Tight-Binding Hamiltonians

Abstract

The use of tight-binding (TB) Hamiltonians as a starting point of many theories is common place in condensed matter physics and materials science. The construction of such Hamiltonians is done with two different philosophies in mind. One is based on atomic level values and the idea of choosing a very small number of hopping integrals usually involving only d orbitals.^1–3 The other approach is in the spirit of the Slater-Koster (SK) interpolation^4,5 method which consists of a fit to the results of a band structure calculation and can easily incorporate hybridization of the d with the s-p orbitals. The practitioners of the first approach wish to retain simplicity in their model and physical significance of the values of their TB parameters. They achieve this at the expense of using a TB Hamiltonian that produces energy bands and densities of states which are of limited accuracy. On the other hand the second approach with the possible deficiency that occasionally produces opposite signs of certain small parameters, can be made to agree, especially for transition metals, almost exactly to the band structure derived from the first principles methods.⁵