Mesoscopic scattering in the half-plane: squeezing conductance through a small hole

摘要

We model the 2-probe conductance of a quantum point contact (QPC), in linearresponse. If the QPC is highly non-adiabatic or near to scatterers in the openreservoir regions, then the usual distinction between leads and reservoirsbreaks down and a technique based on scattering theory in the fulltwo-dimensional half-plane is more appropriate. Therefore we relate conductanceto the transmission cross section for incident plane waves. This is equivalentto the usual Landauer formula using a radial partial-wave basis. We derive theresult that an arbitrarily small (tunneling) QPC can reach a p-wave channelconductance of 2e^2/h when coupled to a suitable reflector. If two or moreresonances coincide the total conductance can even exceed this. This relates torecent mesoscopic experiments in open geometries. We also discuss reciprocityof conductance, and the possibility of its breakdown in a proposed QPC for atomwaves.