Advances in Theoretical and Mathematical Physics

Volume 17 (2013)

Number 6

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

Pages: 1343 – 1355



Koushik Ray (Department of Theoretical Physics, Indian Association for the Cultivation of Science, Calcutta, India)

Siddhartha Sen (CRANN, Trinity College Dublin, Ireland; R.K. Mission, Vivekananda University, Belur, West Bengal, India)


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.

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