Unconventional superconductivity from magnetism in transition-metal dichalcogenides

We investigate proximity-induced superconductivity in monolayers of transition-metal dichalcogenides (TMDs) in the presence of an externally generated exchange field. A variety of superconducting order parameters is found to emerge from the interplay of magnetism and superconductivity, covering the entire spectrum of possibilities to be symmetric or antisymmetric with respect to the valley and spin degrees of freedom, as well as even or odd in frequency. More specifically, when a conventional $s$-wave superconductor with singlet Cooper pairs is tunnel-coupled to the TMD layer, both spin-singlet and triplet pairings between electrons from the same and opposite valleys arise due to the combined effects of intrinsic spin-orbit coupling and a magnetic-substrate-induced exchange field. As a key finding, we reveal the existence of an exotic even-frequency triplet pairing between equal-spin electrons from different valleys, which arises whenever the spin orientations in the two valleys are noncollinear. All types of superconducting order turn out to be highly tunable via straightforward manipulation of the external exchange field.

Figure 1

Structure and properties of our system of interest. (a) Schematics of the hybrid superconductor–TMD-ML–magnetic-insulator system. (b) Valence-band structure of the TMD-ML in the presence of an externally induced exchange field $\mathbf{J}$. The spin states of each subband are indicated for an exchange field of the form $\mathbf{J}=(J_x,0,J_z)$. (c) The effective exchange fields $J_{\mathrm{eff}}^{\zeta }$ in the two valleys arising from the combination of $\mathbf{J}$ and SOC-induced spin splitting, which point at angles ${\phi }_{\pm }=arctan[J_x/(J_z\mp \lambda )]$ with respect to the $z$ axis.

Figure 2

Magnitude of intravalley superconducting order parameters from Eqs. (15) induced in a monolayer TMD when the external exchange field is $\mathbf{J}=(J_x,0,J_z)$. Here $J=\sqrt{J_x^2+J_z^2}, \theta =arctan(J_x/J_z)$, and $E_{\mathbf{k}}=-0.25\lambda$.

Figure 3

Magnitude of intervalley opposite-spin superconducting order parameters induced in a monolayer TMD when the external exchange field is $\mathbf{J}=(J_x,0,J_z)$. Shown are dependencies on $J=\sqrt{J_x^2+J_z^2}$ and $\theta =arctan(J_x/J_z)$, keeping $E_{\mathbf{k}}=-0.25\lambda$ fixed.

Figure 4

Magnitude of intervalley equal-spin superconducting order parameters for the same situation and conventions as in Fig. 3.