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We consider optical response in multiband, multilayer two-dimensional superconductors. Within a simple model, we show that linear response to AC gating can detect collective modes of the condensate, such as Leggett and clapping modes. We show how trigonal warping of the superconducting order parameter can help facilitate detection of clapping modes. Taking rhombohedral trilayer graphene as an example, we consider several possible pairing mechanisms and show that all-electronic mechanisms may produce in-gap clapping modes. These modes, if present, should be detectable in the absorption of microwaves applied via the gate electrodes, which are necessary to enable superconductivity in this and many other settings; their detection would constitute strong evidence for unconventional pairing. Last, we show that absorption at frequencies above the superconducting gap $2\left|\mathrm{\Delta }\right|$also contains a wealth of information about the gap structure. Our results suggest that linear spectroscopy can be a powerful tool for the characterization of unconventional two-dimensional superconductors. Published by the American Physical Society2024 

Many seemingly contradictory experimental findings concerning the superconducting state in Sr2RuO4 can be accounted for on the basis of a conjectured accidental degeneracy between two patterns of pairing that are unrelated to each other under the (D4h) symmetry of the crystal: a dx2-y2-wave (B1g) and a gxy(x2-y2)-wave (A2g) superconducting state. In this paper, we propose a generic multiband model in which the g-wave pairing involving the xz and yz orbitals arises from second-nearest-neighbor BCS channel effective interactions. Even if timereversal symmetry is broken in a d + ig state, such a superconductor remains gapless with a Bogoliubov Fermi surface that approximates a (vertical) line node. The model gives rise to a strain-dependent splitting between the critical temperature Tc and the time-reversal symmetry-breaking temperature TTRSB that is qualitatively similar to some of the experimental observations in Sr2RuO4. 

We study multi-valley electron gases in the low density (rs ≫ 1) limit. Here the ground-state is always a Wigner crystal (WC), with additional pseudo-spin order where the pseudo-spins are related to valley occupancies. Depending on the symmetries of the host semiconductor and the values of the parameters such as the anisotropy of the effective mass tensors, we find a striped or chiral pseudo-spin antiferromagnet, or a time-reversal symmetry breaking orbital loop-current ordered pseudo-spin ferromagnet. Our theory applies to the recently-discovered WC states in AlAs and in mono and bilayer transition metal dichalcogenides. We identify a set of interesting electronic liquid crystalline phases that could arise by continuous quantum melting of such WCs.