Superconductors are topologically ordered

By T. H. Hansson, V. Oganesyan, Shiv Sondhi. 2004

249 citations recorded by the source corpus.

Abstract We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e., that while it lacks a local order parameter, it is sensitive to the global topology of the underlying manifold and exhibits an associated fractionalization of quantum numbers. We show that this perspective unifies a number of previous observations on superconductors and their low lying excitations and that this complex can be elegantly summarized in a purely topological action of the “ BF ” type and its elementary quantization. On manifolds with boundaries, the BF action correctly predicts non-chiral edge states, gapped in general, but crucial for fractionalization and establishing the ground state degeneracy. In all of this the role of the physical electromagnetic fields is central. We also observe that the BF action describes the topological order in several other physically distinct systems thus providing an example of topological universality.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/a5ce61ae2426739ec02bd609b5630840ab34544f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect (2012, background): “Related theories have appeared in the context of 3D topologically ordered phases and superconductors [22] where only the first BF term in Eq.”
Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy (2009, background): “In fact, recently it has been suggested that the double Chern-Simons theory can serve as effective theories to a number of quantum critical phenomena in realistic materials, such as the quantum spin Hall effect, the three-dimensional topological insulators [6], and lattice models with the Z2 topolog”
Coupling a QFT to a TQFT and duality (2014, background): “Their applications in condensed matter physics were discussed, for example, in [22,23,24].”
Non-Abelian Anyons and Topological Quantum Computation (2007, background): “This low-energy physics can be described by an Abelian BF-theory (Hansson et al., 2004):”
Quantum spin liquids (2019, background): “In this description, the fermionic spinon is identified as the cousin of the Bogoliubov quasiparticle (26, 34, 35), whereas the vison is identified as the cousin of the h/2e vortex (26, 34).”
An introduction to spontaneous symmetry breaking (2019, background): “1, may be considered to be topologically ordered [122].”
Spin Ice, Fractionalization, and Topological Order (2011, background): “[10] Although the venerable superconductor [12] is historically the first example of a topologically ordered condensed matter system.”