The Hall number across a van Hove singularity

In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number n(H) of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a universal nonanalytic dependence of n(H) on the electron density in the high-field limit, but a nonsingular dependence at low fields. The existence of an assumed nematic transition produces a doping dependent n(H) similar to that observed in recent experiments in the high-temperature superconductor YBa2Cu3O7-x.