Coexisting topological hinges and 1D Rashba states in Bi${}_{0.97}$Sb${}_{0.03}$ revealed by the Josephson effect

Second-order topological insulating (SOTI) states in three-dimensional materials are helical one-dimensional hinge states. Inducing superconductivity in these states leads to gapless bound states, characterized by the 4$\pi$-periodic current-phase relation. Here, we provide evidence of the topologically protected hinge states in Dirac semimetal Bi${}_{0.97}$Sb${}_{0.03}$ nanoflakes by an unconventional interference pattern in a magnetic field, and the 4$\pi$-periodic supercurrent carried by these states via the suppressed first and third Shapiro steps. Tight-binding simulations confirm the presence of multiple hinge modes, supporting our interpretation of Bi${}_{0.97}$Sb${}_{0.03}$ as a prototypical designable SOTI platform. Quantum confinement effect is identified by a quasi-one-dimensional bulk transport, and the confined Rashba states are responsible for the broadened hinge states.