An Algebraic Geometry Method for Calculating DOS for 2D tight binding models
Other Condensed Matter
2012-06-04 v2 Materials Science
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
math.MP
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.
Cite
@article{arxiv.1205.1122,
title = {An Algebraic Geometry Method for Calculating DOS for 2D tight binding models},
author = {Koushik Ray and Siddhartha Sen},
journal= {arXiv preprint arXiv:1205.1122},
year = {2012}
}
Comments
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