Ballistic Transport in Mesoscopic Systems

Abstract

Recent studies of the ballistic transport in the mesoscopic systems performed in our laboratory are reviewed in the present paper. In the first half of the present paper, we investigate the characteristics of ballistic transport in quantum wires of which the effective confined length (the effective width) varies along the direction parallel to the current. It is shown that the step-wise variation of the conductance as a function of the Fermi energy, corresponding to the ideal quantization of the conductance, is smeared when the effective confined length of the wire varies along the direction parallel to the current and when the temperature increases. In the second half of the present paper, we show the numerical results of wave functions of the stationary states for the geometry of the semi-infinite two­ dimensional region with a narrow channel as an injector in the external magnetic field. In the presence of the magnetic field, we obtain a periodic peak structure in the modulus squared of the wave function along the boundary in the semi-infinite two-dimensional region, the period of which is nearly equal to the classical cyclotron diameter. Moreover, it is shown that small peaks exist between the periodic main peaks, which is considered to be one of the characteristic aspects of the quantum interference effects. The quantization of the conductance is one of the most remarkable findings in the ballistic transport phenomena, which has recently been discovered in the two­ dimensional electron system of GaAs-AlGaAs heterostructures_l),z) An explanation of the observed quantization of the conductance has been given on the basis of the assumption of the quantization of the motion along the direction perpendicular to the current. For simplicity, let us consider a quasi-one-dimensional straight wire. Although the electronic states along the wire are described in terms of plane wave functions, in the direction perpendicular to the current the electronic states are described by localized orbitals, and the energy of the electronic states in this direction is quantized. That is, the electronic states have subband structures. If the number of subbands intersecting the Fermi level is Nc (the number of open channels), the conductance of the system can be given by G=(2e 2 /h)Nc on the basis of the Landauer