Current-phase relation of a WTe2 Josephson junction

Abstract: When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4$\pi$-periodic current-phase relation. Here, we report the measurement of a $4\pi$-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe$2$. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTe${\text{x}}$ inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the $1.5\,\mu \text{m}$ long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.