Gate-tunable Josephson diodes in magic-angle twisted bilayer graphene

Abstract

We report low-temperature measurements of two adjacent, gate-defined Josephson junctions (JJs) in magic-angle twisted bilayer graphene (MATBG) at a moiré filling factor near $ν= -2$. We show that both junctions exhibit a prominent, gate-tunable Josephson diode effect, which we explain by a combination of large kinetic inductance and non-uniform supercurrent distribution. Despite their proximity, the JJs display differences in their interference patterns and different diode behavior, underscoring that microscopic inhomogeneities such as twist angle variations shape the non-uniform supercurrent and drive the diode behavior. As a result, the nonreciprocal supercurrent can be tuned by gate voltage, enabling tuning of the diode efficiency and even reversing the polarity at fixed magnetic fields. Our findings offer potential routes for tailoring Josephson diode performance in superconducting quantum circuits.

Figures (5)

• Figure 1: (a) Schematic of the device and the measurement setup. Inset shows an optical image. The region under investigation is highlighted in the optical image. (b) Differential resistance as a function of $V_\mathrm{BG}$. Highlighted are the correlated and band insulating states (CI/BI), the charge neutrality point (CNP) and the superconducting (SC) area. The vanishing differential resistance in the area marked by the asterisk is a measurement artifact. (c) Differential resistance $\mathrm d V/\mathrm d I$ as a function of $V_\mathrm{BG}$ and $V_\mathrm{L}$. The JJ is formed at the gate configurations where the $\nu = -2$ correlated insulator intersects the superconducting area at fixed $V_\mathrm{BG} = -3.34 \, \mathrm{V}$ (see white bar and label). The used colorscale is linear between $0$ and $10^0\, \mathrm{k \Omega}$ and logarithmic between $10^0$ and $10^3 \, \mathrm{k \Omega}$. (d) Same as in panel (c) but as a function of $V_\mathrm{BG}$ and $V_\mathrm{R}$.
• Figure 2: (a) Differential resistance $\mathrm d V/\mathrm d I$ as a function of bias current $I$ and $V_\mathrm{L}$ measured at fixed $V_\mathrm{BG}$. Inset shows the formation of the JJ by weakly coupling the superconducting leads (S) via the correlated insulator at $\nu = -2$ below $V_\mathrm{L}$ resulting in the formation of a SX($n$)S junction, where $\mathrm{X}(n)$ denotes the gate-tunability of the weak link defined by the correlated insulator. White arrow indicates the sweep direction of the bias current when taking the map. (b) An analogous measurement to panel (a), but using the right top gate to form the JJ. (c-e) Current-voltage characteristics for both bias current sweep directions measured at the positions indicated by the colored arrows in panel (a).
• Figure 3: (a) Magnetospectroscopy measurements taken in the regions II-IV of the junction regime shown in \ref{['f2']}(a) for different fixed $V_\mathrm{L}$. The interference pattern exhibit a complex dependence on the charge carrier density of the weak link. The bias current is swept on the fast axis from negative to positive values, while the magnetic field is stepped on the slow axis from negative to positive values. Before each map is taken, we initialize the magnet at $B = -0.75 \, \mathrm{T}$. (b) Same as in panel (a) but measured for the junction tuned by $V_\mathrm{R}$ as shown in \ref{['f2']}(b).
• Figure 4: (a) Extracted shift in magnetic field $\delta B$ between the supercurrent maxima of the central interference for positive and negative bias currents as a function of $V_\mathrm{L}$ (red trace) and $V_\mathrm{R}$ (blue trace). The shifts are extracted from magnetospectroscopy measurements, partially shown in \ref{['f3']}(a,b). The error bars correspond to an estimated reading uncertainty of $0.2 \, \mathrm{mT}$. (b) Diode efficiency as a function of magnetic field extracted from the interference pattern taken at $V_\mathrm L = 1.06 \, \mathrm V$ and $V_\mathrm R = 1.01 \, \mathrm V$ in \ref{['f3']}. The shaded areas correspond to the errors arising from the fitting procedure. (c) Diode efficiency $\eta_j$ extracted from measurements at constant magnetic field values of $B = 0.45 \, \mathrm{mT}$ and $B = -0.95 \, \mathrm{mT}$ for the junction defined by $V_\mathrm{L}$. The diode efficiency is calculated via \ref{['diode_eff']} for the critical currents $I_\mathrm{sw \pm}$ and analogously for the retrapping currents $I_\mathrm{re \pm}$. The error bars arise from the fitting method used to extract the critical currents (see Supporting Information).
• Figure 5: (a) Schematic illustration of different twist angle domains below a top gate (projection into the plane). The different twist angle domains give rise to multiple current paths. (b) Circuit diagram schematic showing the resulting JJ network defined by $N$ parallel current paths. Each current path is described within the RCSJ model where we additionally incorporate the kinetic inductance of the superconductor. Gray shading indicates a finite area enclosed by two adjacent current paths which is penetrated by the externally applied magnetic field. (c) Magnetotransport simulation of the differential resistance as a function of the total current through the junction for $N = 5$ current paths. The model produces a skewed interference pattern. (d) Line-cut extracted from panel (c) at fixed $\Phi_\mathrm{ext}/\Phi_0 = 0.4$. For equal critical currents of the five individual current paths (blue curve) we do receive an overall symmetric critical current of the JJ for positive and negative bias current. For (slightly) different critical currents of the five current paths (red curve) we observe the onset of a JD effect, i.e. the critical current of the overall JJ is not equal for positive and negative bias current.