Beyond the Fröhlich Hamiltonian: Path integral treatment of large polarons in anharmonic solids

Abstract

The properties of an electron in a typical solid are modified by the interaction with the crystal ions, leading to the formation of a quasiparticle: the polaron. Such polarons are often described using the Fröhlich Hamiltonian, which assumes the underlying lattice phonons to be harmonic. However, this approximation is invalid in several interesting materials, including the recently discovered high-pressure hydrides which superconduct at temperatures above $200$K. In this paper, we show that Fröhlich theory can be extended to eliminate this problem. We derive four additional terms in the Fröhlich Hamiltonian to account for anharmonicity up to third order. We calculate the energy and effective mass of the new polaron, using both perturbation theory and Feynman's path integral formalism. It is shown that the anharmonic terms lead to significant additional trapping of the electron. The derived Hamiltonian is well-suited for analytical calculations, due to its simplicity and since the number of model parameters is low. Since it is a direct extension of the Fröhlich Hamiltonian, it can readily be used to investigate the effect of anharmonicity on other polaron properties, such as the optical conductivity and the formation of bipolarons.

arXiv commentVersion 1.3

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Cited by in corpus (11)

• Fröhlich polaron effective mass and localization length in cubic materials: degenerate and anisotropic electronic bands
• Polaron with Quadratic Electron-phonon Interaction
• Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Soliton States From Quadratic Electron-Phonon Interaction
• Multiple phonon modes in Feynman path-integral variational polaron mobility
• Path-integral approach to the thermodynamics of bosons with memory: Partition function and specific heat
• Optical conductivity of an anharmonic large polaron gas at weak coupling
• Analytic method for quadratic polarons in nonparabolic bands
• Polarons with arbitrary nonlinear electron-phonon interaction
• Stability conditions for a large anharmonic bipolaron