Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene

Abstract

Phosphorene is the monolayer structures of black phosphorous. Its low-energy physics can be described by continuum model in the scheme of k∙p theory. Validity of energy range for this model can be improved by extra terms as trigonal warp effect in graphene. We construct a new continuum model by expanding the tight-binding Hamiltonian of phosphorene up to the order of k 4 . The new quartic model increases the energy range where the eigenvalues of continuum and tight-binding Hamiltonian are matched. Moreover, we examine the Landau levels of phosphorene by the influence of quartic terms. While quartic terms have insignificant effects on the lower Landau levels of phosphorene, they have non-negligible contributions to the higher levels. In this study, we propose a new continuum model which brings better description to the dynamics of phosphorene charge carriers.