Band structure - Definition and Overview

In solid state physics, the electronic band structure, or simply band structure, refers to the dispersion relation (the relation between energy versus momentum) of electrons in a crystal. According to Bloch's Theorem, electrons in a periodic potential have wavefunctions and energies which are periodic in wavevector up to a reciprocal lattice vector. In addition to the wavevector dependence, an electron can be on any one of an infinite set of bands. The band structure determines a material's electronic properties, optical properties, and a variety of other things.

Calculating band structures from first principles is a topic in theoretical solid state physics. A number of methods have been invented, including the nearly-free electron approximation, the tight binding approximation, the k.p method, Green's function methods, and many more.