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The common effects of surface and internal bonds on the electronic structure of Bi2Te3 nano-

films by first-principles calculation

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2014 Mater. Res. Express 1 025043

(http://iopscience.iop.org/2053-1591/1/2/025043)

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The common effects of surface and internal bonds onthe electronic structure of Bi2Te3 nano-films by first-principles calculation

C Li1, Y F Zhao1, C X Fu1, C Q Sun2 and Y Y Gong11 Center for Coordination Bond Engineering, Department of Materials Science and Engineering,China Jiliang University, People’s Republic of China2 School of Electrical and Electronic Engineering, Nanyang Technological University, 639798SingaporeE-mail: ygong2007@163.com

Received 8 April 2014, revised 22 May 2014Accepted for publication 2 June 2014Published 19 June 2014

Materials Research Express 1 (2014) 025043

doi:10.1088/2053-1591/1/2/025043

AbstractThe effects of external stress on Bi2Te3 nano-films have been investigated byfirst-principles calculation, including stability, electronic structure, crystalstructure, and bond order. It is found that the critical thickness of nano-film issensitive to the stress in Bi2Te3 nano-film while the band gap is near constant.The critical thickness decreases under tensile stress, whereas it increases undercompressive stress. The band gap and band order of Bi2Te3 film has beenaffected collectively by the surface and internal crystal structures, the contractionratio between surface bond length of nano-film and the corresponding bondlength of bulk decides the band order of Bi2Te3 film.

Keywords: surface bond contraction, nano-films, critical thickness, electronicstructure

1. Introduction

Topological insulators (TIs) are a new class of quantum matter and have been found in the lastyears. These materials have remarkable electronic properties since the role of relativisticinteractions (e.g. strong spin–orbit coupling (SOC)) is fundamentally different fromconventional insulators and semiconductors [1–3]. Unlike normal insulator (NI) and metal, aTI has an insulating gap in the bulk and a gapless edge on the surface or interface. A TI isprotected by time-reversal symmetry [4, 5], and has attracted great attention both theoreticallyand experimentally in recent years [3, 6–8]. A TI has remarkable electronic properties and greatpotential for electronic, thermoelectric and optoelectronic applications [9–11], superconducting

Materials Research Express 1 (2014) 0250432053-1591/14/025043+11$33.00 © 2014 IOP Publishing Ltd

[12, 13] and magnetic applications [14, 15]. To date, several topological candidates have beenfound, such as HgTe [2, 16], V2VI3 compounds [8, 14, 17, 18], Heusler compounds [19–21],thallium-based ternary chalcogenides [22] and organic Tis [23–25].

To effectively exploit the surface conductivity of TIs, ultrathin films with a large surface-to-volume ratio provide attractive systems for transport studies, which are highly relevant forelectronic device applications. For this purpose, V2VI3 compounds with the layeredrhombohedral crystal structure and space group R-3m are suitable for nano-application. InV2VI3 compound, each basic unit includes five atomic layers named quintuple layers (QLs) (seefigure 1(a)). There is strong chemical bonding within a QL, with weak van der Waals (vdW)interactions between different QLs. Two-dimensional V2VI3 nano-films have been synthesizedeasily in the laboratory by molecular beam epitaxy (MBE) [8, 26, 27] and studied boththeoretically and experimentally; and their electronic structures and topological propertiesdepend on the film thickness, referred to as critical thickness. For Bi2Se3, Sb2Te3 and Bi2Te3,the critical thicknesses (D) are D= 6, 4 and 2 QLs, respectively [28–31]. Below the criticalthickness, a surface band gap opens, and it is a bond inversion between the conduction band andvalence band for TIs.

Several researchers have reported that external stress can change the electronic structureand critical thickness of TI [17, 32, 33]. For instance, Young et al have shown that uniaxialstrain in the <111> direction is an important parameter for dete.rmining the topologicalinsulating phase and the direct band gap of bulk Bi2Se3 at Γ point [33]. Liu et al have alsodemonstrated that mechanical deformation could reduce the band gap at the time-reversal-invariant momentum points so that even materials with relatively weaker SOC could display aband inversion [32]. At present, the mainstream view is when thickness of a film is smaller thanits critical thickness, overlapping between the surface-state wavefunctions from the two surfaceof the film becomes non-negligible, and hybridization between them has to be taken into

Figure 1. (a) Crystal structure of 2QL Bi2Te3 film and surface bond length LsurfacenQL is

shown; (b) crystal structure of bulk Bi2Te3 and corresponding bond length of bulk Lbulk.

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Mater. Res. Express 1 (2014) 025043 C Li et al

account, which leads to a hybridization gap at the Dirac point to avoid crossing of bands withthe same quantum numbers [29]. The view has been accepted by most physicists, and thenontrivial topological of the TI is calculated and confirmed based on the wavefunction parity attime reversal k-points [34].

Although the electronic structure and wavefunction parity at time reversal k-points of bulkand nano-film TIs have been researched widely, the relationships between electronic structureand crystal structure are ambivalent. The changes of electronic structure are surely synchronouswith the changes of crystal structure of materials, the fundamental factor determining theelectronic structures or topological property of materials is the chemical bonds including bondlength, bond angle and electronic distribution [35, 36]. Thus, the surface electronic structure ortopological property of nano-film will be reflected in the surface chemical bonds since thetopological property or band inversion will appear at surface, and the surface chemical bonds orsurface state is the synthesis result caused by both surface and interior. Although the band gapof nano-film is influenced by two effects: the quantum confinement effect in thickness directionand the interaction between the top and bottom surface states [34], Wang et al have recentlyalso indicated that the edge chemical adsorption of 2D TI affects the surface chemical bondsand TI edge (surface) states [37]. Therefore, it is significant to analyze the relationships betweenband order and the surface chemical bond, which will contribute to understanding the nature ofbond inversion in TIs distinctly.

In this paper, Bi2Te3 nano-films under five different external stresses have been calculatedby using the relativistic density functional theory, the interaction energies, chemical bond,electronic structures and their critical thicknesses under different external stresses. Therelationships between surface bond contraction and band order are discussed.

2. Computational method

All density functional theory calculations, including geometry relaxation, interaction energy,band structure and charge distribution, are performed on the basis of the projector augmentedwave method [38] implemented in the VASP 5.2 package [39]. The exchange-correlationfunctional of the generalized gradient approximation (GGA) due to Perdew–Burke–Ernzerhof(PBE) have been used [40], including scalar-relativistic effects in addition to SOC. The kineticenergy cutoff of electron wave function is 400 eV, which is sufficiently large for the systemsconsidered. A k-point sampling of 10 × 10 × 1 for all films is found to be converged. A vacuumlayer of 20Å is used to avoid interactions between repeating slabs, and the relative atomicpositions are relaxed with a force tolerance of 0.01 eVÅ−1. Five different situations have beenconsidered: without strain with equilibrium lattice constant a0, compressive strain with latticeconstants a= a0(1− 2%) and a0(1 − 4%), and tensile strain with lattice constants a = a0(1 + 2%)and a0(1 + 4%), respectively. For all nano-films, the lattice constants are fixed in ab-plane butrelaxed in c axis, and the film thicknesses increase from 1QL to 7QL in c axis. The DFT-D2approach has been used in which dispersion interactions are described by a pair-potential of theCij/R

6ij form [41]. The D2 coefficients are obtained from values tabulated in terms of the

chemical identity of the atoms i and j alone: C6 = 63.565 and 31.750; R0 = 1.725 and 1.720 forBi and Te atoms, respectively [42].

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Mater. Res. Express 1 (2014) 025043 C Li et al

The interaction energies of films EQL from 1QL to 7QLs are calculated by:

= −( )E E nE n (1)QL sys 1QL

where Esys is the total energy of the system, E1QL denotes the energy of one QL without strain inorder to consider the strain energy [43]; n is the amount of QL in each system. Since the basicunit is one QL, EQL denotes the stability of a stacked film.

The contraction ratio (r) between surface bond length of the nano-film and thecorresponding bond length of bulk can be calculated by:

= −( )r L L L (2)surfacenQL

bulk bulk

where LsurfacenQL and Lbulk denotes the surface bond length of nano-film (figure 1(b)) and the

corresponding bond length in bulk (figure 1(a)), respectively. In figure 1(b), the surface bond offilm denotes the bond between the outermost Bi (small) atom and the neighboring Te (big)atom.

3. Results and discussion

3.1. Lattice constants and band gaps

The optimized lattice constants of bulk Bi2Te3 are 4.349Å in a and b axis, 31.09Å in c axis,which are in good agreement with the reported experimental result: 4.383Å in a and b axis,30.49Å in c axis [44], and is more accurate than the previously reported simulation results:4.530Å in a and b axis, 30.63Å in c axis [45]. This means the DFT-D2 approach is reasonablefor these layered systems. We have calculated the band structures of bulk and 1QL film withoutstrain by PBE+SOC method. The band gap of bulk is 0.089 eV for PBE+SOC which is ingood agreement with the theoretical reports with LDA+SOC method (0.090 eV) [46],GGA+SOC method (0.100) [45] and experimental data (0.072 eV) [47]. Also, the band gap of1QL film Δgap is 0.375 eV for PBE+SOC is in good agreement with the theoretical report withPW91+ SOC method (0.391 eV) [48] and experimental data (0.342 eV) [49]. This means thatour calculated parameters for PBE+SOC are reasonable. Next, the same simulation parametershave been used to investigate nano-films.

3.2. Stability of films

To study the stability of our systems, Esys of all films have been calculated by density functionaltheory when SOC have been considered and EQL have been calculated by equation (1). Infigure 2, it is found that EQL are related to the lattice constants of nano-films and have therelationship: > > > > >+ + − −E E E E E04%

QL2%

QL4%

QL0%QL

2%QL , where the subscript denotes the

corresponding strain. The values of EQL of all films become smaller and smaller when thethicknesses of them increase, which means the systems are more and more thermodynamicallystable. Based on values of EQL, nano-films with tensile strain 2% or 4% are thermodynamicallyunstable; conversely, nano-films with compress strain 2% or 4% are thermodynamically stable,and nano-films with 2% compress strain have the lowest EQL values and are the mostthermodynamically stable. At the same time, the interaction energy of bulk Ebulk (=−0.064 eV)was also calculated by equation (1) with n = 3 in order to compare the thermodynamic stability

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Mater. Res. Express 1 (2014) 025043 C Li et al

with nano-films. It is found that all nano-films are less stable than bulk materials except the 7QL nano-film with 2% compress strain = −−E 0.071 eV2%

QL .

3.3. Charge distributions of films

Since TIs have the band inversion, i.e., switching of occupied and unoccupied bands withopposite parity around the EF [50], the value of band gap is not sufficient information andcannot conclude whether the material is TI. To confirm the topological property of our films, thecharge distributions of the highest occupied crystal orbital (HOCO) and the lowest unoccupiedcrystal orbital (LUCO) for all films with the same isosurface level have been calculated toconfirm the band order, since the wavefunction parity at Γ points is consistent with the bondorder of HOCO and LUCO [32]. The charge distributions of HOCO and LUCO at Γ point forsome selected films are shown in figure 3, in which only the outermost QL has been shown. Infigure 3(a), for 1QL films with lattice constant a = a0(1 + 4%), the electrons of HOCO roundeach atom in surface QL since the Pauling electronegative of Bi atom (2.02) is similar to that ofTe atom (2.10), while the LUCO of 1QL film locates around the Te and Bi atoms in both sidesof surface QL but not the middle Te atom. Conversely, as the film thicknesses increase from1QL to 2QL, the charge distributions of LUCO (or HOCO) of 1QL film is similar to that ofHOCO (or LUCO) of 2QL film, which means that the band order has been changed and bandinversion appears, so Bi2Te3 nano-films with lattice constant a= a0(1 + 4%) has the criticalthickness of 2QL. At the same time, similar results have been found when different externalstresses have been applied on Bi2Te3 nano-films. i.e., the charge distributions of HOCO andLUCO are inverted when the thicknesses of Bi2Te3 films increase from 1QL to 2QL witha= a0(1 + 2%) (figure 3(b)); from 2QL to 3QL with a = a0 (figure 3(c)) and a = a0(1 − 2%)(figure 3(d)); and from 3QL to 4QL with a = a0(1− 4%) (figure 3(e)), respectively. So externalstress changes the critical thickness of Bi2Te3 nano-film; tensile stress reduces the criticalthickness, while compressive stress increases the critical thickness.

3.4. Bond length of films

Just as in the analysis in the introduction, the topological property or bond inversion appears atthe surface of film and is caused by the electronic structure and crystal structure of surface

Figure 2. (a) EQL of Bi2Te3 films with different external stains as a function of n.

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Figure 3. Charge distributions of HOCO and LUCO at the Γ point for (a) 1QL and 2QLfilms with lattice constant a= a0(1 + 4%), (b) 1QL and 2QL films with lattice constanta = a0(1 + 2%), (c) 2QL and 3QL films with lattice constant a= a0, (d) 2QL and 3QLfilms with lattice constant a= a0(1 − 2%), and (e) 3QL and 4QL films with latticeconstant a= a0(1 − 4%). a0 is equilibrium lattice constant without strain.

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Mater. Res. Express 1 (2014) 025043 C Li et al

atoms. As above, the electronic structures of surface QL in film have been studied, while thecrystal structure and the relationship between electronic structure and crystal structure isambiguous. Based on other reports, the surface bond contraction changes the band gap of nano-semiconductors [35, 36], so the surface bond length Lsurface

nQL and the corresponding bond length in

bulk Lbulk of each system is obtained and listed in table 1, where a0(1 + 4%), a0(1 + 2%), a0,a0(1− 2%) and a0(1 − 4%) denote the systems with corresponding lattice constants. Although,compared with Lbulk, the surface bonds of all nano-films shrink, the Lsurface

nQL are different for films

with different thicknesses, the values of LsurfacenQL increase little from 7QL to 3QL films and

increase a bit from 3QL to 1QL films. On the other band, the values of Lbulk and LsurfaceQL1 reduce

linearly with the reduced lattice constants in table 1 and figure 4(a); the value of Δgap withequilibrium lattice constant a0 is the biggest 0.375 eV, while the absolute values of latticeconstant and band length are unrelated to Δgap. Especially, Δgap changes 0.009 eV (from 0.375to 0.366 eV) when Lsurface

QL1 changes 0.0177Å (from 3.0828 to 3.0651Å) in table 1. However, the

band gaps of films without strain change 0.370 eV (from 0.375 eV for 1QL film to 0.005 eV for3QL film in figure 5) when the bond lengths change 0.0166Å (from 3.0828Å for 1QL film to3.0662Å for 3QL film) in table 1. To explain this novel phenomenon, the contraction ratiosbetween Lsurface

nQL and Lbulk have been calculated by equation (2), and the results are shown in

figure 4. It is found that the values of r increase along with the increasing film thickness. Bycombining figures 3 with 4(b), we have found the HOCO and LUCO of all films haveexchanged when the values of r are beyond about 0.53%. Based on our analyses above, whenthe film thickness increases, the surface bond shrinks and electric distributions of surface bondare localized, which leads to the reduction of the film band gap; at the same time, the internalcrystal structure protected by time-reversal symmetry also affects the band gap or topologicalproperty of Bi2Te3. Thus, the band gap and band order of Bi2Te3 film has been affectedcollectively by the surface and internal crystals structures. Regulating the contraction ratio r of

Table 1. a denotes the lattice constant, Δgap the band gap of 1QL film, LsurfacenQL and Lbulk

denotes the surface bond length of film and the corresponding bond length of bulk,respectively, where n is the number of QL in film. a0(1 + 4%), a0(1 + 2%), a0, a0(1− 2%)and a0(1− 4%) denote the films with corresponding lattice constants.

a0(1 + 4%) a0(1 + 2%) a0 a0(1 − 2%) a0(1− 4%)

a (Å) 4.5209 4.4323 4.3488 4.2618 4.1748Δgap(eV) 0.361 0.357 0.375 0.366 0.355Lbulk (Å) 3.1205 3.1020 3.0828 3.0651 3.0481Lsurface

QL1 (Å) 3.1050 3.0857 3.0682 3.0504 3.0354

LsurfaceQL2 (Å) 3.1036 3.0853 3.0667 3.0490 3.0329

LsurfaceQL3 (Å) 3.1033 3.0850 3.0662 3.0488 3.0328

LsurfaceQL4 (Å) 3.1025 3.0830 3.0657 3.0486 3.0318

LsurfaceQL5 (Å) 3.1023 3.0828 3.0656 3.0484 3.0316

LsurfaceQL6 (Å) 3.1022 3.0827 3.0650 3.0483 3.0314

LsurfaceQL7 (Å) 3.1021 3.0826 3.0648 3.0482 3.0313

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Mater. Res. Express 1 (2014) 025043 C Li et al

nano- or bulk materials by external stress, the conversion from TI to NI has potentialapplications in nano-circuit switches.

4. Conclusions

The stability of Bi2Te3 nano-films under different external stresses and the effects of strain ontheir crystal and electronic structures have been investigated by first-principles calculation. Thecritical thickness of nano-film is sensitive to the stress in Bi2Te3 nano-film while the band gap isnear constant. The critical thickness decreases under tensile stress, whereas it increases undercompressive stress. The band gap and band order of Bi2Te3 film has been affected collectivelyby the surface and internal crystals structures, the contraction ratio between surface bond lengthof nano-film and the corresponding bond length of bulk decides the band order or topological

Figure 4. (a) The values of Lbulk and LsurfaceQL1 as a function of lattice constants; (b) the

contraction ratio (r) as a function of n.

Figure 5. Band structures of Bi2Te3 films without strain (a) 1QL film and (b) 3QL film,respectively.

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property of Bi2Te3 films. Regulating the contraction ratio r of nano-or bulk materials byexternal stress, the conversion from TI to NI has potential applications in nano-circuit switches.

Acknowledgement

Computational resources have been provided by the Beijing Computing Center.

References

[1] Moore J E 2010 The birth of topological insulators Nature 464 194–8[2] Bernevig B A, Hughes T L and Zhang S-C 2006 Quantum spin Hall effect and topological phase transition in

HgTe quantum wells Science 314 1757–61[3] Li X, Ren H and Luo Y 2011 Electronic structure of bismuth telluride quasi-two-dimensional crystal: a first

principles study Appl. Phys. Lett. 98 083113[4] Hsieh D et al 2009 A tunable topological insulator in the spin helical Dirac transport regime Nature 460

1101–5[5] Song C-L et al 2010 Topological insulator Bi2Se3 thin films grown on double-layer graphene by molecular

beam epitaxy Appl. Phys. Lett. 97 143118[6] Li C, Lian J S and Jiang Q 2011 Antiferromagnet topological insulators with AB2C Heusler structure Phys.

Rev. B 83 235125[7] Mann C et al 2013 Mapping the 3D surface potential in Bi2Se3 Nat. Commun. 4 2277[8] Harrison S E et al 2013 Two-step growth of high quality Bi2Te3 thin films on Al2O3 (0001) by molecular

beam epitaxy Appl. Phys. Lett. 102 171906[9] Maassen J and Lundstrom M 2013 A computational study of the thermoelectric performance of ultrathin

Bi2Te3 films Appl. Phys. Lett. 102 093103[10] Schnyder A P, Timm C and Brydon P M R 2013 Edge currents as a signature of flatbands in topological

superconductors Phys. Rev. Lett. 111 077001[11] Wang K et al 2013 High-quality Bi2Te3 thin films grown on mica substrates for potential optoelectronic

applications Appl. Phys. Lett. 103 031605[12] Wang E Y et al 2013 Fully gapped topological surface states in Bi2Se3 films induced by a d-wave high-

temperature superconductor Nat. Phys. 9 620–4[13] Veldhorst M, Molenaar C G, Wang X L, Hilgenkamp H and Brinkman A 2012 Experimental realization of

superconducting quantum interference devices with topological insulator junctions Appl. Phys. Lett. 100072602

[14] Li S et al 2013 Magnetic properties of gadolinium substituted Bi2Te3 thin films Appl. Phys. Lett. 102 242412[15] Niu C W, Dai Y, Zhang Z K, Ma Y D and Huang B B 2012 Ferromagnetism and manipulation of topological

surface states in Bi2Se3 family by 2p light elements Appl. Phys. Lett. 100 252410[16] Chen Q J, Ang Y S, Lewis R A, Wang X L and Zhang C 2012 Photomixing in topological insulator HgTe/

CdTe quantum wells in terahertz regime Appl. Phys. Lett. 101 211109[17] Zhang J K et al 2013 Electronic topological transition and semiconductor-to-metal conversion of Bi2Te3

under high pressure Appl. Phys. Lett. 103 052102[18] Yashina L V et al 2013 Negligible surface reactivity of topological insulators Bi2Se3 and Bi2Te3 towards

oxygen and water ACS Nano 7 5181–91[19] Chadov S et al 2010 Tunable multifunctional topological insulators in ternary Heusler compounds Nat.

Mater. 9 541–5[20] Li C and Wen Z 2013 Electronic structure of topological insulators with MM’X half-Heusler compounds

using density functional theory Thin Solid Films 546 436–8

9

Mater. Res. Express 1 (2014) 025043 C Li et al

[21] Shekhar C et al 2012 Electronic structure and linear magnetoresistance of the gapless topological insulatorPtLuSb Appl. Phys. Lett. 100 252109

[22] Eremeev S V et al 2011 Ab initio electronic structure of thallium-based topological insulators Phys. Rev. B 83205129

[23] Wang Z F, Su N H and Liu F 2013 Prediction of a two-dimensional organic topological insulator Nano Lett.13 2842–5

[24] Wang Z F, Liu Z and Liu F 2013 Organic topological insulators in organometallic lattices Nat. Commun. 41471

[25] Wang Z F, Liu Z and Liu F 2013 Quantum anomalous Hall effect in 2D organic topological insulators Phys.Rev. Lett. 110 196801

[26] Chen X et al 2011 Molecular beam epitaxial growth of topological insulators Adv. Mater. 23 1162–5[27] Jerng S K et al 2013 Ordered growth of topological insulator Bi2Se3 thin films on dielectric amorphous SiO2

by MBE Nanoscale 5 10618–22[28] Wang G et al 2011 Topological insulator thin films of Bi2Te3 with controlled electronic structure Adv. Mater.

23 2929–32[29] Zhang Y et al 2010 Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional

limit Nat. Phys. 6 584–8[30] Liu C-X et al 2010 Oscillatory crossover from two-dimensional to three-dimensional topological insulators

Phys. Rev. B 81 041307[31] Jiang Y P et al 2012 Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3

Phys. Rev. Lett. 108 016401[32] Liu W et al 2011 Anisotropic interactions and strain-induced topological phase transition in Sb2Se3 and

Bi2Se3 Phys. Rev. B 84 245105[33] Young S M et al 2011 Theoretical investigation of the evolution of the topological phase of Bi2Se3 under

mechanical strain Phys. Rev. B 84 085106[34] Liu Z, Liu C-X, Wu Y-S, Duan W-H, Liu F and Wu, J 2011 Stable nontrivial Z2 topology in ultrathin Bi

(111) films: a first-principles study Phys. Rev. Lett. 107 136805[35] Chen Y M, Li J W, Yang X X, Zhou Z F and Sun C Q 2011 Band gap modulation of the IV, III-V, and II-VI

semiconductors by controlling the solid size and dimension and the temperature of operation J. Phys.Chem. C 115 23338–43

[36] Yang C et al 2012 Correlation between the band gap, elastic modulus, Raman shift and melting point of CdS,ZnS, and CdSe semiconductors and their size dependency Nanoscale 4 1304–7

[37] Wang Z F, Li C and Liu F 2014 Tuning topological edge states of Bi(111) Bilayer film by edge adsorptionNano Lett. 14 2879–83

[38] Kresse G and Joubert D 1999 From ultrasoft pseudopotentials to the projector augmented-wave method Phys.Rev. B 59 1758–75

[39] Kresse G and Furthmüller J 1996 Efficient iterative schemes for ab initio total-energy calculations using aplane-wave basis set Phys. Rev. B 54 11169–86

[40] Perdew J P, Burke K and Ernzerhof M 1996 Generalized gradient approximation made simple Phys. Rev.Lett. 77 3865–8

[41] Grimme S, Antony J, Ehrlich S and Krieg H 2010 A consistent and accurate ab initio parametrization ofdensity functional dispersion correction (DFT-D) for the 94 elements H-Pu J. Chem. Phys. 132 154104

[42] http://toc.uni-muenster.de/DFTD3/[43] Lu G-H, Cuma M and Liu F 2005 First-principles study of strain stabilization of Ge(105) facet on Si(001)

Phys. Rev. B 72 125415[44] Wyckoff R W G 1964 Crystal Structures (New York: Wiley) p 2[45] Wang G and Cagin T 2007 Electronic structure of the thermoelectric materials Bi2Te3 and Sb2Te3 from first-

principles calculations Phys. Rev. B 76 075201

10

Mater. Res. Express 1 (2014) 025043 C Li et al

[46] Yazyev O V, Kioupakis E, Moore J E and Louie S G 2012 Quasiparticle effects in the bulk and surface-statebands of Bi2Se3 and Bi2Te3 topological insulators Phys. Rev. B 85 161101(R)

[47] Chen Y L et al 2009 Experimental realization of a three-dimensional topological insulator, Bi2Te3 Science325 178–81

[48] Dzero M, Sun K, Galitski V and Coleman P 2010 Topological kondo insulators Phys. Rev. Lett. 104 106408[49] Yao Y L et al 2010 Intrinsic topological insulator Bi2Te3 thin films on Si and their thickness limit Adv. Mater.

22 4002–7[50] Fu L and Kane C L 2007 Topological insulators with inversion symmetry Phys. Rev. B 76 045302

11

Mater. Res. Express 1 (2014) 025043 C Li et al