Experimental detection of vortices in magic-angle graphene: Part 2

Planar Josephson junctions made from atomically thin films exhibit poor transverse screening, causing the magnetic-field dependence of the Josephson current Ic(B) to deviate from the standard Fraunhofer pattern of conventional junctions. The relevant flux determining the oscillations in Ic(B) is not the usual flux Φ_λ = 2BWλ_L penetrating the junction but the larger flux Φ_W = 2BW², including the lead areas near the junction, with W the junction width. The envelope of the Fraunhofer-like pattern also differs, with maxima decaying slowly as ∝ 1/√B rather than the usual ∝ 1/B.

Given the weak screening, the junction is highly sensitive to Pearl vortices in the leads. Vortices alter the phase pattern and affect the Josephson current. Thermal fluctuations can cause vortices to jump in and out of the leads, leading to shifts in the Fraunhofer-like pattern, as observed in our experiment [1]. Our model quantitatively explains these jumps, whose timescale depends on magnetic field, current, temperature, and superfluid stiffness. At elevated temperatures, fast vortex jumps may wash out the Fraunhofer pattern well below Tc. By analyzing the timescale of these jumps, we can determine the superfluid stiffness and the Berezinskii-Kosterlitz-Thouless transition temperature of magic-angle twisted four-layer graphene.

[1] Perego, Marta, et al. "Experimental detection of vortices in magic-angle graphene." arXiv preprint arXiv:2410.03508 (2024).