Spin-degenerate regimes for single quantum dots in transition metal dichalcogenide monolayers

Strong spin-orbit coupling in transition metal dichalcogenide (TMDC) monolayers results in spin resolvable band structures about the $K$ and $K'$ valleys such that the eigenbasis of a 2D quantum dot (QD) in a TMDC monolayer in zero field is described by the Kramers pairs $|0\rangle_-=|K'\uparrow\rangle$, $|1\rangle_-=|K\downarrow\rangle$ and $|0\rangle_+=|K\uparrow\rangle$, $|1\rangle_+=|K'\downarrow\rangle$. The strong spin-orbit coupling limits the usefulness of single TMDC QDs as spin qubits. Possible regimes of spin-degenerate states, overcoming the spin-orbit coupling in monolayer TMDC QDs are investigated in both zero field, where the spin and valley degrees of freedom become fourfold degenerate, and twofold degeneracy in some magnetic field, localised to a given valley. Such regimes are shown to be achievable in MoS$_{2}$, where the spin orbit coupling is sufficiently low and of the right sign such that the spin resolved conduction bands intersect at points about the $K$ and $K'$ valleys and as such may be exploited by selecting suitable critical dot radii.