Hybrid superconducting circuit architecture to probe van der Waal heterostructures: part 2

Coupling to microwave photons in high-quality superconducting resonators in a circuit QED architecture enables sensitive readout of artificial atoms. Similar architectures in van der Waals (vdW) systems enable measurements of impedance at relevant frequency scales, which can elucidate the nature of correlated electronic states beyond what’s accessible with conventional DC transport. Superconducting microwave resonators thus coupled to moiré graphene have recently yielded insights into the pairing symmetry of their superconducting states.

Here, we develop a hybrid vdW-superconductor architecture that enables simultaneous quasi-DC electrical transport and microwave impedance measurements of dual-gated vdW heterostructures. In part 1, we demonstrate this architecture by coupling a high-impedance microwave resonator to a vdW hall bar device. In part 2, we show that the resonator frequency shift and quality factor are sensitive probes of the vdW channel resistance as independently measured at quasi-DC frequencies across the phase diagram. Our data are well described by an effective impedance model combining channel resistance with fixed capacitive circuit elements. We also validate the model utilizing higher harmonic modes of the resonator in the 1 - 10 GHz range. Our proposed hybrid architecture provides a general framework for probing the impedance of dual-gated vdW heterostructures at microwave frequencies, including kinetic inductance from vdW superconductivity.