Reexamination of spin decoherence in semiconductor quantum dots from the equation-of-motion approach

The longitudinal and transversal spin decoherence times, T-1 and T-2, in semiconductor quantum dots are investigated from the equation-of-motion approach for different magnetic fields, quantum dot sizes, and temperatures. Various mechanisms, such as the hyperfine interaction with the surrounding nuclei, the Dresselhaus spin-orbit coupling together with the electron-bulk-phonon interaction, the g-factor fluctuations, the direct spin-phonon coupling due to the phonon-induced strain, and the coaction of the electron-bulk- and/or surface-phonon interaction together with the hyperfine interaction are included. The relative contributions from these spin decoherence mechanisms are compared in detail. In our calculation, the spin-orbit coupling is included in each mechanism and is shown to have marked effect in most cases. The equation-of-motion approach is applied in studying both the spin relaxation time T-1 and the spin dephasing time T-2, either in Markovian or in non-Markovian limit. When many levels are involved at finite temperature, we demonstrate how to obtain the spin relaxation time from the Fermi golden rule in the limit of weak spin-orbit coupling. However, at high temperature and/or for large spin-orbit coupling, one has to use the equation-of-motion approach when many levels are involved. Moreover, spin dephasing can be much more efficient than spin relaxation at high temperature, though the two only differ by a factor of 2 at low temperature.