Quantum Metric Induced Critical Current Anomaly in Flat Band Josephson Junctions

Abstract

In well-established theories of Josephson junctions, the superconducting critical current \( I_\mathrm{c} \) increases as the normal state conductance \( \mathcal{G} \) increases. However, in a recent experiment in twisted bilayer graphene (TBG) based Josephson junctions, unexpectedly, it was observed that the increase of the critical current is accompanied by a decrease of the normal state conductance. We call this phenomenon the critical current anomaly. In this work, we point out that in the TBG-based Josephson junction, due to the suppression of the conventional Josephson current by the flatness of the band and the quantum metric enabled Josephson current (QMJC), the critical current anomaly can occur. The QMJC appears if the quantum metric length is comparable or longer than the junction length. We show that both \( \mathcal{G} \) and \( I_\mathrm{c} \) have the conventional and the quantum metric contributions, and there are parameter regimes in which \( I_\mathrm{c} \) increases even when \( \mathcal{G} \) decreases. We first demonstrate the critical current anomaly by a simple modified Lieb-lattice model both analytically and numerically. The incredible consistency with the experimental results is demonstrated using a realistic six-band model of twisted bilayer graphene. Therefore, we suggest that the critical current anomaly observed in the experiment provide strong evidence of QMJC which were ignored in well-established theories of Josephson junctions.