TRANSMISSION OF A 2-DIMENSIONAL QUANTUM POINT-CONTACT WITH THE SIZE VARIED FROM A SINGLE-ATOM TO A CONTINUOUS WIRE - SIZE EFFECTS

The transmission through a two-dimensional (2D) channel, which connect s semi-infinite 2D electron gas reservoirs and can be used as a model of both the few-atom-size (microscopic) and mesoscopic contact, is inv estigated under the assumption of the zero-field ballistic motion of e lectrons in the system. An analytical theory is advanced to a nearly e xact analytical expression for the transmission probability verified b y numerical calculations for a vast variety of channel parameters. On these bases a detailed analytical and numerical analysis of size effec ts in the quantum point contact (QPC) transmission is performed with e mphases put on basic distinctions between atomic-size and mesoscopic-s ize QPC. The QPC properties are visualized in calculations of transmis sion against Fermi energy dependences for some representative channel parameters. The results obtained are directly applicable to the descri ption of coherent excitation energy transfer in relevant molecular 2D geometries. The suggested formalism can be also used for an analytical analysis of some other problems of current dispute, in particular, of non-linear field effects and 3D QPC properties.