The nature of symmetry breaking in the superconducting ground state

Abstract

The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local and gauge dependent. For that reason they are also ambiguous as a guide to phase structure. We point out that a global subgroup of the local U(1) gauge symmetry may be regarded, in analogy to non-abelian theories, as a "custodial" symmetry affecting the matter field alone, and construct, along the lines of our previous work, a new gauge-invariant criterion for breaking symmetries of this kind. It is shown that spontaneous breaking of custodial symmetry is a necessary condition for the existence of spontaneous symmetry breaking of a global subgroup of the (abelian or non-abelian) gauge group in any given gauge, and a sufficient condition for the existence of spontaneous breaking of a global subgroup of the gauge group in some gauge. As an illustration we compute numerically, in the lattice version of the Ginzburg-Landau model, the phase boundaries of the theory and the order parameters associated with various symmetries in each phase.

arXiv comment20 pages, 12 figures. v2: revised discussion of the normal state in section II(C)

References in corpus (5)

• On the Ambiguity of Spontaneously Broken Gauge Symmetry
• Brout-Englert-Higgs physics: From foundations to phenomenology
• What symmetry is actually broken in the Higgs phase of a gauge-Higgs theory?
• Spontaneous Symmetry Breaking and Decoherence in Superconductors
• On the Kertész line: Thermodynamic versus Geometric Criticality

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