A ballistic graphene superconducting microwave circuit

Abstract

Josephson junctions (JJ) are a fundamental component of microwave quantum circuits, such as tunable cavities, qubits, and parametric amplifiers. Recently developed encapsulated graphene JJs, with supercurrents extending over micron distance scales, have exciting potential applications as a new building block for quantum circuits. Despite this, the microwave performance of this technology has not been explored. Here, we demonstrate a microwave circuit based on a ballistic graphene JJ embedded in a superconducting cavity. We directly observe a gate-tunable Josephson inductance through the resonance frequency of the device and, using a detailed RF model, we extract this inductance quantitatively. We also observe the microwave losses of the device, and translate this into sub-gap resistances of the junction at μeV energy scales, not accessible in DC measurements. The microwave performance we observe here suggests that graphene Josephson junctions are a feasible platform for implementing coherent quantum circuits.

Fig. 1

A gate tunable microwave cavity based on an encapsulated graphene Josephson junction. a Optical micrograph of the microwave cavity before placing the BN/G/BN stack. Bright areas are MoRe, dark areas are sapphire substrate. Grey area around the parallel plate capacitors is the Si₃N₄ shunt dielectric. Scale bar 200 μm. b Optical micrograph of the gJJ. The cavity center line and the ground plane are connected through the gJJ and NbTiN leads. The gate line (right) extends over the entire junction. Scale bar 40 μm. c Close-up of b with the graphene channel indicated. Dark areas are HSQ for gate insulation. Scale bar 5 μm. d Sketch of the device circuit. The input signals are filtered and merged using a bias tee before being fed on to the feedline (see Methods section and Supplementary Fig. 1). e Schematic cross-section of the gJJ with top-gate, not to scale

Fig. 2

Observation of the Josephson inductance of a ballistic graphene superconducting junction. a Differential resistance across the gJJ for a wide gate-voltage range. Dark blue denotes area of zero resistance. The device shows signatures of FP oscillations on the p-doped side. b Normal state resistance of the gJJ versus gate voltage. c Microwave spectroscopy of the device in the superconducting state versus gate voltage, plotted as the amplitude of the reflection coefficient |S₁₁| after background subtraction. The graphene junction acts as a tunable inductor in the microwave circuit, resulting in a cavity frequency that is tuned with gate voltage. Inset: The resonance frequency oscillates in phase with the oscillations in a, b

Fig. 3

Josephson inductance extracted from RF and DC measurements. a Schematic representation of L_j and its relation to the CPR of a Josephson junction. L_j can be understood as the slope of the current-phase relation around zero phase bias. b Schematic representation of L_j extraction from the cavity resonance frequency. The potential energy near ϕ = 0 is harmonic, with the fundamental frequency given by the junction inductance L_j and the cavity capacitance C and inductance L_g as $\omega =1\mathrm{∕}\sqrt{\left(L_{\mathrm{j}}+L_{\mathrm{g}}\right)C}$. c Comparison of Josephson inductance L_j extracted from DC measurements (black) and from the microwave measurements (blue). We attribute differences to deviations from a sinusoidal current-phase relation (see main text for details). The error band from our fit of L_j can be found in Supplementary Fig. 4

Fig. 4

Subgap resistance from microwave cavity measurements. a Extracted sub-gap resistance at as a function of gate voltage. The values are calculated by calibrating the cavity properties and using the junction model shown connected to the transmission line cavity to fit the observed cavity response. Inset shows the cavity response at V_g = 30 V. The horizontal and vertical axis divisions are 10 MHz and 10 dB respectively. b Predicted linewidth for a graphene transmon qubit, obtained by taking the RCSJ parameters as a function of gate and adding a capacitance C_q such that the final operating frequency remains $\omega \mathrm{∕}2\pi$ = ${\left(2\pi \sqrt{\left(L_{\mathrm{j}}\left(C_{\mathrm{j}}+C_{\mathrm{q}}\right)\right)}\right)}^{-1}$ = $6\mathrm{GHz}$. We assume the internal junction losses dominate the total linewidth. The horizontal line represents the anharmonicity of a typical SIS transmon E_c/h = 100 MHz. In regions where the blue line falls under the dashed line, a gJJ transmon would be capable of operating as a qubit. The error bands for both panels can be found in Supplementary Fig. 5