Transport evidence of asymmetric spin-orbit coupling in few$-$layer superconducting 1Td$-$MoTe$_2$

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) MX2 (M=W, Mo, Nb, and X=Te, Se, S) with strong spin-orbit coupling (SOC) possess plenty of novel physics including superconductivity. Due to the Ising SOC, monolayer NbSe$_2$ and gated MoS$_2$ of 2H structure can realize the Ising superconductivity phase, which manifests itself with in-plane upper critical field far exceeding Pauli paramagnetic limit. Surprisingly, we find that a few-layer 1Td structure MoTe$_2$ also exhibits an in-plane upper critical field ($H_{c2,//}$) which goes beyond the Pauli paramagnetic limit. Importantly, the in-plane upper critical field shows an emergent two-fold symmetry which is different from the isotropic $H_{c2,//}$ in 2H structure TMDCs. We show that this is a result of an asymmetric SOC in 1Td structure TMDCs. The asymmetric SOC is very strong and estimated to be on the order of tens of meV. Our work provides the first transport evidence of a new type of asymmetric SOC in TMDCs which may give rise to novel superconducting and spin transport properties. Moreover, our findings mostly depend on the symmetry of the crystal and apply to a whole class of 1Td TMDCs such as 1Td-WTe$_2$ which is under intense study due to its topological properties.