Van Hove singularity

A nonanalyticity of the density of states associated with a stationary point of a band dispersion relation. Its form depends on dimension and on whether the stationary point is an extremum or a saddle.

For a one-dimensional subband $E=E_0+\alpha k^2$ with $\alpha >0$, the density of states varies as $(E-E_0{)}^{-1/2}$ just above its edge. Optical peaks also depend on the joint density of states, selection rules and excitons.