Beyond the Fröhlich Hamiltonian: Large polarons in anharmonic solids

The large Fröhlich polaron, an electron interacting with a continuum of lattice phonons, is one of the most fundamental and deeply studied problems in electron-phonon physics. The Fröhlich Hamiltonian assumes a linear electron-phonon interaction. In recent years, however, significant interest has been raised in additional interaction terms, such as the 1-electron-2-phonon interaction. In our work, we extend Fröhlich theory to include this interaction and investigate the properties of the resulting polaron.

We derive an analytical expression for the interaction strength of an electron coupling to LO phonons in a zincblende-structure material. The interaction strength only depends on a single scalar parameter, making it well-suited for analytical calculations. With the path integral method and Green's function expansion, it is shown that the additional term significantly increases the binding energy of the polaron, broadens the bipolaron stability regime, and causes a secondary absorption peak in the optical conductivity. Finally, it is shown that our derivation can be generalized to more complicated materials, where the interaction material parameters are given by third order derivatives of the energy which can be calculated from first principles.