Effect of magnetic field on the quantum capacitance of silicene

Abstract

This paper presents a theoretical study of the quantum magnetocapacitance of spin and valley-polarized silicene in an external perpendicular magnetic field. From the low−energy effective electronic Hamiltonian, the energy spectrum and the wave function of electrons in a monolayer of silicene have been computed in detail. The numerical results show that the electric and magnetic fields have a strong influence on the energy spectrum of electrons. For example, the band gap could be adjusted by the external electric field, and the energy levels exhibit spin splitting, including the zero level. The electronic properties of silicene differ from those of the well-known graphene due to the strong intrinsic spin-orbit interaction and buckled structure of silicene, graphene is a monolayer material with a flat geometric structure, and the spin–orbit interaction is so small that it can be ignored. By analyzing the density of states function, the quantum capacitance is evaluated in relation to Shubnikov–de Haas oscillations calculated using the Poisson summation formula. The numerical results indicated that when the electric field energy was larger than the spin–orbit interaction energy, the capacitance was zero at the Fermi energy level E_F = 0. This indicated that the presence of spin−orbit and electric field interactions lead to the emergence of a beating pattern at low magnetic fields and a peak would split at the higher fields. This behavior could be attributed to the interference of Shubnikov–de Haas oscillations at the two frequencies of the split Landau levels. The calculation presented in this paper on the quantum capacitance of silicene was also valid for germanene with an even stronger spin–orbit coupling .