An Algebraic Geometry Method for Calculating DOS for 2D tight binding models

TL;DR

This paper introduces an algebraic geometry approach to compute the density of states in 2D tight binding models, providing explicit formulas for square and honeycomb lattices.

Contribution

It develops a novel algebraic geometry method to analytically derive the density of states for specific 2D lattice models, advancing computational techniques in condensed matter physics.

Findings

Derived explicit density functions for square and honeycomb lattices

Demonstrated the effectiveness of algebraic geometry in electronic structure calculations

Provided a new analytical framework for DOS calculations in 2D materials

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.