Quantum geometric guiding principles for optically controlling competing superconducting phases*

We have shown that in centrosymmetric superconductors with strong spin-orbit interactions, there can be a sub-gap Bardasis-Schrieffer mode that when driven strongly permits switching between singlet and triplet superconducting states [1]. This can be seen from a generalized Ginzburg-Landau theory of competing superconducting orders in which a linear coupling to light is symmetry-allowed between even-parity and odd-parity orders. When calculating this key coupling parameter from a lattice model, we find that it is dominated by a gauge-invariant quantum geometric quantity even for dispersive bands. This quantity is linear in the non-Abelian Berry connection and has a natural interpretation as a matrix element between neighboring Wannier states. This establishes spin-orbit-coupled materials with nontrivial band geometry, such as moiré heterostructures, as prime candidates for experiments looking to probe and control this collective mode. It also has ramifications for the supercurrent in mixed-parity superconductors. Our findings offer a richer understanding of the interplay between quantum geometry and competing superconducting phases.

[1] S. Gassner, C. S. Weber, and M. Claassen. arXiv:2306.13632 (2023).