Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides

We derive an effective Hamiltonian which describes the dynamics of electrons in the conduction band of transition metal dichalcogenides (TMDC) in the presence of perpendicular electric and magnetic fields. We discuss in detail both the intrinsic and the Bychkov-Rashba spin-orbit coupling (SOC) induced by an external electric field. We point out interesting differences in the spin-split conduction band between different TMDC compounds. An important consequence of the strong intrinsic SOC is an effective out-of-plane $g$-factor for the electrons which differs from the free-electron g-factor $g\simeq 2$. We identify a new term in the Hamiltonian of the Bychkov-Rashba SOC which does not exist in III-V semiconductors. Using first-principles calculations, we give estimates of the various parameters appearing in the theory. Finally, we consider quantum dots (QDs) formed in TMDC materials and derive an effective Hamiltonian which allows us to calculate the magnetic field dependence of the bound states in the QDs. We find that all states are both valley and spin split, which suggests that these QDs could be used as valley-spin filters. We explore the possibility of using spin and valley states in TMDCs as quantum bits, and conclude that, due to the relatively strong intrinsic spin-orbit splitting in the conduction band, the most realistic option appears to be a combined spin-valley (Kramers) qubit at low magnetic fields.