Magnetotunneling relaxation of electrons in double quantum wells

Electron tunneling relaxation in double quantum wells subject to a transverse magnetic field is studied. The resonant peaks in the tunneling relaxation rate appear when the energy splitting Δ of the tunnel-coupled pair of the left- and right- well electron states is a multiple of the cyclotron energy ℏω_c and two series of the Landau levels coincide. The shape of such resonant oscillations of the relaxation rate is determined by the Landau levels' broadening (which is associated with the intrawell scattering in the case of small tunnel coupling), but it is not expressed through the electron density of states directly. The dependence of the tunneling relaxation rate on ℏω_c and Δ is calculated taking into account elastic scattering of the electrons by the inhomogeneities of the structure in the limit when the scattering potential is slowly changing on the magnetic length scale.