Linear response conductance of a two terminal Aharonov-Bohm (AB) interferometer is an even function of magnetic field, as dictated by Onsager-Büttiker relations [1,2]. We discuss an experimental setup in which this phase symmetry can be broken in a controlled way. To this end we consider a "Which Path?" detector [3], which consists of an interferometer with quantum dots (QDs) in each of its arms, one of the QDs being capacitively coupled to a nearby quantum point contact (QPC). This coupling is known to result in breaking of the phase symmetry of the AB oscillations, given that a finite voltage bias is applied to the QPC [4]. We show that this effect becomes more pronounced when the bias on the QPC matches the energy difference between the QD, coupled to the QPC, and the Fermi level of the interferometer leads. This effect  is due to a resonat prosess, similar to the one that we recently studied in connection to non-linear transport. Sweeping in the same time the level in the other QD through the Fermi level allows one to observe smooth change of the phase from 0 to π, rather than the abrupt jump observed in an isolated AB interferometer [2]. We explore the possibility of using this setup in order to measure the transmission phase through a QD.

References

[1] M. Büttiker, “Four-terminal phase coherent conductance,” Phys. Rev. Lett., 57, 1761 (1986).
[2] A. Yacoby et al., “Coherence and phase sensitive measurements in a quantum dot,” Phys. Rev. Lett., 74, 4047 (1995).
[3] E. Buks et al., “Dephasing in electron interference by a ‘which path’ detector,” Nature, 391, 871 (1998).
[4] D. Sánchez and K. Kang, “Validity and breakdown of Onsager symmetry in mesoscopic conductors interacting with environments,” Phys. Rev. Lett., 100, 036806 (2008).
[5] V. Puller et al., “Breaking of phase symmetry in non-equilibrium Aharonov-Bohm oscillations through a quantum dot,” Phys. Rev. B 80, 035416 (2009).