Evidence for topological hinge states in a bismuth nanoring Josephson junction

A striking signature of 2D topological insulators (TIs) and 3D Second Order TIs are 1D helical modes at sample edges or hinges, i.e. modes in which the propagation and spin directions are locked, conferring robustness to transport through these modes. Injecting pairs from superconducting contacts into such helical modes is thus different from pair injection into nontopological, spin-degenerate modes: Cooper pairs of both helicities must now separate according to the mode helicity, leading to two families of helical Andreev hinge modes, one on each hinge. To explore this physics, we have measured and analyzed the statistics of the switching current of a bismuth nanoring connected to two superconducting leads, over a wide range of magnetic fields. The average switching current displays a 2-pi-periodic sawtooth-like current-phase relation (CPR), confirming the long, ballistic nature of transport previously reported in Josephson junctions containing a single bismuth nanowire, and consistent with supercurrent carried by protected 1D helical hinge modes, characteristic of 3D Second Order Topological Insulators. The switching current histograms display an unexpected additional branch that is shifted by pi with respect to the first one. Using a phenomenological model of two helical Andreev hinge modes, we deduce the relative occupation of their ground and excited states, and extract the relaxation times for both a single quasiparticle and a pair of quasiparticles. We find that both times are remarkably long, of the order of milliseconds. Moreover, the ratio of the quasiparticle over the pair relaxation time, about 5, is exceptionally low compared to nontopological systems, which we attribute to the spatial separation of the helical hinge modes. Our results provide new insights into quasiparticle and Cooper-pair relaxation processes in hinge modes of Second Order Topological Insulators.