An algebraic geometry method for calculating DOS for 2D tight binding models

Abstract

An algebraic geometry method is used to calculate the moments of the electron density of states as a function of the energy for lattices in the tight binding approximation. Interpreting the moments as the Mellin transform of the density allows writing down a formula for the density as an inverse Mellin transform. The method is illustrated by working out the density function for the two-dimensional square and honeycomb lattices.The tight binding model is a widely used scheme for studying electronic band structure of solids [1]. The model is defined by a Hamiltonian quadratic in the electron creation and destruction operators indexed by a set of points in the D-dimensional Euclidean space R D , called sites. The sites e-print archive: http://lanl.arXiv.org/abs/1205.1122