Electron-phonon induced spin relaxation in InAs quantum dots

We have calculated spin relaxation rates in parabolic quantum dots due to the phonon modulation of the spin-orbit interaction in presence of an external magnetic field. Both, deformation potential and piezoelectric electron-phonon coupling mechanisms are included within the Pavlov-Firsov spin-phonon Hamiltonian. Our results have demonstrated that, in narrow gap materials, the electron-phonon deformation potential and piezoelectric coupling give comparable contributions as spin relaxation processes. For large dots, the deformation potential interaction becomes dominant. This behavior is not observed in wide or intermediate gap semiconductors, where the piezoelectric coupling, in general, governs the spin relaxation processes. We also have demonstrated that spin relaxation rates are particularly sensitive to the Land\'e $g$-factor.