Two Dimensional Polarons with Linearly Dispersing Self Energy and Other Novel Features in the Study of Bi/Single Layer Graphene, and Semi-Dirac Semi-metals on Polar Substrates

Abstract

We consider the polaron dynamics driven by Frohlich type, long wavelength dominated electron-phonon interaction, for three different semi-metals: single and bilayer graphene, and semi-Dirac, all grown on polar substrates such as, SiC or SiO_2. The problem of polaron has been studied by Feynman and others for ordinary polar crystals. But the study of polaron formation in the context of the above-mentioned 2D semi-metals having non-scalar effective Hamiltonians is novel. When SL and BL graphene are grown on polar substrates, their electrons can interact with the surface phonons of those polar substrates, as has been discussed by Fratini et al. That gives rise to the possibility of polaron formation in the context of SL and BL graphene, although they themselves are non-polar. Semi-Dirac material, like SL and BL graphene, has been considered to be grown on a polar substrate and the resulting polaron-dynamics has been investigated. As was discovered by Pardo and Pickett, the interfaces of (TiO_2)_5/(VO_2)_3 heterostructure, in which semi-Dirac dispersion was observed, are non-polar. This justifies the treatment of semi-Dirac, for the purpose of this paper, in the same footing as non-polar materials like SL and BL graphene. The electron self energy, or polaron energy, calculated analytically for BL graphene for small electron-momentum, is shown to vary linearly with the electron momentum. Despite the similarity between BL graphene and ordinary polar crystals in the parabolic nature of the electronic band-structure in the absence of electron-phonon interaction, the linear energy-momentum dispersion of BL graphene polarons stands in stark contrast to the quadratic energy-momentum dispersion of the polarons produced in ordinary polar crystals. In addition to the polaron energy, the decay rate(in the absence of polaron formation), has been calculated for the above-mentioned materials.