Unconventional Superconductivity in Bilayer Transition Metal Dichalcogenides

Bilayer transition metal dichalcogenides (TMDs) belong to a class of materials with two unique features, the coupled spin-valley-layer degrees of freedom and the crystal structure that is globally centrosymmetric but locally noncentrosymmetric. In this Letter, we will show that the combination of these two features can lead to a rich phase diagram for unconventional superconductivity, including intralayer and interlayer singlet pairings and interlayer triplet pairings, in bilayer superconducting TMDs. In particular, we predict that the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state can exist in bilayer TMDs under an in-plane magnetic field. We also discuss the experimental relevance of our results and possible experimental signatures.

Figure 1

(a) Crystal structure of bilayer TMDs $M{X}_2$ with the inversion center labeled by $P$. (b) Schematics for energy dispersion of bilayer TMDs where red and blue are for spin-up and spin-down, and solid and dashed lines are for the top and bottom layers. Here, each band is doubly degenerate and we shift the dashed lines a little for the view. (c) The phase diagram as a function of $U_0$ and $V_0$. The red, blue, and green lines are the phase boundary, separating three superconducting phases, the $A_{1g}$, $A_{1u}$, and $E_u$ pairings, and the metallic phase. (d) Experimental setup of bilayer TMD SC/conventional SC junction.

Figure 2

(a) Schematics of energy dispersion for bilayer TMDs with an in-plane magnetic field. Here, red and blue colors are for opposite spins and solid and dashed lines are for top and bottom layers. (b) The magnetic field dependence of the critical temperature $T_c$. Here, the black line is for $t=1\mathrm{meV}$, the red line is for $t=5\mathrm{meV}$, while the blue is for $t=10\mathrm{meV}$. Other parameters are chosen as ${\beta }_{\mathrm{SOC}}=40\mathrm{meV}$, $\hslash v_F=30\mathrm{meV}·\mathrm{nm}$ and $m=0.6m_e$ with electron mass $m_e$, $N_0{U}_0=0.3$ and $N_0{V}_0=0.1$. Only the orbital effect is taken into account. (c) The momentum $q_c$ for the stable pairing state as a function of $B_x$. (d) Phase diagram as a function of $B_x$ and $T_c$. Here, I is for conventional SC phase, II is for FFLO state, and III is for normal metal. $B_N=(2k{T}_{c0}/v_f{z}_0)$.