Strain induced phase transitions in silicene bilayers: a first principles and tight-binding study Chao Lian and Jun Ni Citation: AIP Advances 3, 052102 (2013); doi: 10.1063/1.4804246 View online: http://dx.doi.org/10.1063/1.4804246 View Table of Contents: http://scitation.aip.org/content/aip/journal/adva/3/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Tight-binding description of graphyne and its two-dimensional derivatives J. Chem. Phys. 138, 244708 (2013); 10.1063/1.4811841 Tight-binding analysis of coupling effects in metamaterials J. Appl. Phys. 109, 023103 (2011); 10.1063/1.3533948 From multilayered graphite flakes to nanostructures: A tight-binding molecular dynamics study J. Chem. Phys. 129, 224709 (2008); 10.1063/1.3037212 Tight-binding study of nonmagnetic-defect-induced magnetism in graphene Low Temp. Phys. 34, 805 (2008); 10.1063/1.2981392 Transferable tight-binding parametrization for the group-III nitrides Appl. Phys. Lett. 81, 4838 (2002); 10.1063/1.1529312 All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/ Downloaded to IP: 128.114.34.22 On: Fri, 28 Nov 2014 03:14:52 AIP ADVANCES 3, 052102 (2013) Strain induced phase transitions in silicene bilayers: a first principles and tight-binding study Chao Lian and Jun Nia Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, P.R.China (Received 5 February 2013; accepted 23 April 2013; published online 2 May 2013) Using first principles and tight-binding calculations, we have investigated the struc- tures of silicene bilayers under the isotropic tensile strain. We find that (i) the strain induce several barrierless phase transitions. (ii) After the phase transitions, the bilayer structures become planar, similar with the AA-stacking graphene bilayers, but com- bined with the strong covalent interlayer bonds. The tight-binding results demonstrate that this silicene bilayer is characterized by intralayer sp2 hybridization and the inter- layer sp1 hybridization. (iii) The electronic properties of the silicene bilayers change from semiconducting to metallic with the increase of strain. C 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4804246] I. INTRODUCTION Silicene, the two-dimensional silicon nanosheet, has attracted extensive research interests in recent years.1–26 Silicene shares many important properties with graphene, especially the most fas- cinating one: the Dirac-type dispersions at the Fermi surface, which is shown by both first-principles calculations7–14 and the measurements from different experiments.1, 3, 4 Other than the similarity with graphene, silicene has its own advantages. First, the highly developed silicon microelectronic industry provide a strong technologic basis for the applications of silicene. Second, the π electrons in silicene are much more active than that of graphene.24 The active π electrons in silicene lead to a different structure from graphene. The silicene monolayer has low-buckled structure instead of a planar structure.7 The bilayer structures also show different configurations. The most stable graphene bilayer is in the AB stacking and the interlayer bonds in graphene bilayer are the weak Van der Waals interactions. However, if the two silicene monolayers are manipulated into the AB stack- ing silicene bilayer, the strong covalent bonds will form between different layers. The original low buckled silicene monolayer will become a complete sp3 Si(111) sheet. Morishita et.al. have demon- strated that, because of the unpaired pz electrons, this kind of AB stacking silicene bilayer(SSBL) is only metastable.25, 26 Instead, a reconstruction will occur in the SSBL with lower energy. This reconstructed silicene bilayer (RSBL) is the most stable structure. The structures of the silicene monolayers and bilayers show that the π bonds in silicene is not pure sp2 hybridization, but a mixed sp2-sp3 hybridization. Recently, Wu et.al. have demonstrated that the strain will turn several wurtzite materials into stable graphitic thin films.27 However, even under very large strain, the silicene does not become planar but remain buckled. It indicates that the planar monolayer structure is difficult to be obtained because of the active π electrons. In silicene bilayers, the π electrons is partly saturated when the interlayer bonds are formed. It may lead to a possible planar bilayer structure tuned by strain. Thus, it is important to discuss the changes of the silicene bilayer structures under strain. In this paper, we study the structures of silicene bilayers under isotropic tensile strains. Both SSBL and RSBL are considered. We find that the phase transitions occurs under certain tensile strains for SSBL and RSBL, both with no energy barrier. aElectronic mail: [email protected] 2158-3226/2013/3(5)/052102/10 3, 052102-1 C Author(s) 2013 All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/ Downloaded to IP: 128.114.34.22 On: Fri, 28 Nov 2014 03:14:52 052102-2 C. Lian and J. Ni AIP Advances 3, 052102 (2013) After the transition, the SSBL and RSBL turn into a graphene-like silicene bilayer (GBSL) structure. Different from the AB stacking graphene bilayer with the Van der Waals interlayer interactions, the GBSL is combined in the AA stacking with the strong covalent bonds. Using the tight-binding model, we demonstrate that the hybridization of the electrons in the GSBL is the sp2 − sp1 hybridization without any sp3 part. Meanwhile, with the increase of strain, the electronic property of the silicene bilayer also turn from semiconducting to metallic. This article is organized as follows: Section I is the background information. Section II and Section III are the first principles results of the structural transitions and the electronic phase transitions induced by the strain. Section IV is the tight-binding model of the GSBL. Section V is the summary. II. STRUCTURAL TRANSITIONS The first principles calculations are performed with the Vienna Ab initio Simulation Pack- age (VASP).28–30 We use the projector augmented-waves method31 and Perdew-Burke-Ernzerhof exchange-correlation.32 The plane-wave cutoff energy is set to be 250 eV. Using the conjugate gra- dient method, the positions of atoms are optimized until the convergence of the force on each atoms is less than 0.005 eV/Å. The vacuum space is larger than 15 Å and sufficient to make the system isolated. The Monkhorst-Pack scheme33 is used to sample the Brillouin zone. The k mesh of 8 × 8 × 1 including the point is used in the structure optimization, and a larger 12 × 12 × 1kmesh is used in the total energy calculations. There is a 2 × 1 reconstruction in the RSBL, thus a 2 × 2 supercell is chosen to reproduce the RSBL structure. The atom positions in the RSBL are set to be thesameasinRefs.25 and 26, and then relax to ensure it become the most stable configuration. The supercell used in the calculations are the 2 × 2 silicene unit cell, containing 16 silicon atoms. Spin-polarized calculations are performed with both ferromagnetic and antiferromagnetic initial states in all the configurations. No magnetic order emerges in the final state. We apply isotropic tensile strains on the initial structures, including the SSBLs and RSBLs. The RSBL is the most stable structure which will be essentially studied. We also choose the SSBL for comparison. The SSBL is the most important metastable structure which possibly exists in the beginning of the experimental growth procedure at low temperature. Other metastable configurations are also reported in the Ref. 25. However, these configurations can not be synthesized at low tem- perature and will turn into the RSBL at high temperature. Thus we consider the RSBL and the SSBL as the initial structures. The strain is expressed as = (a − a0)/a0, where a and a0 are the lattice constants with and without strain, respectively.√ The strain is applied by extending the basis vec- = , , = 1 , 3 , = + , , = 1 + , tors√ of the cell a1 (a0 0 0), a2 ( 2 a0 2 a0 0) to a1 (a0(1 ) 0 0), a2 ( 2 a0(1 ) 3 + , = α + β = α + 2 a0(1 ) 0). Any direction in the silicene plane a a1 a2 becomes a (1 )a1 + β(1 + )a2 = (1 + )a, which indicates that the strain is equal along every direction and thus isotropic. The coordinates of each atom r = xa1 + ya2 + za3 become r = x(1 + )a1 + y(1 + )a2 + za3 and then relax to the most stable positions. The SSBL is relaxed from the bilayer slice of Si(111) and the RSBL is obtained similarly with the previous work.25, 26 As shown in Fig. 1,the phase I stands for the SSBL and the phase II stands for the RSBL. The mixed sp2-sp3 hybridizations are observed for both SSBL and RSBL. For the SSBL, the T1 atoms in Fig. 1(a) form a nearly regular tetrahedrons with the nearest neighbors, which is a typical feature of the sp3 hybridizations. As for the RSBL, the T2 atoms in Fig. 1(b) protrude and form the 2 × 2 reconstruction, which indicates that there is partial sp3 hybridization.25 Zhao has demonstrated that this sp2-sp3 hybridization is the determining factor of the stability in silicene system.34 The variation of the weight of the sp3 part in the sp2-sp3 hybridizations is important to analyze the stability of the silicene bilayer structures. The 3 2 3 weight of the sp part in the sp -sp hybridizations is measured by the buckle lengths of T1 atoms and T2 atoms, where the T1(T2) atom is the outmost atom in the SSBL(RSBL).