Effect of Impurity on the Gas-Liquid Type Phase Transition of Semimetals

Abstract

The critical temperature of a gas-liquid type first order phase transition which is expected to occur in bismuth at low temperature ( T ≃0.1 K) in a strong magnetic field ( H ≃100 kOe) is calculated. Coulomb interaction between the carriers is treated by a mean field theory and the impurity scattering is treated by a self-consistent Born approximation. It is shown that the impurity scattering lowers the critical temperature, An expression for the critical value of the impurity scattering, which makes the critical temperature vanish, is obtained.