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We study the transport properties of a Josephson junction consisting of twoidentical $s$-wave superconductors separated by an even-layer${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT). Using recursive Green's functionmethod, we calculate the supercurrent in the presence of a perpendicularmagnetic field and find that its quantum interference exhibits distinctpatterns when the MBT is in different magnetic states. In the antiferromagneticstate, the MBT is an axion insulator supporting an extended "hinge"supercurrent, which leads to a sinusoidal interference pattern decaying withthe field strength. In the ferromagnetic state, the MBT is a Chern insulatorand the unbalanced chiral supercurrents on opposite edges give rise to a highlyasymmetric interference pattern. If the MBT turns into a metal as the Fermilevel is tuned into the conduction band, the interference exhibits a Fraunhoferpattern due to the uniformly distributed bulk supercurrent. Our work unravels astrong indicator to identify different phases in the MBT and can be verifieddirectly by experiments.

Quantum interference in a superconductor-${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$-superconductor Josephson junction