Electron Spin Relaxation in a Transition-Metal Dichalcogenide Quantum Dot

We study the relaxation of a single electron spin in a circular quantum dot in a transition-metal dichalcogenide monolayer defined by electrostatic gating. Transition-metal dichalcogenides provide an interesting and promising arena for quantum dot nano-structures due to the combination of a band gap, spin-valley physics and strong spin-orbit coupling. First we will discuss which bound state solutions in different B-field regimes can be used as the basis for qubits states. We find that at low B-fields combined spin-valley Kramers qubits to be suitable, while at large magnetic fields pure spin or valley qubits can be envisioned. Then we present a discussion of the relaxation of a single electron spin mediated by electron-phonon interaction via various different relaxation channels. In the low B-field regime we consider the spin-valley Kramers qubits and include impurity mediated valley mixing which will arise in disordered quantum dots. Rashba spin-orbit admixture mechanisms allows for relaxation by in-plane phonons either via the deformation potential or by piezoelectric coupling, additionally direct spin-phonon mechanisms involving out-of-plane phonons give rise to relaxation. We find that the relaxation rates scale as $\propto B^6$ for both in-plane phonons coupling via deformation potential and the piezoelectric effect, while relaxation due to the direct spin-phonon coupling scales independant to B-field to lowest order but scales strongly on device mechanical tension. We will also discuss the relaxation mechanisms for pure spin or valley qubits formed in the large B-field regime.