Supercurrent interferometry of higher-order topological insulators

A three-dimensional topological insulator (TI) can be uniquely characterized by its boundary modes localized at surfaces, hinges, or/and corners. However, the state-of-the-art experimental techniques often find it challenging to determine the presence and location of the boundary modes particularly if they only exist at selected surfaces and hinges. Here we propose a supercurrent interferometry to solve this problem by exploiting the critical current interference in a superconductor-HOTI-superconductor Josephson junction. We further demonstrate that the spatial information of the surface or hinge modes can be unambiguous determined by retrieving the quantum phase information lost in the critical current measurement, as exemplified by our calculations of the Bi₄Br₄ system.