Bipolaronic High-Temperature Superconductivity from Phonon-Modulated Hopping: A Perspective

TL;DR

This paper reviews a novel route to high-temperature phonon-mediated superconductivity via phonon-modulated hopping, which enables lighter bipolarons and higher transition temperatures than traditional models.

Contribution

It introduces a class of electron-phonon couplings that bypass the conventional Tc bound, demonstrating high Tc in bipolaronic superconductors through quantum Monte Carlo simulations.

Findings

Bipolarons formed via phonon-modulated hopping are lighter than Holstein bipolarons.

Quantum Monte Carlo shows Tc exceeds traditional bounds in these models.

Strong Coulomb repulsion does not suppress high Tc in this mechanism.

Abstract

Phonon-mediated superconductivity is conventionally thought to be capped at a transition temperature $T_{\mathrm{c}}$ no larger than roughly one-tenth of the phonon frequency $\Omega$, a bound rooted in the breakdown of Migdal-Eliashberg theory at intermediate coupling and in the heaviness of bipolarons formed in standard models with phonons that couple to the electron density. In this review I describe a route to phonon-mediated high-$T_{\mathrm{c}}$ superconductivity that bypasses this bound. The key ingredient is a class of electron-phonon couplings in which lattice distortions modulate the electron hopping and therefore its kinetic energy rather than its potential energy, known as the Peierls model (also known as Su-Schrieffer-Heeger model). In these models phonon exchange generates an interaction that binds two electrons into a small but unusually light bipolaron. Using sign-problem-free quantum Monte Carlo simulations of a bond-Peierls model on the square and cubic lattices, my collaborators and I have shown that a dilute liquid of such bipolarons forms an $s$-wave superconductor with a $T_{\mathrm{c}}/\Omega$ that significantly exceeds the conventional bound, that this conclusion is robust against screened Coulomb repulsion, and that $T_{\mathrm{c}}/\Omega$ -- despite being reduced -- remains above bound in presence of strong long-range Coulomb repulsion. A semi-classical instanton analysis explains why, at strong coupling, bipolarons in models with phonon-modulated hopping are lighter than their density-coupled (Holstein) counterparts. I close with a discussion of materials in which this physics may be operative, in particular the iron-based pnictide superconductors, and of design principles that follow from it.