Significance of an external magnetic field on two-phonon processes in gated lateral semiconductor quantum dots

•Calculations of the electron–phonons in coupled quantum dots.•Phonons described by deformation potential and piezoelectric interactions.•Two phonon processes are studied.•The electron scattering rate due to two phonon processes depends strongly on the external field.•The results are interesting for designing and calculating the dynamic inside these devices.

Theoretical and numerical calculations of two-phonon processes on gated lateral semiconductor quantum dots (QDs) are outlined. A heterostructure made with two laterally coupled QDs, in the presence of an external magnetic field, has been employed in order to study the electron scattering rate due to two-phonon processes. The formalism is based on the acoustic phonon modes via the unscreened deformation potential and the piezoelectric interaction whenever the crystal lattice lacks a center of inversion symmetry. The rates are calculated by using second order perturbation theory. The strong dependence of the scattering rate on the external magnetic field, lattice temperature and QDs separation distance is presented.