Aharonov-Bohm effect in three-dimensional higher-order topological insulators

One-dimensional hinge states are the hallmark of three-dimensional (3D) higher-order topological insulators (HOTIs), which may lead to interesting transport properties. Here, we study the Aharonov-Bohm (AB) effect in an interferometer constructed by the hinge states in normal metal-HOTI junctions with a transverse magnetic field. We show that the AB oscillation of the conductance can clearly manifest the spatial configurations of such hinge states. The magnetic fluxes encircled by various interfering loops are composed of two basic ones, so that the oscillation of the conductance by varying the magnetic field contains different frequency components universally related to each other. Specifically, the four dominant frequencies ${\ensuremath{\omega}}_x,y$ and ${\ensuremath{\omega}}_{x\ifmmode\pm\else\textpm\fi{}y}$ satisfy the relations ${\ensuremath{\omega}}_{x\ifmmode\pm\else\textpm\fi{}y}={\ensuremath{\omega}}_x\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}_y$, which generally hold for different magnetic fields, sample sizes, bias voltages, and weak disorders. Our results provide a unique and robust signature of the hinge states and pave the way for exploring the AB effect in 3D HOTIs.