Polaron with Quadratic Electron-phonon Interaction

Abstract

We present the first numerically exact study of a polaron with quadratic coupling to the oscillator displacement, using two alternative methodological developments. Our results cover both anti-adiabatic and adiabatic regimes and the entire range of electron-phonon coupling $g_2$, from the system's stability threshold at attractive $g_2=-1$ to arbitrary strong repulsion at $g_2\gg 1$. Key properties of quadratic polarons prove dramatically different from their linear counterparts. They (i) are insensitive even to large quadratic coupling except in the anti-adiabatic limit near the threshold of instability at attraction; (ii) depend only on the adiabatic ratio but are insensitive to the electron dispersion and dimension of space; (iii) feature weak lattice deformations even at the instability point. Our results are of direct relevance to properties of electrons at low densities in polar materials, including recent proposals for their superconducting states.

6 pages, 6 figures + supplemental material

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Cited by in corpus (7)

• "Quantum bipolaron" superconductivity from quadratic electron-phonon coupling
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Soliton States From Quadratic Electron-Phonon Interaction
• Light polarons with electron-phonon coupling
• Analytic method for quadratic polarons in nonparabolic bands
• Polarons with arbitrary nonlinear electron-phonon interaction
• Global sampling of Feynman's diagrams through Normalizing Flow