Abstract
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this work, we study two collective modes which are unique to unconventional superconductors that spontaneously break time reversal symmetry. We show that these modes are coherent and underdamped for a wide variety of time-reversal symmetry breaking superconducting states. By further demonstrating that these modes can be detected using a number of existing experimental techniques, we propose that our work can be leveraged as a form of “collective mode spectroscopy” that drastically expands the number of experimental probes capable of detecting time-reversal symmetry breaking in unconventional superconductors.
Highlights
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter
The dynamics of the order parameter can be studied to gain insight into its equilibrium structure. Such a scheme has only recently been proposed in the context of anisotropically gapped superconductors, where the spectrum of non-equilibrium Higgs modes can be used to deduce the orbital symmetry of the order parameter[10,11]
time-reversal symmetry breaking (TRSB) superconducting states are characterized by a doubly-degenerate complex multi-component order parameter of the form Δ = Δ1 ± iΔ2, and can be divided into two classes: (1) systems where both components Δ1 and Δ2 belong to the same multidimensional irreducible representation of the crystalline point group, in which case ∣Δ1∣ = ∣Δ2∣ is required by symmetry, and (2) “mixed symmetry” systems where the two components belong to different irrep’s, which can arise due to either an accidental degeneracy between two pairing channels or two successive superconducting transitions, in which case the ratio ∣Δ1∣/∣Δ2∣ is unconstrained
Summary
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. The collective modes of conventional (phonon-mediated) superconductors are well-established, consisting of two modes which correspond to fluctuations in the amplitude and phase of the order parameter.
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