Features of the surface tension for the metal--insulator boundary in the vicinity of MI phase transition in the presence of external magnetic field

Abstract

The self-consistent equations for MI phase transition are formulated. We assume two order parameters which describe the phase transition. The first one is the density distribution at MI boundary $\rho (\vec r)$. The second one is a two component complex vector in spin space $\Psi (\vec r)$. It determines electron density in metallic or semimetallic phase in the presence of external magnetic field. Two different components of the vector describe possible spin states of electrons inserted in the external magnetic field. The first order type MI phase transition determined by the variation of the density distribution is considered by means of the gradient expansion of Cahn and Hillard type \cite{CahnHillard}. The second order type transition of electron density beside MI boundary is described by Ginzburg -- Landau expansion \cite{LandLif2}. The interaction between these two parameters is assumed to be linear as a function of electron density with a coefficient which depends on metallic density (cf. \cite{JinwuYe_Lubensky}). The obtained nonlinear equations are exactly solved in the case of MI boundary in the presence of the parallel to the boundary or perpendicular to it uniform magnetic field. The surface tension $\Sigma _{mi}$ at the MI boundary is calculated. It is shown that $\Sigma _{mi}$ is singular. In particular, $\Sigma _{mi}\sim n^{3/2}$ as $ n\Rightarrow 0$ and $\Sigma _{mi}\sim (T-T_c (\vec h))^{3/2} .$ $T_c (\vec h)$ is the transition temperature in the presence of external magnetic field at MI phase transition. \par The singular behavior of $\Sigma _{mi}$ leads to an emphasized hysteresis at MI transition.