Pseudo-spin triplet superconductivity in transition-metal dichalcogenide monolayers and Andreev reflection in the lateral heterostructures of 2$H$-NbSe$_2$

We study the pseudo-spin of electron pair in superconducting transition-metal dichalcogenide monolayers and show that the pseudo-spin affects the electric transport property of lateral heterojunction of the superconducting and metallic monolayers. The pseudo-spins of two electrons forming a Cooper pair are parallel to each other unlike the real spins being anti-parallel. In the lateral heterojunction, the electronic transport with forming a Cooper pair, the Andreev reflection, is suppressed with the Fermi level crossing the valence band near the edge in the metallic monolayer. We numerically investigate the electric transport property of the lateral heterojunctions of semiconducting and superconducting transition-metal dichalcogenides, MoSe$_2$ monolayer and NbSe$_2$ monolayer with the charge doping, respectively. We find the sign change of conductance difference between the normal and superconducting phases by varying the charge density and show that the sign change is resulted from the pseudo-spin triplet superconductivity.