Highly anisotropic physics in phosphorene

Abstract

Phosphorene, monolayer black phosphorus, is a highly anistropicmaterial, where the band structure is Dirac like in one direction and Schrödinger like in the other direction. We present several analytic formulas to demonstrate the electronic properties. The conductance is highly anisotropic reflecting the anisotropy of the band structure. We also deteminethe cyclotron motion in phosphoreneand Landau level quantization by using the Bohr-Sommerfeldquantization. We show that the Landau-level energy behaves as B2/3 as a function of external magnetic field, which is highly contrasted to the case of graphene where the Landau-level energy behaves as √B.