On-chip superconducting GHz RF reflectometry of the capacitance response in bilayer graphene

Abstract: In dual-gated bilayer graphene, a perpendicular displacement field opens a band gap that modifies both the channel conductance and the electronic compressibility, motivating measurements that resolve resistive and capacitive responses on the same device. We integrate an hBN-encapsulated bilayer graphene heterostructure with an on-chip superconducting Nb lumped-element LC resonator and carry out RF reflectometry near 4.25 GHz. DC transport and finite-bias spectroscopy on the same device provide a transport reference. Top and bottom gates independently set the carrier density and displacement field. The DC and RF gate maps share the same gate-dependent features, with finite-bias measurements revealing a region of suppressed conductance whose bias extent grows with the displacement field, consistent with a field-induced gap. The gate-dependent resonance-frequency shift is converted to the effective capacitance seen by the resonator using an equivalent-circuit model. The capacitance shows a minimum near the conductance-suppressed region, consistent with reduced electronic compressibility in the gapped bilayer graphene, and exhibits an electron-hole asymmetry. The on-chip configuration probes the gate-dependent admittance of a dual-gated van der Waals heterostructure, providing capacitance-sensitive information that complements DC transport within a single device.