s-wave Cooper pair insulators and theory of correlated superconductors

Abstract

The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is "unconventional" (non-pair-breaking) in the BEC regime, identified by either the bosonic mean-field or XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose non-analytic changes define a sharp distinction between band and Mott insulators. The corresponding "second order transition" can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple s-wave picture.

arXiv comment18 pages, 4 figures, published version

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• Exact solution for finite center-of-mass momentum Cooper pairing
• Vortices and vortex states in Rashba spin-orbit-coupled condensates
• Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands
• Interaction proximity effect at the interface between a superconductor and a topological insulator quantum well
• Effective theory of fractional topological insulators in two spatial dimensions
• Charge excitations across a superconductor-insulator transition
• Charge and spin fractionalization in strongly correlated topological insulators
• Pairing instabilities in topological insulator quantum wells