Effective-Mass Theory for Polarons in External Fields

Abstract

Polaron effective-mass wave functions are constructed which diagonalize approximately the Fr\"ohlich Hamiltonian describing a polaron in a weak magnetic field or in a static external potential which varies slowly in space. In this way it is shown that for low-lying states and in weak magnetic fields, polaron energy levels are eigenvalues of the Hamiltonian $\frac{{[\mathrm{p}+(\frac{e}{c})\mathrm{A}]}^{2}}{2{m}_{\mathrm{pol}}}$, where ${m}_{\mathrm{pol}}$ is the polaron effective mass. Likewise, for a slowly varying potential $V(\mathrm{r})$, the effective Hamiltonian describing the polaron motion is $\frac{{\mathrm{P}}^{2}}{2{m}_{\mathrm{pol}}}+V(\mathrm{r})$ for those states in which the polaron momentum remains small. No explicit assumptions about the strength of the electron-LO coupling are made.