Classification of ground states and normal modes for phase-frustrated multicomponent superconductors

Abstract

We classify ground states and normal modes for $n$-component superconductors with frustrated intercomponent Josephson couplings, focusing on $n=4$. The results should be relevant not only to multiband superconductors, but also to Josephson-coupled multilayers and Josephson-junction arrays. It was recently discussed that three-component superconductors can break time-reversal symmetry as a consequence of phase frustration. We discuss how to classify frustrated superconductors with an arbitrary number of components. Although already for the four-component case there are a large number of different combinations of phase-locking and phase-antilocking Josephson couplings, we establish that there are a much smaller number of equivalence classes where properties of frustrated multicomponent superconductors can be mapped to each other. This classification is related to the graph-theoretical concept of Seidel switching. Numerically, we calculate ground states, normal modes, and characteristic length scales for the four-component case. We report conditions of appearance of new accidental continuous ground-state degeneracies.

v3: Published version; only minor changes

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• Non-London electrodynamics in a multiband London model: anisotropy-induced non-localities and multiple magnetic field penetration lengths
• Massless collective excitations in frustrated multi-band superconductors
• Spontaneous Breakdown of Time-Reversal Symmetry Induced by Thermal Fluctuations
• Frustration driven Josephson phase dynamics
• Entropy- and Flow- Induced Superfluid States
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• Interaction between multi components vortices at arbitrary distances using a variational method in the Ginzburg-Landau theory