What is tight binding model?

The tight binding model is a quantum mechanical model used to describe the electronic structure of materials, particularly in condensed matter physics. It is based on the assumption that the wave functions of electrons in a solid can be approximated by a linear combination of atomic wave functions, weighted by the overlap integrals between neighboring atoms.

In this model, the Hamiltonian of the system is expressed as a sum of kinetic and potential energy terms, with the potential energy term representing the interaction between electrons and the atomic cores. The model takes into account the hopping of electrons between adjacent atoms, leading to the formation of energy bands in the electronic structure of the material.

The tight binding model is particularly useful for studying the behavior of electrons in materials with strong electron-electron interactions, such as transition metals and semiconductors. It can be used to predict various electronic properties of materials, such as band structure, density of states, and transport properties.

Although the tight binding model is a simplification of the true electronic structure of materials, it has been shown to be accurate in many cases and provides valuable insights into the behavior of electrons in solids. It is often used in conjunction with more sophisticated methods, such as density functional theory, to study the electronic properties of materials.