Effective Hamiltonian of silicene in the presence of electric and magnetic fields
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ONIC PROPERTIES OF SOLID
Effective Hamiltonian of Silicene in the Presence of Electric and Magnetic Fields A. V. Gert*, M. O. Nestoklon, and I. N. Yassievich Ioffe Physical Technical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia *e-mail: [email protected] Received October 19, 2015
Abstract—An effective Hamiltonian of silicene in the neighborhood of Dirac points in the presence of electric and magnetic fields perpendicular to the plane of the film is constructed on the basis of symmetry analysis. Numerical coefficients of various terms in the Hamiltonian are obtained by the tight binding method in the basis sp3d5s* with regard to the interaction with one nearest neighbor. This method was developed in the previous paper [1] in the case of a sublattice displacement of 0.44 Å, which corresponds to the theoretical value of displacement obtained from first principles for a free film of silicene. The effect of the displacement of sublattices on the orientation of spin and pseudospin in silicene is analyzed. The Hamiltonian obtained allows one to consider spin and electron transport for charge carriers with energy less than 0.5 eV. The orbital motion of electrons in an external magnetic field perpendicular to the film is analyzed in detail. DOI: 10.1134/S1063776116100046
1. INTRODUCTION Silicene is a quasi-two-dimensional material consisting of silicon atoms with hexagonal crystal lattice of two plane sublattices displaced perpendicular with respect to each other. In contrast to graphene, sp2 hybridization in silicene is unstable [2], which leads to a buckled structure of silicene. The hybridization of atomic orbitals becomes mixed: sp2–sp3. Another important difference from graphene is the presence of significant spin–orbit interaction. Today, silicene, a silicon analog of graphene, attracts increasing attention in view of the progress in the technology of its production and the prospects of its application in silicon electronics and spintronics [3–5]. Recently, a group of researchers from Italy and USA has reported the fabrication of a field effect transistor based on silicene that operates at room temperature [6]. The device was developed on the basis of an original technology: silicene was grown on a thin layer of silver deposited on an insulating substrate of mica and was coated with an aluminum oxide film. The three-layer structure thus obtained was taken off from mica and placed on a substrate of heavily doped p+ silicon coated with a thin layer of SiO2. After chemical etching of the central part of the upper silver layer, two contacts were formed that served as the drain and source of the transistor, and the control voltage was applied to the heavily doped layer of p-Si. The current–voltage characteristic of this transistor measured at room temperature corresponded to the theoretical
model of ambipolar Dirac charge transport with a mobility of 100 cm2/(V s). Recently, silicene has also been grown on ZrB2 [7]. In the present paper, in Section 2, we construc
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