𝑖 represent the on-site energy,

invariant, Z2 index based on the U(2N) non-Abelian

creation, and annihilation operators of an electron at the

Berry connection proposed by Rui Yu and co-worker.34

𝑡𝛼𝛽 𝑖𝑗

Each of the nth occupied bands is indexed by |𝑛, 𝑘𝑥, 𝑘𝑦〉,

α-orbital of the i-th atom, respectively. The

parameter is the nearest-neighbor hopping energy of an

and square matrix 𝐹( 𝑘𝑥, 𝑘𝑦) containing overlap integers

electron between α-orbital of i-th atom and β-orbital of j-

defined as

th atom for α, β ∈ (𝑠, 𝑝𝑥, 𝑝𝑦, 𝑝𝑧), which can be

[F(kx, ky)]m,n = 〈m, kx, i, ky|kx, i + 1, ky〉

performed by fitting the DFT results as shown in Fig. 3

Then the complex unitary square matrix can be solved

(b, c and d). According to tight-binding theory, the

as:

hopping energies can be represented as:

Nx ― 1

tss ij = VSSσ x tsp ij

D(ky) =

∏ F(j∆k , k ). x

y

j=0

= Vspσ cosθ

y tsp ij = Vspσ cosφ

In which ∆kx =

2Π Nxa

represents the discrete spacing of 𝑁𝑥

tpijxpx = Vppσ cos2θ + Vppπ sin2θ

points along kx direction. D(ky) is a 2N × 2N matrix

tpijypy = Vppσ cos2φ + Vppπ sin2φ

which has 2N eigenvalues:

tpijxpy = (Vppσ ― Vppπ)cosθ cosφ

D(

)

λDm(ky) = |λDm|eiθm ky , m = 1, 2…, 2N,

Where θ and 𝜑 are the angles of the vector pointing from

where 𝜃𝐷𝑚(𝑘𝑦) is the phase of the eigenvalues

i-th atom to j-th atom with respect to x and y axes. The on-site energies of s and p orbitals are set as εsSi =

θDm(ky) = Im[logλDm(ky)]



Page 6 of 12

Figure 3: (a) The variation of band gap as the function of strain without and with SOC effect. For strain less than 8% without and with SOC are NIs (Cyan color region), ε ≥ 8% with SOC are TIs (yellow color region) and ε ≥ 8 % without SOC are semi-metal materials (pink region). The TB calculations are performed by fitting the DFT bands for (b) at equilibrium state, (c) 8 % strain induced without and (d) with SOC. The TB model data are shown in red dotted line, blue color refers to DFT-PBE (b, c, and d) and the green dotted line shows hybrid HSE06 functional calculations. The tight-binding model based on the Wannier functions

Additionally, to observe the topological nature of

(WFs) correctly reproduces the density functional theory

SiGeCH3 at ε = 8 % induced with SOC interaction, one

band structure and simulates the ARPES with the

needs to also show the existence of edge states protected

calculated surface density of states. The Z2 topological

by TRS, which is an important characteristic of 2D-TIs

invariant is related by counting the number of crossing

material. To achieve the edge state, we have calculated

between any arbitrary horizontal reference line and

the band structure of the ribbon utilizing the Green's

evaluation of θ mod 2π, where the odd and even numbers

function method with the TB models from VASP and

denoted Z2 = 1 and 0 nontrivial and trivial topological

wannier90 package based MLWFs. The edge states

phase, respectively. Figure 4(a) shows that the WCC for

perfectly connect the conduction band and valence band

an effective 1D system with fixed ky in the subspace of

with helical edge states located inside the bulk gap as

occupied bands for the time-reversal plane of SiGeCH3 at

shown in Fig. 4(b). The counter propagating helical edge

ε = 8 % with SOC resulting in a nontrivial topological

states spin up and spin down exhibit polarization edge

invariant Z2 = 1, thereby achieved its 2D-TI.

spectral function as presented in Fig. 4(c).


Page 7 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4: (a) The Wilson loop (wannier charge center) calculated along ky for SiGeCH3 monolayer at 8 % tensile strain yield Z2 = 1, (b) topologically protected conductivity edge states and (c) helical edge spin polarization at 8 % strain with the inclusion of SOC effect. Interestingly, we recognize that the spin-momenta of

SiGeCH3/h-BN heterostructure and its components are

those Dirac-type edge states are locked at the ᴦ-point

further calculated as

within the bulk gap thereby confirming the existence of

Δρ(z) =

nontrivial topology leading to absolutely polarized

where ρT(x,y,z) , ρSiGe(x,y,z) and ρBN(x,y,z) are the total

conductive channels.

∫ρ (x,y,z)dxdy ― ∫ρ T

SiGe(x,y,z)dxdy

―

∫ρ

BN(x,y,z)dxdy

charge density of SiGeCH3/h-BN, SiGe and h-BN

To have practical application, it is highly desirable to

monolayer, respectively. The charge density difference

experimentally realize a substrate to support 2D films.

of SiGeCH3 monolayer also calculated as shown in Fig.

We have chosen bilayer of hexagonal boron nitride (h-

S5. Recently, few of 2D materials have been successfully

BN) as shown in Fig. 5(a), which has been extensively

grown on different substrates such as bismuthene6,

used as a substrate to grow thin films,35 with large band

plumbene,9 germanene and stanene bilayer,7 SiGe,20

gap36-38 and a good dielectric constant for the epitaxial

arsenene,39 β-BiAs21 and Bi monolayer.40 Clearly, the 2D

growth for SiGeCH3 film. A lattice mismatch of 0.031 Å

SiGeCH3/h-BN heterostructure is robust nontrivial

and an interlayer distance = 4.12 Å, results in stable van

topology for which the band inversion is not perturbed

der Waals (vdW) heterostructure. The weak dispersion

by substrate.

interactions results in a binding energy of -0.022 eV per unit cell. It is important to note that the heterostructure of

Since the discovery of TIs, both in prediction and

2D SiGeCH3/h-BN without and with SOC at strain 8 %

experimental there have been plethora of reports on the

the band structures remains unperturbed as presented in

different classes of these materials. Yet, most of the

Fig. 5(c and d), respectively. Bader charge analysis

topological insulators predicted materials are having

confirmed no charge transfer between SiGeCH3 and h-

heavy atoms (strong SOC interactions) such as, Hg, Sb,

BN, as shown in Fig. 5(b). The charges are localized on

Sn, Pb, Te and Bi, which have limitation of toxicity and incompatibility with the current silicon-based electronic

the 𝑠𝑝𝑧 and 𝑝𝑥,𝑦 orbitals of the Si and Ge near the Fermi

technology device.

level. The integral charge density differences between



Page 8 of 12

Figure 5: (a) Top and side views of epitaxial growth of SiGeCH3 of nontrivial topology on bilayer of h-BN substrate, (b) charge density difference top and side view, (c) Electronic band structure without and (c) with SOC at 8 % strain. Although, there has been much research into predicting in

Wilson loop method and recursive Green’s function

some light elements but their bulk gaps are very small,

calculations also reveal a single pair of topologically

induced by weak SOC interaction, including graphene,3

protected

(~10-3 meV), for few-layered black phosphorus (5 meV),41

propagating oppositely spin polarized edge channels in

helical

edge

states,

indicating

counter

silicene (1.55-2.9

SiGeCH3 nanoribbon. The large band gap induced by

meV),7 and Arsenene Oxide (Eg = 232meV).42 In

SOC and tensile strain indicates that methyl-decorated

comparison, our result showed that 2D SiGeCH3 has a

SiGe film is quite promising 2D TIs materials. For

sizable large nontrivial topological gap = 0.35 eV. Thus,

practical applications, h-BN serves as a candidate

predicted nontrivial topological gapless edge states consist

substrate for supporting SiGeCH3 film without altering its

of counter propagating oppositely spin polarized. It has

nontrivial topology.

germanene (Eg = 23.9-108

meV),7

great potential application for spintronic device as well as building blocks for new more exotic states like Majorana

ASSOCIATED CONTENT

Fermions.

Supporting Information Orbital contribution in the band structures at ε = 0 %, ε =

Conclusion

8 % without and with SOC, partial charges of CBM and

In summary, based on the first-principles calculations, SiGeCH3 film is a 2D-TIs with sizable large energy gap of 0.35 eV. By chemical functionalization of SiGe film, it undergoes a topological phase transition under external tensile strain. The nontrivial topological insulator is characterized by topological invariant, Z2 = 1 using

VBM, band structures at equilibrium structure for PBE, HSE06 and TB (wannier90) calculations and charge density difference of SiGeCH3 monolayer. AUTHOR INFORMATION Corresponding Author E-mail: [email protected]. Tel.: +91-33-24734971.


Page 9 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(11) Chen, L.; Liu, C.-C.; Feng, B.; He, X.; Cheng, P.; Ding, Z.; Meng, S.; Yao, Y.; Wu, K. Evidence for Dirac Fermions in a Honeycomb Lattice based on Silicon. Phys. Rev. Lett. 2012, 109, 056804-5. (12) Fleurence, A.; Friedlein, R.; Ozaki, T.; Kawai, H.; Wang, Y.; Yamada-Takamura, Y. Experimental Evidence for Epitaxial Silicene on Diboride Thin Films. Phys. Rev. Lett. 2012, 108, 245501-5. (13) Novoselov, K. S.; Fal, V.; Colombo, L.; Gellert, P.; Schwab, M.; Kim, K. A Roadmap for Graphene. Nature 2012, 490, 192-200. (14) Brahlek, M.; Bansal, N.; Koirala, N.; Xu, S.-Y.; Neupane, M.; Liu, C.; Hasan, M. Z.; Oh, S. Topological-metal to Band-Insulator Transition in (Bi 1− xInx)2Se3 Thin Films. Phys. Rev. Lett. 2012, 109, 1864035. (15) Wu, L.; Brahlek, M.; Aguilar, R. V.; Stier, A.; Morris, C.; Lubashevsky, Y.; Bilbro, L.; Bansal, N.; Oh, S.; Armitage, N. A Sudden Collapse in the Transport Lifetime across the Topological Phase Transition in (Bi1.xInx)2Se3. Nat. Phys. 2013, 9, 410-414. (16) Yan, C.; Liu, J.; Zang, Y.; Wang, J.; Wang, Z.; Wang, P.; Zhang, Z.-D.; Wang, L.; Ma, X.; Ji, S. Experimental Observation of Dirac-like Surface States and Topological Phase Transition in Pb1− xSnxTe(111) Films. Phys. Rev. Lett. 2014, 112, 186801-5. (17) Agapito, L. A.; Kioussis, N.; Goddard III, W. A.; Ong, N. Novel family of Chiral-based Topological Insulators: Elemental Tellurium under Strain. Phys. Rev. Lett. 2013, 110, 176401-5. (18) Winterfeld, L.; Agapito, L. A.; Li, J.; Kioussis, N.; Blaha, P.; Chen, Y. P. Strain-Induced Topological Insulator Phase Transition in HgSe. Phys. Rev. B 2013, 87, 075143. (19) Zhang, H.; Ma, Y.; Chen, Z. Quantum Spin Hall Insulators in Strain-Modified Arsenene. Nanoscale 2015, 7, 19152-19159. (20) Teshome, T.; Datta, A. Topological Insulator in Two-Dimensional SiGe Induced by Biaxial Tensile Strain. ACS Omega 2018, 3, 1-7. (21) Teshome, T.; Datta, A. Phase Coexistence and Strain-Induced Topological Insulator in Two-Dimensional BiAs. J. Phys. Chem. C 2018, 122(26), 15047-15054. (22) Ma, Y.; Dai, Y.; Wei, W.; Huang, B.; Whangbo, M.-H. Strain-Induced Quantum Spin Hall Effect in Methyl-Substituted Germanane GeCH3. Sci. Rep. 2014, 4, 7297. DOI: 10.1038/srep07297 (23) Kresse, G.; Hafner, J. Ab-Initio Molecular-Dynamics Simulation of the Liquid-Metal– Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49, 14251. (24) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758. (25) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Phys. Rev. B 1992, 45, 13244.

Notes The authors declare no competing financial interest. ACKNOWLEDGEMENT We acknowledge The World Academy of Sciences (TWAS) - Indian Association for the Cultivation of Science (IACS) (FR number: 3240280472) financial support and AD thanks, DST, TATA Steel and BRNS for partial funding. TT is thankful to Addis Ababa Science and Technology University (AASTU) for financial assistance. References (1) Fu, L.; Kane, C. L. Topological Insulators with Inversion Symmetry. Phys. Rev. B 2007, 76, 045302. (2) Fu, L.; Kane, C. L.; Mele, E. J. Topological Insulators in three Dimensions. Phys. Rev. Lett. 2007, 98, 106803-106807. (3) Kane, C. L.; Mele, E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 2005, 95, 226801-4. (4) 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. (5) Knez, I.; Du, R.-R.; Sullivan, G. Evidence for Helical Edge modes in Inverted InAs/GaSb Quantum Wells. Phys. Rev. Lett. 2011, 107, 136603-5. (6) Reis, F.; Li, G.; Dudy, L.; Bauernfeind, M.; Glass, S.; Hanke, W.; Thomale, R.; Schäfer, J.; Claessen, R. Bismuthene on a SiC Substrate: A candidate for a High-Temperature Quantum Spin Hall Material. Science 2017, 357, 287-290. (7) Liu, C.-C.; Feng, W.; Yao, Y. Quantum Spin Hall Effect in Silicene and twoDimensional Germanium. Phys. Rev. Lett. 2011, 107, 076802-4. (8) Wang, D.; Chen, L.; Liu, H.; Shi, C.; Wang, X.; Cui, G.; Zhang, P.; Chen, Y. Strain Induced Band Inversion and Topological Phase Transition in Methyl-Decorated Stanene Film. Sci. Rep. 2017, 7, 17089. (9) Zhao, H.; Zhang, C.-w.; Ji, W.-x.; Zhang, R.-w.; Li, S.-s.; Yan, S.-s.; Zhang, B.-m.; Li, P.; Wang, P.-j. Unexpected Giant-Gap Quantum Spin Hall Insulator in Chemically Decorated Plumbene Monolayer. Sci. Rep. 2016, 6, 20152. (10) Vogt, P.; De Padova, P.; Quaresima, C.; Avila, J.; Frantzeskakis, E.; Asensio, M. C.; Resta, A.; Ealet, B.; Le Lay, G. Silicene: Compelling Experimental Evidence for Graphene like twoDimensional Silicon. Phys. Rev. Lett. 2012, 108, 1555015.



(41) Liu, Q.; Zhang, X.; Abdalla, L.; Fazzio, A.; Zunger, A. Switching a Normal Insulator Into a Topological Insulator via Electric Field with Application to Phosphorene. Nano Lett. 2015, 15, 1222-1228. (42) Wang, Y.-p.; Ji, W.-x.; Zhang, C.-w.; Li, P.; Zhang, S.-f.; Wang, P.-j.; Li, S.-s.; Yan, S.-s. TwoDimensional Arsenene Oxide: A Realistic Large-Gap Quantum Spin Hall Insulator. Appl. Phys. Lett. 2017, 110, 213101-213106.

(26) Grimme, S. Semiempirical GGA‐Type Density Functional Constructed with a Long‐Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787-1799. (27) Qi, X.-L.; Zhang, S.-C. Topological Insulators and Superconductors. Rev. Mod. Phys. 2011, 83, 1057-1110. (28) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207-8215. (29) Refson, K.; Tulip, P. R.; Clark, S. J. Variational Density Functional Perturbation Theory for Dielectrics and Lattice Dynamics. Phys. Rev. B 2006, 73, 155114. (30) Mostofi, A. A.; Yates, J. R.; Lee, Y.S.; Souza, I.; Vanderbilt, D.; Marzari, N. wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions. Comput. Phys. Commun. 2008, 178, 685-699. (31) Li, L.; Zhang, X.; Chen, X.; Zhao, M. Giant Topological Nontrivial Band Gaps in Chloridized Gallium Bismuthide. Nano Lett. 2015, 15, 1296-1301. (32) Lu, Q.; Ran, R.; Cheng, Y.; Wang, B.; Zeng, Z.-Y.; Chen, X.-R. Robust Large Gap Quantum Spin Hall Insulators in Methyl and Ethynyl Functionalized TlSb Buckled Honeycombs. J. Appl. Phys. 2018, 124, 035305-035312. (33) Vogl, á.; Hjalmarson, H. P.; Dow, J. D. A Semi-Empirical Tight-Binding Theory of the Electronic Structure of Semiconductors. J. Phys. Chem. Solids 1983, 44, 365-378. (34) Yu, R.; Qi, X. L.; Bernevig, A.; Fang, Z.; Dai, X. Equivalent Expression of Z2 Topological Invariant for Band Insulators Using the non-Abelian Berry Connection. Phys. Rev. B 2011, 84, 075119. (35) Liu, Z.; Song, L.; Zhao, S.; Huang, J.; Ma, L.; Zhang, J.; Lou, J.; Ajayan, P. M. Direct Growth of Graphene/Hexagonal Boron Nitride Stacked Layers. Nano Lett. 2011, 11, 2032-2037. (36) Özçelik, V. O.; Cahangirov, S.; Ciraci, S. Epitaxial Growth Mechanisms of Graphene and Effects of Substrates. Phys. Rev. B 2012, 85, 235456. (37) Sachs, B.; Wehling, T.; Katsnelson, M.; Lichtenstein, A. Adhesion and Electronic Structure of Graphene on Hexagonal Boron Nitride Substrates. Phys. Rev. B 2011, 84, 195414. (38) Teshome, T.; Datta, A. TwoDimensional Graphene-Gold Interfaces Serve as Robust Templates for Dielectric Capacitors. ACS Appl. Mater & Interfaces 2017, 9, 34213-34220. (39) Wang, Y.-p.; Zhang, C.-w.; Ji, W.-x.; Zhang, R.-w.; Li, P.; Wang, P.-j.; Ren, M.-j.; Chen, X.-l.; Yuan, M. Tunable Quantum Spin Hall Effect via Strain in two-Dimensional Arsenene Monolayer. J. Phys. D: Appl. Phys. 2016, 49, 055305-055311. (40) Li, S.-s.; Ji, W.-x.; Hu, S.-j.; Zhang, C.-w.; Yan, S.-s. Effect of Amidogen Functionalization on Quantum Spin Hall Effect in Bi/Sb(111) Films. ACS Appl. Mater & interfaces 2017, 9, 41443-41453.


Page 10 of 12

Page 11 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC graphic



Dr. Ayan Datta is currently a Professor in the School of Chemical Sciences in Indian Association for the Cultivation of Science (IACS), Kolkata, India. He obtained his PhD from JNCASR-Bangalore in 2007 and worked as a Postdoctoral fellow in University of North Texas (UNT). His research interests span over computational study in molecules and materials and studying emerging properties under strong and weak perturbations in nature using relevant models and methods at various length and time-scales. The group has studied systems like silicene, phosphorene, non-statistical dynamics in organic molecular reactivity, homogeneous and heterogeneous catalysis, singlet fission in organic chromophores and dynamics and structures of unnatural DNA bases. Though computational methods are evolving and improving, we do realize that quantitative assessments are model dependent. So, our primary goal is to provide a qualitative and predictable understanding for experiments. Hence, most importantly, to gain a qualitative picture, we are always eager to work very closely with experimentalists to refine, reframe and even refute existing models in chemistry.


Page 12 of 12

Strain-Induced Topological Insulator in Methyl-Decorated SiGe Films

Recommend Documents