Phase measurements in Aharonov-Bohm interferometers

Amnon Aharony*, Ora Entin-Wohlman, Yoseph Imry

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper we address measurements of the resonant quantum transmission amplitude tQD = -i\tQD\eiαQD 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, αQD, 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 Φ = ℏcφ/e threading the ABI ring. Therefore, if one fits G to A + B cos(φ + β) then β only "jumps" between 0 and π, with no relation to αQD. Additional terminals open the ABI, break the Onsager relations and yield a non-trivial variation of β 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 ∝ sin2QD) allows a direct measurement of αQD. (ii) In many cases, the measured G in the closed ABI can be used to extract both |tQD| and αQD. (iii) For open ABI's, β depends on the details of the opening. We present quantitative criteria (which can be tested experimentally) for β to be equal to the desired αQD: the "lossy" channels near the QD should have both a small transmission and a small reflection.

Original languageEnglish
Pages (from-to)299-312
Number of pages14
JournalTurkish Journal of Physics
Issue number5
StatePublished - 2003


  • Aharonov-Bohm interferometer
  • Interference in nanostructures
  • Quantum dots
  • Resonant transmission


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