Polarons in an Electric Field

Abstract

Wave functions for a polaron in a uniform external electric field $\frac{F}{e}$ are calculated in the weak coupling approximation to first order in the electron-phonon interaction at zero temperature. The electric field is treated exactly. It is shown that the wave function is not an analytic function of the applied field in the neighborhood of $F=0\mathrm{}$, but can be expanded in an asymptotic power series in $F$ valid near $F=0\mathrm{}$. The distortion, due to $F$, of the distribution of polarization potential around the electron is calculated in the weak-field limit. It is shown that this distortion effect in typical crystals is small for reasonable values of the applied field.