Study of Magnetic Field Resilient High Impedance High-Kinetic Inductance Superconducting Resonators

Abstract: Superconducting resonators with high-kinetic inductance play a central role in hybrid quantum circuits, enabling strong coupling with quantum systems with small electric dipole moment and improved parametric amplification. However, optimizing these resonators simultaneously for high internal quality factors ($Q_i$) and resilience to strong magnetic fields remains challenging. In this study, we systematically compare superconducting resonators fabricated from niobium nitride (NbN) and granular aluminum (grAl) thin films, each having similar kinetic inductance values ($L_k \sim 100$ pH/sq). At zero magnetic field, resonators made from grAl exhibit higher $Q_i$ compared to their NbN counterparts. However, under applied magnetic fields, NbN resonators demonstrate significantly better resilience. Moreover, NbN resonators exhibit an unexpected increase in $Q_i$ at intermediate in-plane magnetic fields ($B_{\parallel} \sim 1$ T), which we attribute to an enhanced frequency detuning that reduce coupling to two-level system defects. In contrast, grAl resonators show a distinct critical field above which $Q_i$ rapidly decreases, strongly depending on resonator cross-section respect to the applied field direction. Characterization of the nonlinear properties at zero magnetic field reveals that the self-Kerr coefficient in grAl resonators is more than an order of magnitude higher than in NbN resonators, making grAl particularly attractive for applications requiring pronounced nonlinear interactions. Our findings illustrate a clear trade-off between the two materials: NbN offers superior magnetic-field resilience beneficial for hybrid circuit quantum electrodynamics applications, while grAl is more advantageous in low-field regimes demanding high impedance and strong nonlinearity.