Investigation of short and ballistic coupling in vertical NbSe$_{\mathrm{2}}$ - graphene - NbSe$_{\mathrm{2}}$ Josephson junctions

2H-NbSe$_{\mathrm{2}}$ is a layered two-dimensional superconducting material, which can be constructed into a van der Waals heterostructure with versatile functionality. Here we fabricated a vertically stacked NbSe$_{\mathrm{2}}$ - graphene - NbSe$_{\mathrm{2}}$ heterostructure by the dry transfer technique, where defect-free contact via van der Waals force provides the high interfacial transparency. Insertion of an atomically thin graphene layer between two NbSe$_{\mathrm{2}}$ flakes ensures the formation of highly coherent proximity Josephson coupling. Observed temperature dependence of the junction critical current ($I_{\mathrm{c}})$ and large value of $I_{\mathrm{c}}R_{\mathrm{n}}$ product (as large as 2.3$\Delta _{\mathrm{NbSe2}})$ reveal the short and ballistic Josephson coupling characteristics. Large junction critical current density of \textasciitilde 10$^{\mathrm{4}}$ A/cm$^{\mathrm{2}}$, multiple Andreev reflection in the subgap structure of the differential conductance, and magnetic field modulation of $I_{\mathrm{c}}$ also suggest the strong Josephson coupling via the graphene layer.