Abstract
Recent theories of Sr$_2$RuO$_4$ based on the interplay of strong interactions, spin-orbit coupling and multi-band anisotropy predict chiral or helical ground states with strong anisotropy of the pairing states, with deep minima in the excitation gap, as well as strong phase anisotropy for the chiral ground state. We develop time-dependent mean field theory to calculate the Bosonic spectrum for the class of 2D chiral superconductors spanning $^3$He-A to chiral superconductors with strong anisotropy. Chiral superconductors support a pair of massive Bosonic excitations of the time-reversed pairs labeled by their parity under charge conjugation. These modes are degenerate for 2D $^3$He-A. Crystal field anisotropy lifts the degeneracy. Strong anisotropy also leads to low-lying Fermions, and thus to channels for the decay of the Bosonic modes. Selection rules and phase space considerations lead to large asymmetries in the lifetimes and hybridization of the Bosonic modes with the continuum of un-bound Fermion pairs. We also highlight results for the excitation of the Bosonic modes by microwave radiation that provide clear signatures of the Bosonic modes of an anisotropic chiral ground state.
Highlights
Superfluid 3He and unconventional superconductors share a common and fundamental property that the ground state breaks one or more symmetries of the normal Fermionic vacuum in conjunction with the usual U(1)gauge symmetry associated with BCS condensation
For a 3D chiral p-wave superconductor in the clean limit the coupled set of linearized dynamical equations for the Bosonic mode spectra, including the reaction of the Fermionic vacuum to the excitation of Bosonic modes, as well as the coupling of Bosonic and Fermionic excitations to the EM field are formulated in Yip and Sauls [38]. We have extended this theory to 2D chiral superconductors with anisotropic, quasi2D Fermi surfaces, multi-band pairing and weak disorder, to make predictions for signatures of anisotropic chiral and helical superconductivity based on the Bosonic mode spectrum and the microwave response for recent theoretical models for the superconducting state of Sr2RuO4 [39]
Chiral superconductors which break time-reversal symmetry necessarily belong to a higher dimensional representation of the crystalline point group
Summary
Superfluid 3He and unconventional superconductors share a common and fundamental property that the ground state breaks one or more symmetries of the normal Fermionic vacuum in conjunction with the usual U(1)gauge symmetry associated with BCS condensation. Spin-triplet correlations, which differentiate between the Anderson-Morel (AM) state and BW states, feedback to modify the spin-fluctuation exchange interaction, leading to stabilization of the AM state at high pressures [5, 6] This is the chiral A-phase which breaks time-reversal (T) symmetry and reflection symmetry in any plane containing the chiral axis (P2), but preserves T × P2 (chiral symmetry). If spin-fluctuation exchange is the mechanism for pairing in Sr2RuO4, we expect the strong-coupling feedback effect will stabilize the chiral AM state. Spin-orbit coupling, and the possibility of pairing on multiple Fermi surface sheets likely play important roles in determining the pairing symmetry class, ground state order parameter [8,9,10,11,12] as well as the Bosonic excitation spectrum in Sr2RuO4. Key predictions of a microscopic theory of interacting Fermionic and Bosonics modes are summarized, including microwave spectroscopic signatures of the Bosonic excitation spectrum
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