Effects of surface roughness on quasi-one-dimensional and -two-dimensional ballistic channels

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Abstract
Effects of rough boundaries on electron transport in tight-binding, quasi-one-dimensional (Q1D) and quasi-2D (Q2D) channels are studied. The Q1D channels have uncorrelated edge roughness over a distance that is long compared with the width, and are connected to semi-infinite, perfect leads. The Q2D channels have uncorrelated washboardlike edge roughness with translation symmetry perpendicular to the current flow. The standard Green-function method is applied with high resolution to the Q1D sample while the leads are treated exactly by a Green-function extension theory [Phys. Rev. B 37, 9524 (1988)]. The extension theory also gives the density of states and Kubo-Greenwood conductance of the Q2D case exactly in terms of Q1D results. Analytical results are presented for the conductance of ordered cases. In the Q1D case, it is found that edge roughness can create gaps in the spectrum and induce strongly localized states, similar to states found in quantum percolation. No such gaps or isolated states appear in the Q2D case. However, localized states with energies in the band continuum, but decoupled from the current-carrying states, cause a reduction in conductance for Fermi energy in a certain range. For comparison several Q1D models with periodic edge roughness are also studied.