Hall number across a van Hove singularity

In this paper, 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. Finally, 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 YBa₂Cu₃O_7-x.