Florian Simon (TUM)

Quantum geometry: a white cane for unconventional and topological superconductivity ?

In this talk, I will present a recent preprint on the quantum geometry of superconductors [1]. I will begin by introducing quantum geometry as a general consequence of the U(1) gauge invariance of quantum mechanics, leading to different incarnations throughout physics (and beyond). I will then discuss the specific example of quantum geometry in the band theory of crystals, along with its physical interpretations. I will then summarize my PhD research, where I studied the influence of the normal state quantum geometry on the superconducting phase. From this discussion, I will then motivate the study of the quantum geometry of the superconducting state itself, notably regarding the limitations of classification schemes in topological superconductivity and experimental studies of unconventional superconductivity. I will then present the results of Ref. [1], where we determine sufficient conditions for the quantum geometry of the superconducting phase To exactly separate into a normal-state contribution and a "pairing" quantum geometry, driven by superconductivity. We then determine explicit expressions for the pairing quantum geometry of all pairings, including non-unitary triplet pairings. These results will hopefully serve as a foundation for geometry-based design rules for superconductors, and contribute to the experimental exploration of unconventional superconductivity.

[1] F. Simon, T. Bernat & A.M. Black-Schaffer, Composite quantum geometry of superconductors (2026). Arxiv. doi:10.48550/arXiv.2608.02434