Topological superconductivity, topological confinement, and the vortex quantum Hall effect

Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confin...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2011-09, Vol.84 (9), Article 094520
Main Authors: Diamantini, M. Cristina, Trugenberger, Carlo A.
Format: Article
Language:English
Subjects:
BOSONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONDENSATES
CONFINEMENT
DEFECTS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ELECTROMAGNETIC FIELDS
ELEMENTARY PARTICLES
ENERGY LEVELS
FLUCTUATIONS
GAUGE INVARIANCE
GROUND STATES
HALL EFFECT
HIGGS BOSONS
HIGGS MODEL
INVARIANCE PRINCIPLES
LIE GROUPS
MAGNETIC FLUX
MASSLESS PARTICLES
MATHEMATICAL MODELS
MATHEMATICS
PARTICLE MODELS
PHASE TRANSFORMATIONS
PHOTONS
PHYSICAL PROPERTIES
POSTULATED PARTICLES
SUPERCONDUCTIVITY
SUPERCONDUCTORS
SYMMETRY BREAKING
SYMMETRY GROUPS
TOPOLOGY
U GROUPS
U-1 GROUPS
VARIATIONS
VORTICES
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Summary:Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.84.094520