Hinge states of second-order topological insulators as a Mach-Zehnder interferometer

Three-dimensional higher-order topological insulators can have topologically protected chiral modes propagating on their hinges. Hinges with two copropagating chiral modes can serve as a “beam splitter” between hinges with only a single chiral mode. Here we show how such a crystal, with Ohmic contacts attached to its hinges, can be used to realize a Mach-Zehnder interferometer. We present concrete calculations for a lattice model of a first-order topological insulator in a magnetic field, which, for a suitable choice of parameters, is an extrinsic second-order topological insulator with the required configuration of chiral hinge modes.