Phase Measurements in Aharonov-Bohm Interferometers
Authors : Amnon Aharony, Ora Entin-wohlman, Yoseph Imry
Pages : 299-312
Doi:10.3906/sag-1202-104
View : 13 | Download : 8
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper we address measurements of the resonant quantum transmission amplitude tQD = -i|tQD|eiaQD through a quantum dot (QD), as function of the plunger gate voltage V. Mesoscopic solid state Aharonov-Bohm interferometers (ABI) have been used to measure the ``intrinsic" phase, aQD, when the QD is placed on one of the paths. In a ``closed" interferometer, connected to two terminals, the electron current is conserved, and Onsager's relations require that the conductance G through the ABI is an even function of the magnetic flux F = \hbar cf/e threading the ABI ring. Therefore, if one fits G to A+B \cos(f+b) then b only ``jumps" between 0 and p, with no relation to aQD. Additional terminals open the ABI, break the Onsager relations and yield a non-trivial variation of b with V. After reviewing these topics, we use theoretical models to derive three results on this problem: (i) For the one-dimensional leads, the relation |tQD|2 \propto \sin2(aQD) allows a direct measurement of aQD. (ii) In many cases, the measured G in the closed ABI can be used to extract both |tQD| and aQD. (iii) For open ABI's, b depends on the details of the opening. We present quantitative criteria (which can be tested experimentally) for b to be equal to the desired aQD: the ``lossy" channels near the QD should have both a small transmission and a small reflection.Keywords : interference in nanostructures, Aharonov-Bohm interferometer, quantum dots, resonant transmission