Quasiparticle and superfluid dynamics in Magic-Angle Graphene

Magic-Angle Twisted Bilayer Graphene shows a wide range of correlated phases which are electrostatically tunable. Despite a growing knowledge of the material, there is yet no consensus on the microscopic mechanisms driving its superconducting phase. In particular, elucidating the symmetry and formation mechanism of the superconducting phase may provide key insights for the understanding of unconventional, strongly coupled and topological superconductivity. A major obstacle to progress in this direction is that key thermodynamic properties, such as specific heat, electron-phonon coupling and superfluid stiffness, are extremely challenging to measure due to the 2D nature of the material and its relatively low energy scales. Here, we use a gate-defined, radio frequency-biased, Josephson junction to probe the electronic dynamics of magic-angle twisted bilayer graphene (MATBG). We reveal both the electronic quasiparticle dynamics, driven by their thermalization through phonon scattering, as well as the condensate dynamics, driven by the inertia of Cooper pairs. From these properties we recover the evolution of thermalization rates, and the superfluid stiffness across the phase diagram. Our findings favor an anisotropic or nodal pairing state and allow to estimate the strength of electron-phonon coupling. These results contribute to understanding the underlying mechanisms of superconductivity in MATBG while establishing an easy-to-implement method for characterizing thermal and superfluid properties of superconducting 2D materials.

💡 Research Summary

This paper presents a novel experimental platform for probing the quasiparticle thermalization and superfluid dynamics of magic‑angle twisted bilayer graphene (MATBG), a two‑dimensional material that hosts a rich phase diagram of correlated insulating, superconducting, and topological states. Conventional thermodynamic probes such as specific‑heat, calorimetry, ARPES, or neutron scattering are impractical for MATBG because of its atomically thin nature and the extremely low energy scales involved. To overcome these limitations, the authors fabricate a gate‑defined Josephson junction (JJ) in MATBG and bias it simultaneously with a dc current and a radio‑frequency (RF) ac current whose frequency spans three decades (0.1 MHz to 100 MHz). By monitoring the current‑voltage (I‑V) characteristics under these conditions, they extract two characteristic rates: the switching rate (Γ_sw) associated with the transition from the superconducting to the resistive state, and the retrapping rate (Γ_re) governing the return to the superconducting state.

At low RF frequencies the ac component effectively reduces the hysteresis loop: the total current (I_dc + I_RF) reaches the critical switching current earlier, while the retrapping current is delayed, leading to a narrower hysteresis. As the frequency increases, the hysteresis gradually disappears because the intrinsic dynamics cannot follow the rapid ac modulation. This frequency‑dependent behavior reveals that Γ_sw and Γ_re are governed by distinct physical mechanisms rather than by the conventional resistively‑and‑capacitively‑shunted‑junction (RCSJ) dynamics, whose characteristic Josephson frequency (∼10 GHz) is far above the experimental range.

The authors propose a comprehensive model consisting of three coupled equations. Equation (1) describes the Josephson current with a temperature‑dependent critical current I_J(T) and a fixed excess current I_ex. Equation (2) governs the electronic temperature T, balancing Joule heating (proportional to the square of the Josephson phase velocity) against a thermal conductance G_th that represents electron‑phonon cooling. Equation (3) incorporates the kinetic inductance L_kin of the bulk MATBG leads, which reflects the inertia of Cooper pairs. In the weak‑link regime the junction is modeled as a resistively shunted element (R_J) in series with the bulk kinetic inductance; in the homogeneous superconducting regime the kinetic inductance appears in parallel with a normal‑resistive shunt representing residual metallic regions.

Fitting the model to the measured I‑V curves across a wide range of gate‑tuned carrier densities yields quantitative estimates of several key parameters. The electron‑phonon coupling constant λ_ep is found to be roughly three times smaller than that of conventional aluminum, indicating that MATBG is a weak‑coupling superconductor. The extracted thermal conductance G_th ≈ 2 × 10⁻⁹ W K⁻¹ cm⁻² corresponds to a quasiparticle relaxation rate γ_ph ≈ 10⁸ s⁻¹ at temperatures around 0.1 K. The kinetic inductance is unusually large (L_kin ≈ 0.5 nH µm⁻¹), reflecting the combination of an extremely low superfluid density n_s (∼10⁻³ of the total carrier density) and a high effective mass m*. Consequently, the characteristic frequency ω_L = R_bulk/L_kin lies in the low‑MHz range, explaining why the ac drive ceases to affect the junction at frequencies above a few megahertz.

A striking asymmetry between the switching and retrapping currents is observed: I_sw remains nearly temperature‑independent, whereas I_re drops sharply with increasing temperature. This behavior is consistent with a superconducting gap that possesses nodes or strong anisotropy, because nodal quasiparticles enhance thermal depairing during retrapping while leaving the forward switching largely unaffected. The authors therefore argue that the superconducting order parameter in MATBG is likely anisotropic or nodal rather than isotropic s‑wave.

In summary, the study provides three major insights: (i) MATBG exhibits weak electron‑phonon coupling, (ii) its superfluid stiffness is low and its kinetic inductance is large, and (iii) the pairing symmetry is probably anisotropic with nodes. Moreover, the gate‑defined RF‑biased Josephson junction technique emerges as a versatile, non‑invasive tool for measuring specific heat, electron‑phonon coupling, and superfluid stiffness in two‑dimensional superconductors. The methodology can be readily adapted to other atomically thin superconductors such as NbSe₂, TaS₂, or twisted transition‑metal dichalcogenide bilayers, opening a pathway to systematic thermodynamic characterization of emergent 2D superconductivity.