Landau levels and magneto-transport property of monolayer phosphorene

Xiaoying Zhou, Rui Zhang, Jianpeng Sun, YongLian Zou, Guanghui Zhou, Feng Zhai, Kai Chang

Published 2014-11-16Version 1

We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective \textbf{\emph{k$\cdot$p}} Hamiltonian and tight-binding (TB) model. At low field regime, we find that the LLs linearly depend both on the LL index $n$ and magnetic field $B$, which is similar with that of conventional semiconductor two-dimensional electron gas. The Landau splittings of conduction and valence band are different and the wavefunctions corresponding to the LLs are strongly anisotropic for a fixed magnetic field due to the different anisotropic effective masses. An analytical expression for the LLs in low energy regime is obtained via solving the decoupled Hamiltonian, which agrees well with the numerical calculations. At high magnetic regime, a self-similar Hofstadter butterfly (HB) spectrum is obtained by using the TB model. The HB spectrum is consistent with the Landau level fan calculated from the effective \textbf{\emph{k$\cdot$p}} theory in a wide regime of magnetic fields. The Hall and the longitudinal conductances (resistances) clearly reveal the structure of LLs.