Highly anisotropic physics in phosphorene

Phosphorene, monolayer black phosphorus, is a highly anistropic material, where the band structure is Dirac like in one direction and Schrdinger 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 detemine the cyclotron motion in phosphorene and Landau level quantization by using the Bohr-Sommerfeld quantization. We show that the Landau-level energy behaves as B-2/3 as a function of external magnetic field, which is highly contrasted to the case of graphene where the Landau-level energy behaves as root B.