Electronic band structure

Summary

The electronic band structure of a crystal is the family of energy functions $k \mapsto E_m(k)$ of an electron in a periodic potential. Here $m$ is a band number and $k$ is a wave vector in the Brillouin zone. It comes from Bloch's theorem: eigenstates of a periodic Hamiltonian can be labelled by a crystal momentum $k$. The allowed energies form intervals, the bands, which can be separated by forbidden intervals, the gaps. Whether the Fermi energy falls in a band or in a gap decides whether the solid is a metal or an insulator.