Anomalous behavior of the surface tension at the interface of the metallic and insulating phases in the vicinity of the metal-insulator phase transition in a magnetic field

Mean-field equations describing the metal-insulator (MI) transition are formulated. They involve two coupled order parameters characterizing this transition: (i) a scalar order parameter describing the density change accompanying the transition from the insulating state to the metallic one and (ii) an order parameter (a two-component vector) describing the electron density in the metallic or semimetallic phase affected by the applied magnetic field. Two components of this vector correspond to different possible spin states of electrons in the applied magnetic field. The transition in the density of metallic and insulating phases being a first order phase transition is treated in terms of the Cahn-Hilliard-type gradient expansion. The transition in the electron density is a second order phase described by the Ginzburg-Landau-type functional. The coupling of these two parameters is described by the term linearly dependent on the electron density n in the metal with the proportionality factor being a function of the density of the metallic phase. The derived equations are solved in the case of the MI interface in the presence of both parallel and perpendicular uniform magnetic fields. The calculated surface tension Σmi between the metallic and insulating phases has a singular behavior. In the limit of zero electron density n ⟹ 0, Σmi ∼ n3/2. Near the MI transition point Tc(h) in the applied magnetic field, Σmi ∼ [T - Tc(h)]3/2. The singular behavior of the surface tension at the MI interface results in the clearly pronounced hysteresis accompanying the transition from the insulating to metallic state and vice versa.