Topological superconductivity at the edge of transition-metal dichalcogenides

Time-reversal breaking topological superconductors are new states of matter which can support Majorana zero modes at the edge. In this Rapid Communication, we propose a different realization of one-dimensional topological superconductivity and Majorana zero modes. The proposed system consists of a monolayer of transition-metal dichalcogenides ${MX}_2$ $(M=\text{Mo},\text{W}$; $X=\text{S},\text{Se})$ on top of a superconducting substrate. Based on first-principles calculations, we show that a zigzag edge of the monolayer ${MX}_2$ terminated by a 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 ${\mathrm{NbS}}_2$ as a natural choice of substrate, and estimate the proximity induced superconducting gap based on first-principles calculation and a low energy effective model. As an experimental consequence of our theory, we predict that Majorana zero modes can be detected at the 120° corner of a ${MX}_2$ flake in proximity to a superconducting substrate.

Figure 1

(a)–(c) Zigzag ${MX}_2$ nanoribbons with three different boundary conditions zz-MX, zz-$M$, and zz-$X$, respectively. (d) and (e) Top and side view of a monolayer zz-MX ribbon with a saturated hydrogen configuration. (f) The heterostructure of a ${MX}_2$ nanoribbon on a ${\mathrm{NbS}}_2$ substrate.

Figure 2

Spin-polarized band structures without SOC for (a) zz-MoS, (b) zz-Mo, and (c) zz-S. Red circles and blue diamonds denote the projections to the up and down spin $d$ orbitals of the Mo atoms on the right edges shown in Fig. 1. The projections to Mo on the left edges are indicated as green squares and brown triangles, respectively. The Fermi level is defined at 0 eV.

Figure 3

Electronic structures with the Rashba SOC effect of (a) the zz-MoS nanoribbon and (b) the zz-MoS on a ${\mathrm{NbS}}_2$ substrate. The sizes of the red circles and green squares stand for the projection to Mo located on the right and left edges, respectively. The red and black dashes stand for the suitable Fermi level $\left(E_f\right)$ for S-terminated and Mo-terminated edges, respectively. $\pm K_{E_f}^{\text{S}}$ and $\pm K_{E_f}^{\text{Mo}}$ are defined on each $E_f$ to compare their spin moments. The inset of (b) is the zoom-in of the blue box, in which the red dashes are the schematic curves of the hybridization splitting between ${\mathrm{MoS}}_2$ and ${\mathrm{NbS}}_2$ bands.

Figure 4

Schematic picture of the proposed device with a ${\mathrm{MoS}}_2$ flake on the ${\mathrm{NbS}}_2$ substrate. The Mo-terminated edges are TSC and the S-terminated edges are trivial, so that each ${120}^{\circ }$ corner traps a Majorana zero mode (blue disk).