Spin-valley qubits in gated quantum dots in a single layer of transition metal dichalcogenides

We develop a microscopic and atomistic theory of electron-spin-based qubits in gated quantum dots in a single layer of transition metal dichalcogenides. The qubits are identified with two degenerate locked spin and valley states in a gated quantum dot. The two qubit states are accurately described using a multimillion atom tight-binding model solved in wave-vector space. The spin-valley locking and strong spin-orbit coupling result in two degenerate states, one of the qubit states being spin down located at the $+K$ valley of the Brillouin zone, and the other state located at the $-K$ valley with spin up. We describe the qubit operations necessary to rotate the spin-valley qubit as a combination of the applied vertical electric field, enabling spin-orbit coupling in a single valley, with a lateral strongly localized valley-mixing gate.

Figure 1

(Top) A schematic view of the device. Quantum dot in monolayer TMDC is induced by the top gate (gold), and highly localized potential necessary for valley mixing is controlled here by the scanning tunneling microscope tip. Additional vertical electric field is induced by potentials applied to two graphite layers. (Bottom) Schematic view of the spin-valley qubit (red arrow).

Figure 2

Bulk band structure of ${\text{MoS}}_{\text{2}}$. (a) Blue lines correspond to energy levels of even orbitals and red lines correspond to energy levels of odd orbitals. (b) Lowest conduction band energy levels on allowed values of $k$ points. $+K$ and $-K$ are global valley minima of the conduction band while the three $+Q$ and $-Q$ points correspond to local minima of the conduction band states.

Figure 3

QD spectrum. Harmonic oscillator shell-like electronic states are formed due to the applied negative gate potential. Two qubit states are indicated, well isolated from the rest of the energy levels. Inset shows the highly localized qubit wave function in the $k$ space.

Figure 4

Logical qubit coupling matrix element as a function of position of the local gate $R_0$ for a given vertical electric field $V_E$.