  Electron spin decoherence caused by elastic spin-phonon processes is
investigated comprehensively in a zero-dimensional environment. Specifically, a
theoretical treatment is developed for the processes associated with the
fluctuations in the phonon potential as well as in the electron procession
frequency through the spin-orbit and hyperfine interactions in the
semiconductor quantum dots. The analysis identifies the conditions (magnetic
field, temperature, etc.) in which the elastic spin-phonon processes can
dominate over the inelastic counterparts with the electron spin-flip
transitions. Particularly, the calculation results illustrate the potential
significance of an elastic decoherence mechanism originating from the
intervalley transitions in semiconductor quantum dots with multiple equivalent
energy minima (e.g., the X valleys in SiGe). The role of lattice anharmonicity
and phonon decay in spin relaxation is also examined along with that of the
local effective field fluctuations caused by the stochastic electronic
transitions between the orbital states. Numerical estimations are provided for
typical GaAs and Si-based quantum dots.
