Multi-channel second-order topological states in 3D Dirac semimetal Bi$_{0.97}$Sb$_{0.03}$

Second-order topological insulating (SOTI) states in three-dimensional materials are helical dissipation-less one-dimensional (1D) hinges, which are of great interest for fundamental physics and potential topological quantum computing. Here, we report the discovery of SOTI states in Bi$_{0.97}$Sb$_{0.03}$ nano-flakes by tuning junction length, flake thickness, and temperature. We identify signatures of higher-order topology from a strong correlation between the fractional Shapiro step, a signature of 4$\pi$-periodic supercurrent, and the presence of the hinge states. Tight-binding simulations confirm the presence of multiple hinge modes, supporting our interpretation of Bi$_{0.97}$Sb$_{0.03}$ as a prototypical SOTI platform with tunable superconducting properties.