Quantum Geometric Helical Superconductivity
Abstract
Several physical phenomena in superconductors, such as helical superconductivity and the diode effect, rely on breaking time-reversal symmetry. This symmetry-breaking is usually accounted for via the Lifshitz invariant, a contribution to the free energy which is linear in the phase gradient of the order parameter. In dispersive single-band superconductors with conventional pairing, the Lifshitz invariant can be computed from the asymmetries of the spectrum near the Fermi surface. We show that in multi-band superconductors, the quantum geometry also contributes to the Lifshitz invariant, and this is the dominant contribution when the low-energy bands are flat. We also analogously demonstrate quantum-geometry-driven commensurate-incommensurate transitions in charge and pair density waves.
Cite
@article{arxiv.2503.14721,
title = {Quantum Geometric Helical Superconductivity},
author = {Aaron Dunbrack and Pauli Virtanen and Tero T. Heikkilä},
journal= {arXiv preprint arXiv:2503.14721},
year = {2026}
}