Polaron catastrophe within quantum acoustics

TL;DR

This paper models the complex dynamics of electrons and acoustic phonons in quantum acoustics, revealing how various parameters influence polaron formation and providing new insights into electron-lattice interactions.

Contribution

It introduces a novel non-perturbative framework for simulating electron-phonon interactions using coherent states and wavepackets, differing from traditional tight-binding models.

Findings

Polaron formation is favored at low temperatures and high deformation potentials.

External fields weakly suppress polaron formation at high strengths.

Conditions for polaron stability depend on material parameters like sound velocity and effective mass.

Abstract

The quantum acoustic framework has recently emerged as a non-perturbative, coherent approach to electron-lattice interactions, uncovering rich physics often obscured by perturbative methods with incoherent scattering events. Here, we model the strongly coupled dynamics of electrons and acoustic lattice vibrations within this framework, representing lattice vibrations as coherent states and electrons as quantum wavepackets, in a manner distinctively different from tight-binding or discrete hopping-based approaches. We derive and numerically implement electron backaction on the lattice, providing both visual and quantitative insights into electron wavepacket evolution and the formation of acoustic polarons. We investigate polaron binding energies across varying material parameters and compute key observables, including mean square displacement, kinetic energy, potential energy, and vibrational energy. over time. Our findings reveal the conditions that favor polaron formation, which is enhanced by low temperatures, high deformation potential constants, slow sound velocities, and high effective masses. Additionally, we explore the impact of external electric and magnetic fields, showing that while polaron formation remains robust under moderate fields, it is weakly suppressed at higher field strengths. These results deepen our understanding of polaron dynamics and pave the way for future studies into non-trivial transport behavior in quantum materials.