A Van Hove singularity occurs where the gradient of the dispersion relation ∇_k E(k) = 0, causing the density of states D(E) = ∫ δ(E − E(k)) d^dk / (2π)^d to diverge. For a 2D square lattice with tight-binding dispersion E(k) = −2t(cos k_x + cos k_y), there is a logarithmic divergence at the saddle point E = 0. These features are experimentally visible in optical conductivity and ARPES, and are implicated in superconductivity when the Fermi level is tuned to a Van Hove point (as in twisted bilayer graphene at magic angle).