Ubiquity of superconducting domes in BCS theory with finite-range potentials

Abstract

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized BCS gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature $T_c$ with the carrier density, $n$, predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasi-local. In contrast, we show that any well-defined non-local potential leads to a "superconducting dome", i.e. a non-monotonic $T_c(n)$ exhibiting a maximum value at finite doping and going to zero for large $n$. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity. Our results provide a prototype example and guide towards improving ab-initio predictions of $T_c$ for real materials.

5 pages, 1 figure, + supplemental material

References in corpus (8)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Quantum Criticality in Heavy Fermion Metals
• Theory of Intertwined Orders in High Temperature Superconductors
• Metallicity and superconductivity in doped strontium titanate
• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• A bound on superconducting $T_c$'s
• The BCS Critical Temperature for Potentials with Negative Scattering Length

Cited by in corpus (8)

• Screening of pair fluctuations in superconductors with coupled shallow and deep bands: a route to higher temperature superconductivity
• Domes of $T_c$ in single-band and multiband superconductors with finite-range attractive interactions
• The BCS Critical Temperature at High Density
• The BCS Energy Gap at High Density
• Universality in low-dimensional BCS theory
• Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions
• High-Temperature Superconductivity from Finite-Range Attractive Interaction
• Finite-range effect in the two-dimensional density-induced BCS-BEC crossover