  Time-reversal breaking topological superconductors are new states of matter
which can support Majorana zero modes at the edge. In this paper, we propose a
new realization of one-dimensional topological superconductivity and Majorana
zero modes. The proposed system consists of a monolayer of transition metal
dichalcogenides MX2 (M=Mo, W; X=S, Se) on top of a superconducting substrate.
Based on first-principles calculations, we show that a zigzag edge of the
monolayer MX2 terminated by metal atom M has edge states with strong spin-orbit
coupling and spontaneous magnetization. By proximity coupling with a
superconducting substrate, topological superconductivity can be induced at such
an edge. We propose NbS2 as a natural choice of substrate, and estimate the
proximity induced superconducting gap based on first-principles calculation and
low energy effective model. As an experimental consequence of our theory, we
predict that Majorana zero modes can be detected at the 120 degree corner of a
MX2 flake in proximity with a superconducting substrate.
