Hysteresis of axionic charge density waves

Magnetic catalysis is a known proposal for inducing dynamical axionic gapped phases by means of external magnetic fields from a Weyl or Dirac semimetal phase. At finite Fermi level, the phase transition is of first-order type and the magnetic field needs to reach a critical value for the transition to take place. Using the theory of bubble nucleation, we predict the order parameter features a hysteretic behavior as a function of the external magnetic field. We also analyze the experimental consequences of this hysteretic behavior in several observables like magnetoconductivity, magnetic susceptibility, and nonlinear optical coefficients. This hysteretic behavior might serve as a fingerprint of magnetic catalysis in condensed matter systems.