Square lattice tight-binding: ε(k) = −2t(cos kₓ + cos k_y) — van Hove singularities
The tight-binding dispersion ε(k) = −2t(cos kₓ + cos k_y) on a square lattice has van Hove singularities at M=(π,0) where ε = 0 (half-filling). The Fermi surface undergoes a Lifshitz transition from electron to hole pockets as μ crosses these saddle points. Nesting vectors Q=(π,π) connect opposite sides of the half-filled Fermi surface, driving antiferromagnetic instability in cuprate superconductors.