Two-band k.p Hamiltonian of phosphorene based on the infinitesimal basis transformations approach

Abstract

In this work, the two-band Hamiltonian of phosphorene (the two-dimensional black phosphorus) was derived in the framework of k.p theory using infinitesimal basis transformation approach. Our main focus was on the lowest subband in conduction band and the highest subband in valence band belonging to the irreducible representations Г4− and Г2+, respectively. We have extended our modeling up to the second-order corrections in the Hamiltonian elements. Our results show the indirectness of the band gap and the anisotropy of the energy dispersion relations for electrons and holes, which is naturally endowed by the orthorhombic symmetry of the crystal lattice.