Magnetic field compatible circuit quantum electrodynamics with graphene Josephson junctions.

Circuit quantum electrodynamics has proven to be a powerful tool to probe mesoscopic effects in hybrid systems and is used in several quantum computing (QC) proposals that require a transmon qubit able to operate in strong magnetic fields. To address this we integrate monolayer graphene Josephson junctions into microwave frequency superconducting circuits to create graphene based transmons. Using dispersive microwave spectroscopy we resolve graphene's characteristic band dispersion and observe coherent electronic interference effects confirming the ballistic nature of our graphene Josephson junctions. We show that the monoatomic thickness of graphene renders the device insensitive to an applied magnetic field, allowing us to perform energy level spectroscopy of the circuit in a parallel magnetic field of 1 T, an order of magnitude higher than previous studies. These results establish graphene based superconducting circuits as a promising platform for QC and the study of mesoscopic quantum effects that appear in strong magnetic fields.

Introduction

A superconducting transmon qubit[1] resilient to strong magnetic fields is an important component for proposed topological[2-4] and hybrid quantum computing (QC) schemes[5,6]. A transmon qubit consists of a Josephson junction (JJ) shunted by a large capacitance, coupled to a high quality factor superconducting resonator. In conventional transmon devices, the resonator is fabricated from Al and the JJ is fabricated from an Al/AlO/Al tunnel junction[1], both of which cease operation above the critical magnetic field of bulk Al, ~10 mT. Even when considering alternative type II superconductors such as NbTiN or MoRe that can sustain superconductivity beyond B = 8 T[7], when subjected to a strong magnetic field the superconductor will experience detrimental effects such as reduction of the superconducting gap, increased quasiparticle generation[8] and the formation of Abrikosov vortices that cause resistive losses in a microwave field. In addition to disrupting the superconductivity, magnetic flux penetrating the JJ produces electron interference effects that reduce the Josephson energy EJ and strongly suppress the transmon energy spectrum. If the transmon is to be used for fast quantum gates, fast charge-parity detection and long range quantum state transfer in QC schemes[3,9,10] we are compelled to consider alternatives to conventional Al based JJs. Proximitised semiconducting nanowires, acting as gate-tuneable superconductor-normal-superconductor JJs[11] have been used successfully in a variety of microwave frequency superconducting circuits, allowing for studies of Andreev bound states[12,13], electrically tuneable transmon qubits[14,15] and transmons that exhibit substantial field compatibility[16]. Graphene JJs are an attractive alternative as they exhibit ballistic transport, high critical currents[7,17,18] and the atomic thickness of the graphene junction greatly reduces flux penetration, protecting the JJ from orbital interference effects that would suppress EJ in high parallel fields. When combined with geometric techniques that protect the superconducting film, such as critical field enhancement[19] and lithographically defined vortex pinning sites[20,21], the transmon circuit can be protected at magnetic fields relevant to these proposals, which approach and in some cases exceed 1 T[22-24].

In this work we report the integration of ballistic graphene JJs into microwave frequency superconducting circuits to create graphene based transmons. Using dispersive microwave spectroscopy we resolve the characteristic band dispersion of graphene, and observe coherent electronic interference effects that confirm the ballistic nature of our graphene JJs. We perform energy level spectroscopy at B|| = 0 T to resolve a linewidth of ≃ 400 MHz. Although the large linewidths prevent coherent qubit control, we demonstrate the device is insensitive to the applied magnetic field up to B|| = 1 T.

Results

Device structure

Figure 1a shows an optical microscope image of a typical graphene transmon device. It consists of four λ/4 coplanar waveguide (CPW) resonators multiplexed to a common feedline. Each resonator is capacitively coupled to a graphene transmon, with the graphene JJ being shunted by capacitor plates that provide a charging energy EC ≃ 360 MHz. The resonators and capacitor plates are fabricated from 20 nm NbTiN due to its enhanced critical magnetic field[19], and we pattern the resonators with a lattice of artificial pinning sites to protect the resonator from resistive losses due to Abrikosov vortices[20,21]. The van der Waals pickup method is used to encapsulate monolayer graphene (G) between two hexagonal boron nitride (hBN) flakes and deposit it between the pre-fabricated capacitors plates (Fig. 1b)[7], before contacting the hBN/G/hBN stack by dry etching and sputtering MoRe. In this work, we present results from two graphene JJ transmon devices, with slightly different fabrication techniques. Device A uses a Ti/Au gate stack deposited directly on the hBN, before the junction is shaped via dry etching. Device B is shaped (Fig. 1c) before a Ti/Au gate stack with a SiNx interlayer is deposited (Fig. 1d).

Fig. 1

Device structure a Optical image showing multiple CPW resonators frequency multiplexed to a common feedline (device B). Scale bar 1 mm. b Zoomed optical image of the capacitor plates that shunt the Josephson junction, with the gate, junction and contacts visible. Scale bar 100 μm. c SEM micrograph of a contacted boron nitride-graphene-boron nitride stack before fabrication of the gate. A magnetic field B|| can be applied parallel to the film along the length of the junction contacts using a 3-axis vector magnet. Scale bar 500 nm. d Cross sectional diagram showing the fully contacted and gated stack

Dispersive Fabry–Perot oscillations

We begin by performing spectroscopy of the resonator in device A as a function of the input power Pin (Fig. 2a). Varying the resonator’s photon occupation from to 〈nph〉 = 1 we observe a dispersive shift χ = fr − fbare in the resonator frequency fr from the high power value fbare. This occurs due to a Jaynes-Cummings type interaction between the harmonic readout resonator and the anharmonic transmon spectrum, with the anharmonicity provided by the Josephson junction[25]. The magnitude of the shift χ = g2/Δ depends on the transmon-resonator coupling g, and the difference Δ = fr − ft between fr and the ground state to first excited state transition frequency , allowing us to infer EJ from χ[1]. Studying χ as a function of gate voltage VG reveals the characteristic band dispersion of graphene (Fig. 2b) and allows the voltage at the charge neutrality point (CNP) VCNP to be identified. At negative VG − VCNP, the chemical potential μ is below the CNP and the graphene is in the p-regime where holes are the dominant charge carrier. Deep into the p-regime, the high carrier density (nC) gives a large EJ, placing ft above the resonator and giving χ a small negative value (Fig. 2c). As VG approaches the CNP, the Dirac dispersion minimises the density of states reducing EJ and ft to a minimum. Since χ = g2/Δ, as Δ approaches zero, χ diverges. Once on resonance, the resonator acquires some characteristic of the qubit, significantly broadening the lineshape. Simultaneously, the critical photon number nCrit = Δ2/4g2 collapses[26], moving the measurement into the ‘transitionary’ regime between high and low photon number as in Fig. 2a, causing the anomalous lineshapes visible in Fig. 2c near CNP. As VG is increased past the CNP, nCrit and the lineshapes recover, with electrons becoming the dominant charge carrier and EJ increasing to a maximum as expected from removal of the n-p-n junction formed by the contacts[7]. The p-regime also experiences periodic fluctuations in EJ as a function of VG due to coherent electron interference effects in a Fabry–Perot cavity formed by n-p interfaces at the MoRe contacts[7]. Extracting a line trace (white line Fig. 2c) to study the modulation in |S21| with nC (Fig. 2d), and performing a Fourier transform (Fig. 2e) gives a cavity length of 220 nm in agreement with the device dimensions. The observation of a Dirac dispersion relation in combination with coherent electron interference effects confirm the successful integration of ballistic graphene JJs into a superconducting circuit.

Fig. 2

Resonator spectroscopy as a function of Pin and VG a |S21| (Norm.) as a function of input frequency f and input power Pin. At single photon occupancy the resonator experiences a frequency shift χ due to repulsion from an energy level above the resonator (device A). b Diagram of the Dirac cone band structure of graphene. Changing VG to tune μ allows the dominant charge carriers to be varied between hole, charge neutral and electron-like regimes. c At single photon occupancy, |S21| (Norm.) is measured as f and VG are varied, with the voltage at CNP (VCNP = 7.8 V) subtracted. In the p-regime, χ oscillates as VG is varied. We extract the charge carrier density nc d from the white linecut to generate a Fourier transform e that is consistent with Fabry-Perot oscillations in a cavity of d = 220 nm

Insensitivity to applied parallel magnetic field

In device B we observe additional coherent electronic interference effects in the form of universal conductance fluctuations (UCF)[14,27]. As we move from the p to the CNP regime, χ is seen to diverge repeatedly as ft anti-crosses multiple times with fr (Fig. 3a). This behaviour is repeated moving from the CNP to the n-regime, where EJ is again maximised. We demonstrate the field compatibility of the junction by applying a magnetic field B|| along the length of the junction contacts, parallel to the plane of the film, using the resonator as a sensor for field alignment (see Supplementary Figs. 1 and 2 for alignment procedure details). Monitoring χ as B|| is varied between 0 and 1 T (Fig. 3b) and calculating ft (using g = 43 MHz, extracted from measurements in Fig. 4), demonstrates that χ and thus EJ are not significantly affected by the applied B||. The small amount of variation observed is attributed to charge noise induced gate drift which was observed throughout the duration of the experiment. Studying χ as a function of VG at B|| = 1 T (Fig. 3c) again reveals the characteristic Dirac dispersion as seen in Fig. 3a, with modified UCF and shifted VCNP due to slow gate drift. The insensitivity of ft to applied field and similarity of device operation at B|| = 0 and 1 T confirm the field resilience of both the graphene JJ and superconducting circuit.

Fig. 3

Dispersive shift as a function of VG and B|| a At B|| = 0 T, |S21| (Norm.) versus f and VG (with VCNP = 300 mV subtracted) shows the symmetric band dispersion of graphene with additional fluctuations we attribute to UCF. b ft (red circles) extracted from χ (black diamonds) versus B|| at VG = 0 V, showing ft is not significantly affected. c Repeating a at B|| = 1 T with VCNP = 430 mV subtracted confirms the graphene JJ behaves equivalently to B|| = 0 T. The variation observable in b and shift in VCNP between a and c we attribute to slow gate drift

Fig. 4

Two tone spectroscopy a Normalised |S21| at fr as fd is varied can be fitted to extract ft and γ at VG = 0 V. At B|| = 1 T, γ shows a 25% increase compared to B|| = 0 T. b At B|| = 1 T, ft and γ are extracted as VG is varied, demonstrating ft can be swept over a wide frequency range. Lines bisecting each ft are not error bars, but represent the extracted γ at each ft

Two tone spectroscopy in high parallel magnetic fields

In order to better understand the microwave excitation spectra of our system we proceed to measure it directly via two-tone spectroscopy[1]. The readout tone is set to fr whilst a second tone fd is used to drive the circuit. Excitation of the system results in a state dependent shift of the resonator frequency, and is detected by measuring the change in the complex transmission S21 at fr. At VG = 0 V (p-regime), two-tone spectroscopy at B|| = 0 and 1 T (Fig. 4a) can be fitted with a Lorentzian to extract the transmon transition and transition linewidth . At B|| = 1 T, ft and thus EJ differ only slightly with γ increasing slightly from 350 to 425 MHz. The transmon resonator coupling is extracted from the observed dispersive shift χ and detuning Δ, and used in the calculation of ft in Fig. 3. We attribute the change in ft from Fig. 3b and the large γ to the dielectric induced charge noise mentioned previously. An estimate of EJ = 40.2 μeV = 9.72 GHz can be provided using the relation . Performing two-tone spectroscopy in the n-regime while tuning VG reveals a gate-tunable energy level that is visible above and below the resonator (Fig. 4b, VCNP not specified due to gate drift during measurement) that can be fitted to extract ft and γ, giving a minimum linewidth of 166 MHz (see Supplementary Fig. 3 for the raw data).

Discussion

The observation of a transition and the inferred high value of EJ in the n and p-regimes (Fig. 4a) provides additional confirmation of the electron-hole symmetry expected in graphene. Additional measurement of the higher order two-photon f02 transition would allow for exact measurements of EJ and EC via diagonalisation of the Hamiltonian, enabling investigations into mesoscopic effects of interest in graphene JJs[28,29]. Importantly, the transition and thus EJ can be varied over a wide frequency range, satisfying a key requirement for implementation into topological QC proposals[3]. If graphene based transmons are to be successfully implemented into these proposals however, the large linewidths that currently prevent measurements of relaxation and coherence lifetimes must be reduced. We believe that material improvements to the dielectric materials can achieve this.

In conclusion, we have integrated a graphene JJ into a superconducting circuit to make a graphene based transmon. Additionally, we have achieved operation at B|| = 1 T, a magnetic field more than an order of magnitude higher than previous studies[16,30]. While the broad linewidths prevented the demonstration of coherent qubit control, these results establish graphene based microwave circuits as a promising tool for topological and hybrid QC schemes, and for probing mesoscopic phenomena of interest at high magnetic fields.

Methods

Sample fabrication

To fabricate the two devices (A and B) 20 nm of NbTiN is sputtered onto intrinsic Si wafers in an Ar/N atmosphere. The resonators, feedline and transmon are reactive ion etched in an SF6/O2 atmosphere. In this etching step, an array of artificial pinning sites is also defined. Monolayer graphene is encapsulated between two hBN flakes (t ≃ 15 nm each), then deposited between pre-fabricated capacitors using a PMMA based van der Waals pickup method. Contact to the graphene stack is made by etching in a CHF3/O2 environment, followed by sputtering MoRe (t = 80 nm). As shown in Supplementary Fig. 4, device A was contacted to give a junction length of 300 nm. A Ti/Au top gate is then sputtered on top of the stack. The device is then shaped in a CHF3/O2 plasma to be 1000 × 300 nm2 in size. Device B was contacted to provide a junction length of 500 nm. The long thin leads were geometrically restricted in two dimensions, making it less favourable for vortices to form, protecting the superconductivity of the contacts proximitising the junction. The junction is then shaped in a CHF3/O2 plasma to be 500 × 500 nm2. A SiN/Ti/Au top gate stack is then sputtered to give full junction coverage, giving greater control of μ in the junction.

Sample characterisation

All measurements were performed in a dilution refrigerator with a base temperature of 15 mK. The samples were enclosed in a light tight copper box, and thermally anchored to the mixing chamber. An external magnetic field is applied to the sample using a 3-axis vector magnet. The two different measurement configurations used in this manuscript are depicted in Supplementary Fig. 5. Two coaxial lines and one DC line were used to control the sample. The sample was connected to the DC voltage source by a line that was thermally anchored at each stage and heavily filtered at the mixing chamber by low frequency RC, π and copper powder filters. The line used to drive the feedline input was heavily attenuated to reduce noise and thermal excitation of the cavity, allowing the single photon cavity occupancy to be reached. The output line of the feedline was connected to an isolator (Quinstar QCI-080090XM00) and circulator (Quinstar QCY-060400CM00) in series to shield the sample from thermal radiation from the HEMT amplifier (Low Noise Factory LNF-LNC4-8_C) on the 4 K stage. Resonator spectroscopy of device A was performed using circuit (a) to measure the amplitude and phase response of the complex transmission S21 as the frequency was varied. Resonator and two-tone spectroscopy of device B was performed using circuit (b), with a splitter used to combine the readout and excitation tones. This allows the complex S21 to be measured, but only at fixed resonator readout frequency otherwise only |S21| can be recorded.