Effective Hamiltonian of silicene in the presence of electric and magnetic fields

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.