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 magneto-conductivity, magnetic susceptibility and nonlinear optical coefficients. This hysteretic behavior might serve as a fingerprint of Magnetic Catalysis in Condensed Matter systems.