Dynamical conductivity of a two-dimensional weakly doped Holstein system

Abstract

The generalized Drude formula is used to study conductivity properties of the two-dimensional weakly doped Holstein model with a free-electron-like dispersion. The relaxation processes associated with the scattering of conduction electrons by optical phonons are described in terms of a frequency- and temperature-dependent memory function. The imaginary and real parts of the memory function are analyzed in detail in the regime when characteristic energy scales of the problem, i.e., electron Fermi energy and optical phonon energy, are comparable in size. Results obtained at zero temperature and at finite temperatures are used to determine temperature effects in the real part of the dynamical conductivity as well as the frequency dependence of the optical electron mass and the electron relaxation rate. Finally, the characteristic fingerprints of a Holstein system with multiple phonon branches are identified in the dynamical electron conductivity.