Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasi-flat band: Enhanced critical temperature evading particle-hole fluctuations

Abstract

In superconductivity, a surge of interests in enhancing $T_{\mathrm{c}}$ is ever mounting, where a recent focus is toward multi-band superconductivity. In $T_{\mathrm{c}}$ enhancements specific to two-band cases, especially around the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover considered here, we have to be careful about how quantum fluctuations affect the many-body states, i.e., particle-hole fluctuations suppressing the pairing for attractive interactions. Here we explore how to circumvent the suppression by examining multichannel pairing interactions in two-band systems. With the Gor'kov-Melik-Barkhudarov (GMB) formalism for particle-hole fluctuations in a continuous space, we look into the case of a deep dispersive band accompanied by an incipient heavy-mass (i.e., quasi-flat) band. We find that, while the GMB corrections usually suppress $T_{\mathrm{c}}$ significantly, this in fact competes with the enhanced pairing arising from the heavy band, with the trade-off leading to a peaked structure in $T_{\mathrm{c}}$ against the band-mass ratio when the heavy band is incipient. The system then plunges into a strong-coupling regime with the GMB screening vastly suppressed. This occurs prominently when the chemical potential approaches the bound state lurking just below the heavy band, which can be viewed as a Fano-Feshbach resonance, with its width governed by the pair-exchange interaction. The diagrammatic structure comprising particle-particle and particle-hole channels is heavily entangled, so that the emergent Fano-Feshbach resonance dominates all the channels, suggesting a universal feature in multiband superconductivity.

12 pages, 9 figures, Accepted version for Physical Review B

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• Upper critical magnetic field and multiband superconductivity in artificial high-Tc superlattices of nano quantum wells
• Lattice Quantum Geometry Controlling 118 K Multigap Superconductivity in Heavily Overdoped CuBa2Ca3Cu4O10+d
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Closed-channel parameters of Feshbach resonances
• High magnetic field response of superconductivity dome in quantum artificial High Tc superlattices with variable geometry