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

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.

13 pages including appendices, 11 figures

References in corpus (10)

• Heavy Fermions and Quantum Phase Transitions
• Enhancement of superconductivity near a nematic quantum critical point
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Low-energy microscopic models for iron-based superconductors: a review
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Higgs criticality in a two-dimensional metal
• Phonon mediated superconductivity in low carrier-density systems
• Influence of the ferroelectric quantum critical point on SrTiO${}_3$ interfaces
• Superfluid-Insulator Transition and Fermion Pairing in Bose-Fermi Mixtures

Cited by in corpus (5)

• Interplay between singlet and triplet pairings in multi-band two-dimensional oxide superconductors
• Two-particle bound states on a lattice
• Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions
• Stable pair liquid phase in fermionic systems
• High-Temperature Superconductivity from Finite-Range Attractive Interaction