Magnetic catalysis and Hall conductivity of excitonic insulators in a planar four-Fermi model

Abstract

We study the effects of a perpendicular magnetic field on the excitonic insulator (EI) phase in the semiconductor regime using an extended planar four-Fermi model. Within the large-$N$ approximation, we determine the coupled scalar and excitonic condensates at finite temperature, chemical potential, and magnetic field. The field enhances the EI condensate and raises its critical temperature, providing an excitonic realization of magnetic catalysis, while the scalar condensate remains constant throughout the EI phase. By contrast, the critical chemical potential depends nonmonotonically on the field because of the successive occupation of Landau levels. The magnetic field also shifts the mean-field tricritical point and enlarges the first-order region of the temperature--chemical-potential phase diagram. We further analyze the Hall conductivity and find that increasing the field reduces the number of plateaus and modifies the threshold for a finite Hall response. For the parameters considered, the emergence of the EI condensate is accompanied by a characteristic change in the Hall conductivity, including a field-dependent change of slope near a continuous transition. These results show that the combined phase structure and Hall response can provide complementary signatures of excitonic ordering in planar fermionic systems.