The three-dimensional (3D) topological insulators (TIs), hosting topologically protected helical surface states, can be promoted into second-order TIs when a diagonal Zeeman term, typical of magnetic doping, is introduced. The latter hosts exotic chiral one-dimensional (1D) topological hinge states (THSs). In this paper, we investigate the electronic transport of THSs through a magnetic domain wall (DW) in a 3D TI nanowire. Because of the sign reversal of the out-of-plane magnetization across the DW, four 1D topological boundary states, residing on the edge of the DW, arise and form an enclosed loop mediating the counterpropagating THSs. By applying a uniform magnetic field parallel to the nanowire, we obtain a perfect sinusoidal Aharonov-Bohm oscillation in the two-terminal conductance $G$, formulated by $G=\frac{e^2}{2h}[1-cos(\pi \mathrm{\Phi }/{\mathrm{\Phi }}_0)]$, with $\mathrm{\Phi }$ the magnetic flux through the DW and ${\mathrm{\Phi }}_0=h/2e$ the flux quantum. Applying a phenomenological scattering matrix approach, we explain this Aharonov-Bohm oscillation perfectly, and attribute the constructive (destructive) interference of transmission at $\mathrm{\Phi }={\mathrm{\Phi }}_0$ (0) to the $\pi$-spin rotation of the THSs traveling through the DW. Extending our study to a double-DW junction, where the central region has antiparallel magnetization to the leads, we observe Fabry-Pérot oscillations, in which the conductance minima are tuned by the magnetic flux. Our findings open an avenue for finely controlling the quantum transport of THSs in magnetic systems using magnetic flux, and provide a faithful way for detecting THSs in experiments.

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• Aharonov-Bohm effect
• Domain walls
• Quantum transport
• Topological insulators
• Nonequilibrium Green's function
• S-matrix method in transport