Abstract
Spin-orbit coupling in transition metal dichalcogenides (TMDCs) causes spin-valley locking giving rise to unconventional optical, transport, and superconducting properties. In this paper, we propose exotic superconductivity in bilayer group-IV TMDCs by symmetry control. The sublattice-dependent hidden spin-orbit coupling arising from local inversion symmetry breaking in the crystal structure may stabilize the odd-parity superconductivity by purely $s$-wave local pairing interaction. The stability of the odd-parity superconducting state depends on the bilayer stacking. The 2H$_b$ stacking in MoX$_2$ and WX$_2$ (X =S, Se) favors the odd-parity superconductivity due to interlayer quantum interference. On the other hand, the odd-parity superconductivity is suppressed by the 2H$_a$ stacking of NbSe$_2$. Calculating the phase diagram of the tight-binding model derived from first principles band calculations, we conclude that the intercalated bilayer MoS$_2$ and WS$_2$ are candidates for a new class of odd-parity superconductors by spin-orbit coupling.
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