<title>Controlled interference effects of spatial reproduction and multiplication for electron waves in semiconductor 2D nanostructures</title>

Abstract

Effects of spatial nonhomogeneity for the probability current density j_x (x,z) (or a quantum-mechanical current density ej_x (x,z), e is the electron charge) in the semiconductor 2D nanostructures in the form of joints in the direction of propagation of the electron wave (the x-axis) of narrow and wide (on the z-axis) rectangular quantum wells (QWs) (z-axis is the axis of the quantization) and the possibility to control these effects have been theoretically studied. In the first part of our article we show that the nonhomogeneous distribution of the j_x (x,z) arises because ofthe interference of electron waves spreading in the wide QW simultaneously in different electron subbands. Special attention is given to effects of spatial reproduction and multiplication for electron waves in such nanostructures. It is shown that transverse distribution j_x (0,z) existing at the entry of the wide QW is reproduced with some accuracy at a definite distance X₁ from the joint and splits in symmetric (along the z-axis) 2D nanostructures into p identical profiles of the intensity lower by p times at the distance X₁/p. This picture is reproduced periodically in cross-sections X_q = qX₁ (q and p are integers). The results of numerical calculations of these effects in symmetric nanostructures are given. The possibility to control these effects by the transverse (along z -axis) constant electric field strength F being created by gates in the wide QW in symmetric 2D nanostructures with rectangular QWs was studied theoretically.