Massless modes and abelian gauge fields in multi-band superconductors

Abstract

In $N$-band superconductors, the $U(1{)}^N$ phase invariance is spontaneously broken. We propose a model for $N$-band superconductors where the phase differences between gaps are represented by abelian gauge fields. This model corresponds to an $SU(N)$ gauge theory with the abelian projection. We show that there are massless modes as well as massive modes when the number of gaps $N$ is greater than 3. There are $N-3$ massless modes and two massive modes near a minimum of the Josephson potential when $N$ bands are equivalent and Josephson couplings are frustrated. The global symmetry $U(1{)}^{N-1}$ is broken down by the Josephson term to $U(1{)}^{N-3}$. A non-trivial configuration of the gauge field, that is, a monopole singularity of the gauge field results in a fractional quantum-flux vortex. The fractional quantum-flux vortex corresponds to a monopole in superconductors.

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• Massless collective excitations in frustrated multi-band superconductors
• Fluctuation-induced Nambu-Goldstone bosons in a Higgs-Josephson model
• Nambu-Goldstone bosons characterized by the order parameter in spontaneous symmetry breaking
• Gauge Invariance and Spontaneous Symmetry Breaking in Two-Gap Superconductors
• Fractional skyrmion and absence of low-lying Andreev bound states in a micro fractional-flux quantum vortex