Domes of $T_c$ in single-band and multiband superconductors with finite-range attractive interactions

TL;DR

This paper investigates the emergence of superconducting domes in $T_c$ by modeling electrons with finite-range attractive interactions, revealing that the domes occur when the interaction range is comparable to the Fermi wavelength, with implications for various quantum materials.

Contribution

The study extends beyond the Hubbard model to include finite-range interactions and uses both mean-field and renormalization group methods to analyze $T_c$ domes in single- and multiband systems.

Findings

Superconducting $T_c$ domes appear when the interaction range is around the Fermi wavelength.

Multiband systems exhibit additional $T_c$ domes near Lifshitz transitions.

Results are applicable in both 2D and 3D systems, relevant for dilute superconductors and cold atom setups.

Abstract

The rise and fall of the superconducting transition temperature $T_c$ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of $T_c$, we go beyond the prototypical attractive Hubbard model, and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. By numerically solving the mean-field equations, as well as going beyond mean field theory using a functional renormalization group approach, we find that for a characteristic interaction range $\ell$, there exists a dome in $T_c$ around $k_F \ell \! \sim \! {\mathcal{O}}(1)$. For multiband systems, our mean field theory shows the presence of additional domes in the vicinity of Lifshitz transitions. Our results hold in both two and three dimensions and can be intuitively understood from the geometric relation between the Fermi surface and the interaction range. Our model may be relevant for domes of $T_c$ in dilute weakly coupled superconductors or in engineered cold atom systems.