Quantum ballistic transport in semiconductor nanostructures; effect of smooth features in confining potentials

Analysis of electron transport in a two-dimensional structure using quantal trajectories

“…For our structure, the staircase dependence of the conductance on the energy for a narrow channel [4,5] is replaced by a complex pattern of peaks and dips in the case of a cross-bar structure (a detailed discussion of this can be found in [17]; see also the inset in figure 7, later). Peaks are caused by resonant tunnelling via quasi-bound states in the centre of the cross.…”

“…Here we only give an outline of how to solve the Schrödinger equation. A more detailed description is given in [17].…”

“…we have used the convention (−1) 1/2 = −i. Using a transfer matrix method (see [17] and references therein) we find the expansion coefficients B, C, A L and A R , and hence the wavefunction in all regions. We consider the temperature T = 0 K and an infinitesimally small potential difference U between the source and the drain, the so-called linear response regime.…”

Nonlinear Quantum Motions in 2D Nano-channels Part II: Quantization and Wave Motion

“…Conventional studies on conductance quantization in straight channels [3,4], crossbar channels with sharp corner [5,6] and crossbar channels with round corner [7] were mainly based on the analysis of probability and current density functions, which are able to describe the average behavior of an ensemble of electrons. As to the motion of a single electron, Bohmian mechanics [8] has been exploited to compute electron's trajectories in the channel according to the Bohm's guidance condition [9] proposed in 1952.…”