Pearl-Vortex Tunneling in Magic-Angle Twisted Graphene

Abstract

Twisted graphene provides a tunable platform for studying superconductivity in two dimensions. In the presence of electric currents and magnetic fields, vortices determine the phenomenological properties of the material. Related studies usually address bulk properties averaging over ensembles of vortices. Here, we employ a gate-defined Josephson junction as a single-vortex sensor, enabling direct access to individual vortex dynamical events. Our measurements reveal that, at elevated temperatures (T > 100 mK), vortices enter the superconducting leads via classical thermal activation over energy barriers. At lower temperatures (T < 90 mK), we observe macroscopic quantum tunneling through these barriers. The data are consistent with a sharp, first-order type quantum-to-classical transition. From our measurements, we extract vortex entry and exit energy barriers on the order of a few Kelvin and estimate the barrier thickness to be approximately 100 nm, corresponding to about one tenth of the device width.

Figures (4)

• Figure 1: (a) Temperature evolution of rates $\Gamma(T)$ for vortex-entry into- and vortex-exit out of the superconducting leads. (b) Illustration of the free-energy landscape $G(y/W)$ for vortex motion across the leads. (c) Fitting the sharp rise in $\Gamma(T)$ at $T > 100mK$ with an Arrhenius law, see red dashed line, provides a thermal barrier of height $U/k_{\rm B} \approx 2.6K$. (d) The rates saturate at low temperatures to provide a dimensionless action $S/\hbar = \ln (\nu_0'/\Gamma)$ between 24 and 27. The red dashed line extrapolates the thermal activation law $S/\hbar = U/k_{\rm B}T$.
• Figure 2: (a) Layer structure with gates for device tuning, including a graphite bottom gate (BG), a gold top gate (TG), and a gold finger gate (FG) defining the JJ. (b) Device geometry with thickness $d = 1nm$, width $W = 1.1\upmu m$ along the $y$-direction, and length $L = 6W$ along $x$; the junction width is $L_{\rm j} = 150nm$. Vortices penetrate the leads (red dot) and are detected as jumps in the Fraunhofer pattern. (c) The field dependence of the critical current $I_c(B)$ measured at $T = 7mK$ in a film with 'strong-leads' tuning assumes the form of a Fraunhofer-like interference pattern (FP), see Ref. perego2024experimental. A vortex entering a lead produces a sudden rightward shift in the Fraunhofer pattern, see red arrow. (d) Schematic illustrating the change in the dissipation upon vortex entry into a lead: Measuring the voltage $V$ across the junction at fixed current $I^\ast$ and field $B^\ast < B_0$, with $B_0$ the zero of the FP, the response is dissipative when no vortex is present in the lead ($I_c < I^\ast$), while the junction is superconducting in the presence of a vortex ($I_c > I^\ast$). The response is reversed when $B^\ast > B_0$.
• Figure 3: (a) $V$--$I$ voltage--current characteristic at $B^\ast = 2mT$ and high temperature $T = 100mK$ with low- (blue) and high-dissipative (red) traces. Vortices traversing the leads produce switching between the two states, see blowup. (b) The same at $T = 7mK$ where the $V$--$I$ characteristic exhibits a sharp critical current $I_c$. (c) Time trace $V(t)$ of the voltage across the junction taken at $B^\ast = 2mT$ and $I^\ast = 4nA$, see dotted line in (a). The trace $V(t)$ exhibits segments with switching events (red--blue) due to the passage of vortices across one of the leads; these 'switching segments' are interrupted by 'silent' ones (cyan). (d) The same at $T = 7mK$ with the previously 'silent segments' (cyan in (c)) now exhibiting jumps to the superconducting state (orange).
• Figure 4: Critical current $I_c$ at $B=0mT$ as a function of temperature $T$ obtained from the sharp $V$--$I$ characteristics shown in the inset; the characteristics becomes rounded at higher temperatures $T > 70mK$.