Hyperfine Interaction in a MoS$_2$ Quantum Dot: Decoherence of a Spin-Valley Qubit

A successful and promising device for the physical implementation of electron spin-valley based qubits is the Transition Metal Dichalcogenide monolayer (TMD-ML) semiconductor quantum dot. The electron spin in TMD-ML semiconductor quantum dots can be isolated and controlled with high accuracy, but it still suffers from decoherence due to the unavoidable coupling with the surrounding environment, such as nuclear spin environments. A common tool to investigate systems like the one considered in this work is the density matrix formalism by presenting an exact master equation for a central spin (spin-qubit) system in a time-dependent and coupled to a nuclear spin bath in terms of hyperfine interaction. The master equation provides a unified description of the dynamics of the central spin. Analyzing this in more detail, we calculate fidelity loss due to the Overhauser field from hyperfine interaction in a wide range number of nuclear spins $\mathcal{N}$.