Superconductivity and superfluidity as universal emergent phenomena

Abstract

Superconductivity (SC) or superfluidity (SF) is observed across a remarkably broad range of fermionic systems: in BCS, cuprate, iron-based, organic, and heavy-fermion superconductors, and superfluid helium-3 in condensed matter; in a variety of SC/SF phenomena in low-energy nuclear physics; in ultracold, trapped atomic gases; and in various exotic possibilities in neutron stars. The range of physical conditions and differences in microscopic physics defy all attempts to unify this behavior in any conventional picture. Here we propose a unification through the shared symmetry properties of the emergent condensed states, with microscopic differences absorbed into parameters. This, in turn, forces a rethinking of specific occurrences of SC/SF such as cuprate high-T c superconductivity, which becomes far less mysterious when seen as part of a continuum of behavior shared by a variety of other systems.Superconductivity and superfluidity are collective phenomena owing their existence to many-body interactions; the corresponding emergent states are not related perturbatively to the parent state. Thus, characterization of SC and SF through microscopic properties of the parent system fails on two levels: (1) It cannot provide a unified view, since microscopic physics differs fundamentally between fields. (2) The transition from the microscopic parent state to the collective emergent state is not analytic; thus it is conjecture to assume that microscopic tendencies of the parent state are related directly to collective properties of the emergent state.Conventional understanding of SC and SF is built on the idea of a Fermi liquid, for which single-particle states of the interacting system are in one-to-one correspondence with those of the non-interacting system. Superconductivity is assumed to develop from a Fermi-liquid parent through the Cooper instability, in which two fermions outside a filled Fermi sea can form a bound state for vanishingly small attraction [1]. In the solid state the weak attraction is assumed conventionally to arise from interaction of electrons with lattice vibrations.The Cooper instability was developed into a many-body theory by the Bardeen-Cooper-Schrieffer (BCS) postulate that the SC state is a coherent superposition of fermion pairs in a weak coupling limit [2], and this was generalized to Eliashberg theory, which removed the weak-coupling restrictions. The BCS idea was soon adapted to applications in nuclear physics [3], with pairs bound by attractive nucleon-nucleon forces.BCS theory in condensed matter and nuclear physics involves quite different interactions operating on energy and distance scales differing by many orders of magnitude. However, emergent SC/SF properties were unified through sharing the same form for the BCS wavefunction, which implied a common pseudospin symmetry of the effective Hamiltonians that could be expressed elegantly in terms of an SU(2) Lie algebra [4]. Thus similarities between these fields could be understood through a common algebraic structure, while differen...

Universal thermodynamics of a trapped Fermi gas in the superfluid regime: the role of the Pauli principle

“…As pointed out by Anderson in his treatise, More is Different , 'the whole becomes not only more than but very different from the sum of its parts' [70]. The appearance of zeroviscosity in superfluids, zero resistivity in superconducting metals, and magnetism are all examples of simple behaviors that arise, not from detailed microscopic forces, but from the emergence of collective organizational phenomena [71][72][73]. These phenomena depend on powerful and general principles of organization that, while they are not generally understood, can provide great insight into macroscopic collective behavior [73,74].…”

The Superconducting Critical Temperature

“…(d) Phase diagram for an organic superconductor (SDW denotes spin density waves) [39]. (e) Generic correlation-energy diagram for nuclear structure [40].…”

“…shows that phase diagrams for unconventional SC emergent states in a broad range of condensed matter systems and in nuclear structure are remarkably similar, despite completely different microscopic physics (see Refs. [33,40] for further discussion). An even more remarkable universality of emergent states is shown in the coherent state energy surfaces displayed in Figure 8.…”

Complexity in Biological Organization: Deconstruction (and Subsequent Restating) of Key Concepts

“…The corresponding emergent states are not related perturbatively to the parent state. Therefore, in understanding such properties, we cannot focus on microscopic properties of the normal state, as the transition from the microscopic parent state to the collective emergent state is not analytic [ 15 ]. To quote Anderson’s words, “the whole is not only greater than but very different from the sum of the parts” [ 16 ].…”