Probing topology with superconductivity : Measurement of equilibrium noise in NS ring and current-phase relation of helical hinge states of WTe2

An SNS junction formed by a non-superconducting material (N) between two superconducting contacts (S) can sustain a supercurrent carried by Andreev bound states (ABS) which is determined by the superconducting phase difference across the superconducting contacts. The value of this current and its dynamics are very sensitive probes of the coherent and topological transport properties in the non-superconducting material.

In an initial experiment, we demonstrated the topological character of tungsten ditelluride (WTe₂) by measuring the supercurrent/phase relation using an asymmetric superconducting quantum interference device (SQUID), consisting of two SNS junctions in parallel. The sawtooth shape of the current-phase relation for a lateral facet of the crystal and the robustness of the supercurrent at high magnetic field reveals the ballistic and one-dimensional character of the transport along certain edges over more than 500 nm. This is a signature of the presence of one-dimensional states protected from disorder in this material, confirming the predictions of a phase close to a higher-order topological insulator for this material.

In a second experiment, a mesoscopic wire (Au) is inserted into a superconducting ring has made it possible to explore the dynamics of the ABS. At finite temperature, thermal fluctuations in ABS should give rise to fluctuations in the supercurrent and therefore to a finite-frequency dissipation, the amplitude of which depends on their relaxation time, as predicted by the fluctuation-dissipation theorem. By coupling this ring to a superconducting resonator, we were able to measure independently the fluctuations in the supercurrent at equilibrium and the dissipation that occurs when the ring is subjected to an oscillating magnetic flux. This experiment constitutes the first confirmation of this theorem in an SNS junction.