Van Hove Singularities

Density of states divergences where the group velocity vanishes

Band Structure E(k)
Density of States g(E)
1D DOS
2D DOS
Van Hove points
Band Parameters
1.50
0.20
1D
0.00
Van Hove singularities occur at k-points where ∇_k E(k) = 0 — the group velocity vanishes. In 1D, the DOS diverges as g(E) ∝ |E − E_c|^{-1/2} (integrable). In 2D, a saddle point gives a logarithmic divergence. These kinks and peaks are observable in spectroscopy experiments and determine optical absorption edges.