Band Structures of Narrow Gap Semiconductors in Terms of Coulombic Polaron Effect

Abstract

We consider the formation of a polaron in an interacting Fermi gas due to Coulomb polarization of electron gas by a single electron. We show that the polarization effect due to the Coulomb field in an interacting Fermi gas leads to the Coulomb polaron caused by the exchange-correlation hole and the electron spectrum shows an insulating behavior with the dispersion law of quasiparticles similar to the Kane kp-model of a band structure for narrow gap semiconductors. We apply the polaronic model to the case of inhomogeneous periodic and interacting electron Fermi gas of crystals. We show that the formation of the Coulomb polaron leads to the transition to the semiconductor with the energy bands similar to the well-known semiempirical Kane kp-model of the band structure of narrow gap semiconductors. We also discuss the impact of the results on band structure calculations.