Superconductivity from energy fluctuations in dilute quantum critical polar metals

Abstract

Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. Here we demonstrate that pairing mediated by energy fluctuations, ubiquitously present close to continuous phase transitions, occurs in dilute quantum critical polar metals and results in a dome-like dependence of the superconducting Tc on carrier density, characteristic of non-BCS superconductors. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optical phonons decouple from the electron charge. In the resulting vacuum, long-range attractive interactions emerge from the energy fluctuations of the critical phonons, resembling the gravitational interactions of a chargeless dark matter universe. Our estimates show that this mechanism may explain the critical temperatures observed in doped SrTiO3. 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.

Superconductivity enhancement in polar metal regions of Sr0.95Ba0.05TiO3 and Sr0.985Ca0.015TiO3 revealed by systematic Nb doping

“…Another theoretical work on Dirac semimetals predicted that the superconductivity will only appear in the ferroelectric region 25 . The two-phonon exchange superconductivity scenario [58][59][60][61] requires neither quantum criticality nor quantum fluctuations, but can predict a reasonable T c value in the dilute carrier-density region 60 . Therefore, we considered whether the ferroelectric fluctuations that occur around n* may not be the main driving force for enhancement of the superconductivity.…”

“…Although no compelling theories have been proposed that encompass the disparate existing ideas, some unconventional mechanisms have recently sparked new research interest in this field. Typical examples include the Cooper pairings driven by plasmon and plasmon-polariton coupling with longitudinal optical (LO) phonons [55][56][57] and by ferroelectric fluctuations [15][16][17]22,24,29 , particularly those driven via the two phonons [58][59][60][61] of a soft transverse optical (TO) mode, which explain the T 2 -dependence of the resistivity very well 62,63 . There were also some remarkable experimental discoveries: carrier doping of two ferroelectric matrices, (Sr,Ca)TiO 3 (refs.…”

Generalized Rashba Electron-Phonon Coupling and Superconductivity in Strontium Titanate

“…Proposed pairing theories include the dynamical screening of the Coulomb interaction due to longitudinal modes [16][17][18][19] recently challenged in Ref. [20], bipolaron formation [21], and diverse approaches to linear coupling [1,[22][23][24][25][26][27][28][29][30] or quadratic coupling to the FE mode [31][32][33][34][35]. The last two proposals have the advantage that, coupling electrons directly to the FE soft mode, provide a natural explanation to the sensitivity to the FE instability.…”

“…Within the conventional electron-phonon interaction scheme, this implies a decoupling of the soft modes from the electronic density to linear order [39]. One promising alternative route involves going to next order by coupling the electrons to pairs of TO modes [31][32][33][34]40]. Another possibility, and subject of the present article, is the linear vector coupling to the electrons, allowed in the presence of spin-orbit coupling (SOC) [13,24,25,37,[41][42][43][44].…”

Anisotropic resistivity and superconducting instability in ferroelectric metals

“…Proximity to a ferroelectric instability strongly suggests that the soft TO phonons play an influential role. Thus, the model of two-phonon scattering was brought forward to revisit the temperature dependence of charge transport [16,17] and study the effect of oxygen isotope substitution on superconducting transition temperature [18][19][20].…”