Description
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.
Primary author
Prof.
Predrag Nikolic
(George Mason University)
