Unitarity in periodic potentials: a renormalization group analysis

Abstract

We explore the universal properties of interacting fermionic lattice systems, mostly focusing on the development of pairing correlations from attractive interactions. Using renormalization group we identify a large number of fixed points and show that they correspond to resonant scattering in multiple channels. Pairing resonances in finite-density band insulators occur between quasiparticles and quasiholes living at different symmetry-related wavevectors in the Brillouin zone. This allows a BCS-BEC crossover interpretation of both Cooper and particle-hole pairing. We show that in two dimensions the run-away flows of relevant attractive interactions lead to charged-boson-dominated low energy dynamics in the insulating states, and superfluid transitions in bosonic mean-field or XY universality classes. Analogous phenomena in higher dimensions are restricted to the strong coupling limit, while at weak couplings the transition is in the pair-breaking BCS class. The models discussed here can be realized with ultra-cold gases of alkali atoms tuned to a broad Feshbach resonance in an optical lattice, enabling experimental studies of pairing correlations in insulators, especially in their universal regimes. In turn, these simple and tractable models capture the emergence of fluctuation-driven superconducting transitions in fermionic systems, which is of interest in the context of high temperature superconductors.

16 pages, 6 figures, published version

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• Funtional Renormalization Group Study of the Pairing Symmetry and Pairing Mechanism of the FeAs Based High Temperature Superconductors
• Molecular Probe of Pairing in the BEC-BCS Crossover
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Molecules of Fermionic Atoms in an Optical Lattice
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Critical velocity for superfluid flow across the BEC-BCS crossover
• Large-N expansion for unitary superfluid Fermi gases
• Fermi gas near unitarity around four and two spatial dimensions
• Superfluid-Insulator Transition of Strongly Interacting Fermi Gases in Optical Lattices
• Dressed molecules in an optical lattice

Cited by in corpus (9)

• Two-dimensional heavy fermions on the strongly correlated boundaries of Kondo topological insulators
• Fractional topological insulators of Cooper pairs induced by proximity effect
• Mott-insulator-to-superconductor transition in a two-dimensional superlattice
• Vortices and vortex states in Rashba spin-orbit-coupled condensates
• Fermionic Superfluid from a Bilayer Band Insulator in an Optical Lattice
• Interaction proximity effect at the interface between a superconductor and a topological insulator quantum well
• Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands
• Charge excitations across a superconductor-insulator transition
• Pairing instabilities in topological insulator quantum wells