Nonlinear Dynamics and Time Reversal Symmetry Breaking in a Superconducting Ring*

In search of a novel apparatus for detecting time reversal symmetry breaking (TRSB), we analyze a two-component superconducting ring resonator using nonlinear kinetic inductance theory. When integrated with quantum materials, these resonators may exhibit emergent behavior owing to the unique symmetry properties of their constituents. Here, we propose a design that incorporates a closed-loop resonator geometry and allows us to utilize the counter- and co-propagating, i.e., angular momentum, superconducting states to study TRSB behavior. We theoretically analyze this ring resonator device using a Ginzburg-Landau approach and examine the relationships between input power, supercurrent density, and external fields. The nonlinear dynamics of the superconducting states give rise to inhomogeneous densities that experience level repulsion when time reversal symmetry is explicitly broken. Thus, we are able to assess the device's efficacy in disentangling geometrical coupling with TRSB properties. Our technique provides the opportunity to address new materials and frequency regimes. We therefore offer an alternative for probing non-reciprocal effects such as TRSB in the near gap frequency regime and systems where changes in magnetic fields are subtle. This includes 2D ferromagnetic materials such as CrI3 [1], TRSB superconductors candidates like magic angle twisted trilayer graphene [2], or magnetizations in other heterostructures.

[1] Meseguer-Sánchez, J., Popescu, C., García-Muñoz, J.L. et al. Coexistence of structural and magnetic phases in van der Waals magnet CrI3. Nat Commun 12, 6265 (2021).

[2] Lin, JX., Siriviboon, P., Scammell, H.D. et al. Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nat. Phys. 18, 1221–1227 (2022).