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.

Latex. 1+10 pages. Noted that the parameter $\epsilon$ is related to the square of the energy, rather than the energy itself. Corresponding corrections in the dispersion relations made

References in corpus (3)

• Lattice Green functions in all dimensions
• Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices
• Density of electron states in a rectangular lattice under uniaxial stress