Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, unlike the usual BCS state, for the Cooper pair to have a nonzero total momentum. For this reason, in this state the gap varies in space, the ground state is inhomogeneous, and a crystalline structure might be formed. This situation was considered for the first time by Fulde and Ferrell (1964) and Larkin and Ovchinnikov (1964), after whom the corresponding state is called the LOFF state. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated with the presence of long-wavelength excitations of zero mass. The situation described here is of interest both in solid-state and in elementary-particle physics, in particular in quantum chromodynamics at high density and low temperature. This review presents the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

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Inhomogeneous superconductivity in condensed matter and QCD

The research on the superfluidity of neutron matter can be traced back to Migdal’s observation that neutron stars are good candidates for being macroscopic superfluid systems [1] And, in fact, during more than two decades of neutron-star physics the presence of neutron and proton superfluid phases has been invoked to explain the dynamical and thermal evolution of a neutron star The most striking evidence is given by post-glitch timing observations [2],[3], but also the cooling history is strongly influenced by the possible presence of super- fluid phases [4],[5] On the theoretical side, the onset of superfluidity in neutron matter or in the more general context of nuclear matter was investigated soon after the formulation of the Bardeen, Cooper, and Schrieffer (BCS) theory of superconductivity [6] and the pairing theory in atomic nuclei [7],[8]

Superfluidity in Neutron Star Matter

The research on the superfluidity of neutron matter can be traced back to Migdal’s observation that neutron stars are good candidates for being macroscopic superfluid systems [1]. And, in fact, during more than two decades of neutron-star physics the presence of neutron and proton superfluid phases has been invoked to explain the dynamical and thermal evolution of a neutron star. The most striking evidence is given by post-glitch timing observations [2],[3], but also the cooling history is strongly influenced by the possible presence of super- fluid phases [4],[5]. On the theoretical side, the onset of superfluidity in neutron matter or in the more general context of nuclear matter was investigated soon after the formulation of the Bardeen, Cooper, and Schrieffer (BCS) theory of superconductivity [6] and the pairing theory in atomic nuclei [7],[8].

The physics of dense hadronic matter and compact stars

Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet S-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-S proton pairing and triplet coupled P-F-wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors.

A. Sedrakian

Papers

3D2 pairing in asymmetric nuclear matter