Pearl-Vortex Tunneling in Magic-Angle Twisted Graphene

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.

💡 Research Summary

In this work the authors investigate the dynamics of individual Pearl vortices in magic‑angle twisted four‑layer graphene (MAT4G) by using a gate‑defined Josephson junction (JJ) as a single‑vortex sensor. The device consists of a narrow (150 nm) electrostatically defined weak link flanked by superconducting leads that are tuned to the edge of the superconducting dome (“weak‑leads” regime). A perpendicular magnetic field penetrates the atomically thin graphene uniformly, creating a dense array of vortices that must overcome Bean‑Livingston edge barriers in order to enter or exit the leads.

By fixing the magnetic field at ≈2 mT and the bias current at ≈4 nA, the authors record the voltage across the junction with a bandwidth of ~1.1 kHz for several hours. The voltage time traces display telegraph‑type switching between high‑dissipation (normal) and low‑dissipation (superconducting) levels. These switches correspond to the passage of a single Pearl vortex across one of the leads, which in turn shifts the Fraunhofer interference pattern of the JJ. When a vortex enters the lead, the effective flux through the junction changes by roughly one flux quantum, moving the interference pattern to higher field; vortex exit produces the opposite shift. Consequently the critical current I_c of the junction toggles between two values, giving rise to the observed voltage jumps.

Statistical analysis of the dwell times in the vortex‑free (τ_nv) and vortex‑present (τ_v) states yields entry and exit rates Γ_nv and Γ_v. At temperatures above ~100 mK the rates follow an Arrhenius law Γ = ν₀ exp(−U/k_BT) with an attempt frequency ν₀≈2 × 10¹¹ Hz and barrier heights U/k_B≈2.6 K for both entry and exit. This thermal activation regime is consistent with the expected edge‑barrier energy derived from the free‑energy landscape G(y;H,I) that includes logarithmic vortex core energy, magnetic‑field‑induced attraction to the edge, and a tilt from the bias current.

Below ~90 mK the rates saturate and become temperature‑independent, indicating a crossover to macroscopic quantum tunneling (MQT). In this regime the rates are described by Γ = ν₀′ exp(−S/ħ), where the dimensionless Euclidean action S/ħ≈24–27 (using ν₀′≈ν₀). The nearly constant action over the low‑temperature range signals a sharp, first‑order quantum‑to‑classical transition, as predicted by theories of vortex tunneling in thin superconducting films.

Fitting the full G(y) expression to the measured barrier heights allows the authors to estimate the effective barrier thickness as ~100 nm, i.e. roughly one‑tenth of the lead width (W≈1.1 µm). This length scale reflects the narrow region near the edge where the vortex must tunnel.

The study demonstrates that magic‑angle twisted graphene, with its low superfluid density and large sheet resistance, provides an ideal platform for observing macroscopic quantum phenomena in two‑dimensional superconductors. Direct detection of single‑vortex tunneling offers new insight into vortex‑induced dissipation, which is crucial for the performance of superconducting qubits, nano‑SQUIDs, and other quantum devices based on 2D superconductors. Moreover, the ability to resolve individual vortex events opens a pathway to explore fundamental questions such as Berezinskii‑Kosterlitz‑Thouless physics, vortex‑glass dynamics, and the interplay between disorder and quantum fluctuations in atomically thin superconductors.