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

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.