Hysteresis of axionic charge density waves

We investigate the metal-insulator transition induced by magnetic fields in Weyl and Dirac semimetals. As this phase transition is of first order at zero temperature and finite chemical potential, we employ nucleation theory to analyze the hysteretic behaviour in the order parameter as a function of the magnetic field. This hysteresis in the order parameter permeates into observables like the magneto-conductivity, magnetic susceptibility and nonlinear optical responses. We suggest that our findings could serve as a signature of magnetic catalysis in condensed matter systems.