Spin relaxation in a single-electron bilayer graphene quantum dot

We study the spin relaxation in a single-electron bilayer graphene quantum dot due to the spin-orbit coupling. The spin relaxation is assisted by the emission of acoustic phonons via the bond-length change and deformation potential mechanisms and $1/f$ charge noise. In the perpendicular magnetic-field dependence of the spin relaxation rate $T_1^{-1}$, we predict a monotonic increase of $T_1^{-1}$ at higher fields where the electron-phonon coupling via the deformation potential plays a dominant role in spin relaxation. We show a less pronounced dip in $T_1^{-1}$ at lower magnetic fields due to the competition between the electron-phonon coupling due to bond-length change and $1/f$ charge noise. Finally, detailed comparisons of the magnetic-field dependence of the spin relaxation with the existing experiments by Banszerus et al. [Nat. Commun. 13, 3637 (2022)] and G\"achter et al. [PRX Quantum 3, 020343 (2022)] are reported.