Experimental detection of vortices in magic-angle graphene

Abstract

Superconducting magic-angle twisted-layer graphene (MATLG) is a promising candidate for superconducting electronics due to its electrical tunability. While the microscopic origins of superconductivity in MATLG have been intensively studied, many aspects of its phenomenology remain unexplored due to the challenges associated with studying two-dimensional (2D) materials. Here, we report the first direct experimental evidence of superconducting vortices in MATLG, a hallmark of type-II superconductors. Field-dependent critical current measurements in a gate-tuned Josephson junction reveal Fraunhofer-like patterns characteristic of ultrathin films with weak transverse screening. These patterns exhibit sudden shifts attributed to spontaneous vortex penetration into the leads. With the leads at the edge of the superconducting dome, we observe bistable V-I fluctuations linked to rapid vortex dynamics. Time-dependent measurements provide the vortex energy scale, the London penetration depth, and superfluid stiffness, consistent with recent kinetic inductance studies. These findings establish gate-defined Josephson junctions as versatile sensors of vortex dynamics in 2D superconductors.

Fig. 1. Device setup and bulk phase diagram.

a Schematic cross-section of the thin film JJ device and measurement setup; V is the measured voltage drop and I is the applied current. The top gate (TG), finger gate (FG), and back gate (BG) are indicated. b Schematic top view of the film with width W (along the y-axis) and overall length L (along the x-axis); L_j is the thickness of the JJ along x. The densities in the leads and junction are denoted by n_l and n_j, the field B and current I directions are indicated. Screening currents j_s (in green) and vortex currents j_v (light blue) circulate in opposite directions. c Phase diagram of the film material, with the voltage V (blue color scale) versus leads' density n_l and displacement field D_l, measured in a 4-terminal configuration not crossing the junction at a constant current I = 10 nA. The filling factor ν is plotted on the top axis. The blue dark regions around ∣ν∣ ≈ 2–3 signal superconductivity. Red dots indicate full filling where the junction is tuned into the resistive state. d Differential resistance R measured as a function of I and B with the device tuned to the superconductiong state (green square in (c)). The orange dashed line indicates the fit to extract the edge penetration field B_e, with the inset showing a line trace recorded at the white circle B = 72 mT.

Fig. 2. Josephson junction device and Fraunhofer pattern.

a Differential resistance R measured as a function of I while sweeping n_j and keeping n_l fixed. D_j is fixed at zero whereas D_l is swept as shown on the top axis, following the yellow dashed line in Fig. 1c. By sweeping n_j, the junction can be tuned from a resistive to a superconducting state, resulting in a SJS or SSS configuration, with the critical currents of the bulk and junction denoted by I_cb and I_cj. A line trace of the differential resistance R is shown with n_j fixed at the dotted orange line. b Differential resistance R measured as a function of I and B for n_l = − 3.5 × 10¹² cm⁻², D_l/ϵ₀ = 0.2 V/nm and n_j = − 6.3 × 10¹² cm⁻², D_j/ϵ₀ = 0.45 V/nm (blue-red-blue setting in Fig. 1c). The orange and yellow dashed lines show the theoretical predictions for a 2D JJ under weak screening conditions, whereas the dotted yellow line shows the rapid decay  ∝ 1/B for a standard JJ. c Differential resistance R measured as a function of I and B with the entire device tuned to the pink triangle shown in the phase diagram Fig. 1c, implying that no junction is formed. This SSS configuration exhibits no interference pattern.

Fig. 3. Vortex penetration.

Differential resistance R measured as a function of I and B, for a forward magnetic-field sweep in (a) and a backward sweep in (b). The bottom axes show the corresponding scaled flux Φ_W/Φ₀ penetrating junction and leads, where Φ_W = BW². The tuning parameters are n_l = 4.2 × 10¹² cm⁻², D_l/ϵ₀ = −0.3 V/nm and n_j = 6.2 × 10¹² cm⁻², D_j/ϵ₀ = −0.5 V/nm (‘strong-leads’ setting). Sudden shifts of the interference pattern are highlighted with black arrows. Theoretical fits of the measured Fraunhofer patterns (a) and (b) on the basis of the analysis in Ref. , with 7 (in (c)) and 4 (in (d)) vortices leaving/penetrating the leads.

Fig. 4. Vortex fluctuations.

a Differential resistance R measured at T = 100 mK as a function of I and B with parameters n_l = 4.8 × 10¹² cm⁻², D_l/ϵ₀ = −0.3 V/nm and n_j = 6.2 × 10¹² cm⁻², D_j/ϵ₀ = − 0.5 V/nm (‘weak-leads’ setting). The Fraunhofer pattern is smoothed and white—dark-blue speckles mark the presence of bistabilities in the V—I characteristic. b Voltage—current trace at B* = 2.0 mT, see arrows in Fig. 4a. The V—I characteristic is rounded and exhibits pronounced steps; we associate the rounding with the presence of phase slips in the junction and the steps with vortex fluctuations in the leads. The steps manifest in the speckles visible in Fig. 4a. c Time trace of the voltage V measured at fixed B* = 2.0 mT and current I* = 4 nA, see dotted line in Fig. 4b. We associate the telegraph-type noise with vortex fluctuations in the leads. (d) In green, vortex fluctuations timescale t versus temperature T extracted from the statistical analysis (Fig. S8) of the telegraph-type noise in Fig. 4c. The measured time scales decay in temperature from t ∼ 1.2 s to t ∼ 0.04 s. The expected theoretical decay of t is plotted with the black dashed line. The corresponding barrier $U_{\mathrm{e}}=Tln\left(t/t_0\right)\approx 2.56\mathrm{K}$ is shown in orange and is seen to remain constant as expected for an activated process.