The Form and Properties of the Tight-Binding Density of States in Two Dimensions. Possible Application to Superconductivity |
| M. Gładysiewicz, R. Gonczarek and M. Mulak Institute of Physics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland |
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| Received: November 5, 2001; revised version March 18, 2002 |
| The form of the density of states for a tight-binding model with the first and the next-nearest neighbour hoppings for a rectangular planar lattice and a shift of the chemical potential are calculated. This is newly and comprehensively formulated integral form illustrated numerically, helpful in approach to two-dimensional superconducting models. In some particular cases the complete analytical forms of the density of states are obtained. It is shown that for all cases the density of states has a single van Hove singularity of the logarithmic type at the identically defined point. The proper approximate analytical representations are found. The difference between the exact numerical and approximate analytical forms is evaluated and illustrated. |
| DOI: 10.12693/APhysPolA.101.865 PACS numbers: 74.20.-z, 74.20.Fg |