Nature of symmetry breaking in the superconducting ground state

Kazue Matsuyama; Jeff Greensite

doi:10.1103/PhysRevB.100.184513

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Nature of symmetry breaking in the superconducting ground state

Kazue Matsuyama, Jeff Greensite

DOI 10.1103/PhysRevB.100.184513 · Physical Review B

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Abstract

The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both nonlocal 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 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 a lattice version of the Ginzburg-Landau model, the phase boundaries of the theory and the order parameters associated with various symmetries in each phase.