Effect of external strain on electronic structure of stanene M. Modarresi a,⇑ , Alireza Kakoee b , Y. Mogulkoc c , M.R. Roknabadi a a Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran b Department of Mechanical Engineering, Amirkabir University, Tehran, Iran c Department of Engineering Physics, Ankara University, Ankara, Turkey article info Article history: Received 4 November 2014 Received in revised form 5 January 2015 Accepted 25 January 2015 Keywords: Stanene Electronic structure Density functional theory Young’s modulus abstract In this article we study the effect of applied strain on the electronic and mechanical properties of stanene, the Tin counterpart of graphene. Due to the relatively large intrinsic spin–orbit coupling we used the fully-relativistic pseudo-potentials to consider the effect of spin–orbit in the density functional calcula- tions. The spin–orbit interaction opens a 70 meV energy gap in the K point but by applying strain the energy gap in the band structure is closed. The density functional theory and simple molecular mechanic models are used to estimate the Young’s modulus of stanene. According to our calculations we estimate the in-plane stiffness of stanene Y s = 40 N/m. By matching DFT and molecular mechanic results of stanene, we investigate the size and chirality effects on the in-plane stiffness of stanene nano ribbons. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction Graphene is the two dimensional hexagonal array of carbon which is considered as a semi-metal or zero-gap semiconductor which has strong potential for future applications [1]. Due to its interesting properties graphene is considered as a key for future researches and technologies. The zero energy gap, limits applica- tion of graphene for future transistors. By cutting and rolling of graphene the graphene nano ribbon and carbon nano tubes are constructed that have a tunable energy gap [2–5]. Also it was shown that absorption of hydrogen atoms transforms graphene to an insulator [6]. Recently, scientists tried to solve the zero-gap problem by new 2D hexagonal materials from other elements in the fourth column of the periodic table. Firstly, the silicene and germanene that are 2D analogue of silicon [7] and germanium [6] were fabricated in laboratory. The last suggestion in this field is related to the 2D Tin which is called stanene [8]. Ezawa investi- gated topological insulators as stanene and emphasized that they exhibit like quantum spin-Hall insulators due to their spin–orbit coupling (SOC). Rachel and Ezawa suggested the silicene, german- ene and stanene as two-dimensional topological insulators which display helical edge states. As a consequence; this type of materials put forward new applications like a giant magneto-resistance and a perfect spin filter [9]. In the case of graphene the intrinsic spin– orbit coupling is negligible [10,11] but a large Rashba spin–orbit coupling was reported for graphene fabricated on the nickel substrate [12,13]. For stanene the relatively large intrinsic spin– orbit interaction opens an energy gap in the electronic band struc- ture [8,14]. The density functional theory (DFT) provides a good approximation for ground state of materials. The DFT, molecular mechanic methods and their combination have been widely used to study the mechanical properties of different structures. The Young’s modulus explains the relation between uniaxial strain and stress. A comparison between the Young’s modulus of graph- ene, stanene and other 2D hexagonal materials shows the effect of buckled structure on the mechanical properties of 2D materials. In this work, we study the effect of applied strain on the elec- tronic properties of stanene. We investigate the Young’s modulus of stanene by using the DFT and molecular mechanic models. By matching both models, we obtained the stretching and bending coefficients in the molecular mechanic for future works on stanene nano structures. Also, we investigate the size and chirality effects on the in-plane stiffness of stanene nanoribbons in the molecular mechanic model. 2. Model and methods We consider a 2D hexagonal unit cell for the stanene as shown in Fig. 1. Tin atoms are not arranged in a flat plate and the atomic posi- tions are buckled. The buckling of atomic structure changes the hybridization between r and p states. Generally there is not an exact solution for ground state of a many body system. In the DFT calculations, this problem is reduced to a self-consistent one- electron form, through the Kohn–Sham equations [15]. In practice the Kohn–Sham equations are solved with many approximations. http://dx.doi.org/10.1016/j.commatsci.2015.01.039 0927-0256/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: mo_mo226@stu-mail.um.ac.ir (M. Modarresi). Computational Materials Science 101 (2015) 164–167 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci