Conductance oscillations of antiferromagnetic layer tunnel junctions

We study conductance oscillations of antiferromagnetic layer tunnel junctions composed of antiferromagnetic topological insulators such as ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$. In the presence of an in-plane magnetic field, we find that the two terminal differential conductances across the junction oscillates as a function of field strength. Notably, the quantum interference at weak fields for the even-layer case is distinctive from the odd-layer case due to the scattering phase shift $\ensuremath{\pi}$. Consequently, the differential conductance vanishes (maximized) at integer magnetic flux quanta for even-layer (odd-layer) junctions. The conductance oscillations manifest the layer-dependent quantum interference in which symmetries and scattering phases play essential roles. In numerical calculations, we observe that the quantum interference undergoes an evolution from superconducting quantum interference device-like to Fraunhofer-like oscillations as the junction length increases.