Acceleration theorem for low-dimensional electron systems with off-diagonal effective-mass components

The motion of electrons under homogeneously applied electric fields in low-dimensional systems with non-zero off-diagonal effective mass (ODEM) is studied. The equation describing the time evolution of a probability coefficient of finding an electron in a subband is derived using the Krieger–Iafrate theory in the effective-mass approximation. It is shown that an electron can change subbands during free flight due to the ODEM-induced inter-subband transitions. By introducing an effective dispersion defined as a weighted average of the subband dispersions, it is also shown that the initial acceleration of an electron effectively follows the bulk dispersion relation. The results obtained suggest that the transport properties of the quantized systems when many subbands are occupied in the weak confinement limit approach the values one would find without considering the quantization.