Superconductivity With Deformed Fermi Surfaces and Compact Stars

Abstract

I discuss the deformed Fermi surface superconductivity (DFS) and some of its alternatives in the context of nucleonic superfluids and two flavor color superconductors that may exist in the densest regions of compact stellar objects. IntroductionThe astrophysical motivation to study the superconducting phases of dense matter arises from the importance of pair correlations in the observational manifestations of dense matter in compact stars. If the densest regions of compact stars contain deconfined quark matter it must be charge neutral and in β equilibrium with respect to the Urca processes d → u + e +ν and u + e → d + ν, where e, ν, andν refer to electron, electron neutrino, and antineutrino. The u and d quarks in deconfined matter fill two different Fermi spheres which are separated by a gap of the order of electron chemical potential. At high enough densities (where the typical chemical potentials become of the order of the rest mass of a s quark), strangeness nucleation changes the equilibrium composition of the matter via the reactions s → u + e +ν and u + e → s + ν. Although the strangeness content of matter affects its u-d flavor asymmetry, the separation of the Fermi energies remains a generic feature. The dense quark matter is expected to be a color superconductor (the early work is in Refs. [1]; recent developments are summarized in the reviews [2]).Accurate description of the matter in this regime requires, first, tools to treat the Lagrangian of QCD in the nonperturbative regime and, second, an understanding of the superconductivity under asymmetry in the population of fermions that pair. The first principle lattice QCD calculations are currently not feasible for the purpose of understanding the physics of compact stars; the effective models that are used rarely incorporate all aspects of the known phenomenology like de-confinement and chiral restoration. Despite of the limitations of current models, a lot can be learned about generic features of possible