BCS superconductivity near the band edge: Exact results for one and several bands

Abstract

We revisit the problem of a BCS superconductor in the regime where the Fermi energy is smaller than the Debye energy. This regime is relevant for low-density superconductors such as SrTiO${}_3$ that are not in the BEC limit, as well as in the problem of "shape resonances" associated with the confinement of a three-dimensional superconductor. While the problem is not new, exact results were lacking in the low-density limit. In two dimensions, we find that the initial rise of the pairing temperature $T_c$ at low density $n$ is nonanalytic and faster than any power of $n$. In three dimensions, we also find that $T_c$ is nonanalytic, but starts with zero slope at weak coupling and infinite slope at strong coupling. Self-consistent treatment of the chemical potential and energy dependence of the density of states are crucial ingredients to obtain these results. We also present exact results for multiband systems and confirm our analytical expressions by numerical simulations.

Published version

References in corpus (6)

• Electric Field Control of the LaAlO${}_3$/SrTiO${}_3$ Interface Ground State
• Resonant and crossover phenomena in a multiband superconductor tuning the chemical potential near a band edge
• The gap amplification at a "shape resonance" in a superlattice of quantum stripes: a mechanism for high Tc
• Superconductivity vs bound state formation in a two-band superconductor with small Fermi energy -- applications to Fe-pnictides/chalcogenides and doped SrTiO3
• Band-edge BCS-BEC crossover in a two-band superconductor: physical properties and detection parameters
• Critical Temperature and Energy Gap for the BCS Equation

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• High-Tc superconducting dome in artificial heterostructures made of nanoscale quantum building blocks
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• Multifaceted impact of a surface step on superconductivity in atomically thin films
• Constraints on the total coupling strength to bosons in iron based superconductors
• Strong Landau-quantization effects in high-magnetic-field superconductivity of a two-dimensional multiple-band metal near the Lifshitz transition
• Interplay between orbital-quantization effects and the Fulde-Ferrell-Larkin-Ovchinnikov instability in multiple-band layered superconductors
• Theory of dual fermion superconductivity in hole-doped cuprates
• Periodicity of superconducting shape resonances in thin films
• Terahertz spectroscopy evidence of possible 40 K superconductivity in rhenium-doped strontium ruthenates
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