Transport through quantum systems in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-matrix formalism

Abstract

The $R$-matrix method can be used to reduce computing times for the calculation of transmission probabilities in mesoscopic semiconductor systems. We generalize results by Smr\ifmmode \check{c}\else \v{c}\fi{}ka [Superlatt. Microstruct. 8, 221 (1990)] for strictly one-dimensional transport to systems which show confinement in more dimensions like a point contact. The formalism is applied to a tunneling barrier with a Kronig-Penney-type potential modulation in the lateral direction. In the limit of very high barriers we find resonances which are created by the mismatch of the wave functions inside and outside the barrier. It is shown that this type of resonance has a qualitatively different behavior than resonant tunneling peaks.