Superconductivity from energy fluctuations in dilute quantum critical polar metals

TL;DR

This paper proposes a novel mechanism for superconductivity in dilute quantum critical polar metals, where energy fluctuations act as the pairing glue, potentially explaining observed critical temperatures in materials like doped SrTiO3.

Contribution

It introduces a new pairing mechanism based on energy fluctuations in quantum critical polar metals, differing from traditional electron-phonon interactions.

Findings

Superconducting $T_c$ shows a dome-like dependence on carrier density.

The mechanism may account for $T_c$ in doped SrTiO$_3$.

Predictions are made for enhanced superconductivity near polar quantum criticality.

Abstract

Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optic phonons decouple from the electron charge. In the resulting vacuum, the residual interactions between quasiparticles are carried by energy fluctuations of the polar medium, resembling the gravitational interactions of a dark matter universe. Here we demonstrate that pairing inevitably emerges from "gravitational'' interactions with the energy fluctuations, leading to a dome-like dependence of the superconducting $T_c$ on carrier density. Our estimates show that this mechanism may explain the critical temperatures observed in doped SrTiO$_3$. We provide predictions for the enhancement of superconductivity near polar quantum criticality in two and three dimensional materials that can be used to test our theory.