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

TL;DR

This paper classifies ground states and normal modes in four-component superconductors with frustrated Josephson couplings, revealing equivalence classes and new degeneracies, with implications for multiband and Josephson-junction systems.

Contribution

It introduces a classification scheme for frustrated multicomponent superconductors using graph theory, reducing complexity by identifying equivalence classes and analyzing ground states and excitations.

Findings

Identified a smaller number of equivalence classes for frustrated superconductors.

Calculated ground states, normal modes, and length scales for four-component systems.

Discovered conditions for new accidental continuous degeneracies.

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.