Theory of the Excitonic Insulator in the Presence of Normal Impurities

Abstract

Recently several papers have discussed the possibility of a new kind of insulating phase in semimetals or semiconductors with small band gap. This phase can be described as a condensate of electron-hole pairs (excitons) due to an effective interaction between valence and conduction electrons. This paper extends the analysis of the excitonic phase in the semimetallic region in the presence of randomly distributed normal (i.e., nonmagnetic) impurities. It is shown that the impurities have a pair-breaking effect similar to the case of magnetic impurities in superconductors. The Abrikosov-Gorkov theory developed for the latter case is applied with minor modifications to the excitonic phase. It is shown that beyond a critical impurity concentration the excitonic phase cannot exist. Changes in the transition temperature and in the order parameter are calculated, as well as the density of states. It is found that in a region close to the critical concentration the excitation spectrum of the system has no energy gap.