Time-reversal symmetry broken superconductors admit a type II Lifshitz invariant that renders the Higgs mode optically active in conductivity spectra, with a full classification of allowed magnetic point group corepresentations.
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Two-orbital models with interorbital t-J or t-V interactions exhibit incommensurate d_xy pair density wave superconductivity driven by interband pairing, confirmed by RPA and strong-coupling hard-core pair calculations showing period-2 PDW over wide fillings.
Unbiased QMC simulations of a bilayer t-J⊥-V model map a doping-driven transition from a spontaneous interlayer loop-current state to interlayer s-wave superconductivity, including a coexisting time-reversal-symmetry-breaking superconducting phase near the boundary.
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