Heavy-hole spin relaxation in quantum dots: Isotropic versus anisotropic effects

Non-charge-based logic in single-hole spin of semiconductor quantum dots (QDs) can be controlled by anisotropic gate potentials providing a notion for making next-generation solid-state quantum devices. In this study, we investigate the isotropic and anisotropic behavior of phonon-mediated spin relaxation of heavy-hole spin hot spots in QDs. For the electron spin in isotropic QDs, hot spots are known to be always present due to the Rashba spin-orbit coupling. But for heavy holes in isotropic dots, we show that the occurrences of spin hot spots are sensitive to the bulk $g$ factor. The hot spot for Rashba coupling in InAs and GaSb dots arises because these materials possess negative bulk $g$ factor, while that for the Dresselhaus coupling in GaAs and InSb dots is found due to their positive bulk $g$ factor. For anisotropic QDs, on the other hand, the spin hot spot is universally present due to their broken in-plane rotational symmetry. Further, the increasing electric field, that strengthens the Rashba coupling, is shown to cover a wide range of magnetic field by the hot spots. Results demonstrate that the magnetic field, choice of dot materials, and size anisotropy can act as effective control parameters, which can be experimentally used to design the device for detecting the phonon-mediated heavy-hole spin-relaxation behavior of III-V semiconductor QDs.