## Fabry Perot interferometer with Quantum Point Contact

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## Supervisor(s):

.Quantum point contact (QPC) is a one dimensional constriction in a two dimensional electron gas. Conductance of a QPC has been known to be quantized in units of G0 = 2e^2/h since 1988 [1,2]. The observed conductance plateaus can be easily understood in the single-electron picture and the saddle point potential model of the

QPC [3,4]. Since the original experimental discovery of the quantised conductance, a consistent anomaly at approximately G = 0.7G0 has been noted, commonly referred to in literature as '0.7 anomaly'. It was first explored in Refs.[5,6], where the authors concluded that the anomaly is due to many body correlation between

electrons. For a recent review of experiments related to the 0.7 anomaly see Ref.[7]. We believe that the 0.7 anomaly is due to the enhanced inelastic electron-electron scattering on the top of the potential barrier [8,9]. There are also alternative theoretical models of the 0.7 anomaly based on various assumptions, see e.g.

Refs. [10-14]. Zero Bias Anomaly (ZBA) observed in QPCs is closely related to the 0.7 anomaly, see e.g. Ref. [7].

While conductance of a QPC has been studied in thousands of experimental and theoretical works since 1988, the scattering and transmission phases remained an open problem till recently. The problem has been addressed only in recent works [15-17]. For the first time the transmission phase has been measured in Ref. [15]. Authors of Ref. [15] argued that they observed correlations effects. However, it has been shown in the theoretical work [16] (3d year project of Bryce Lackenby) that the experimental results [15] are consistent with simple mean field picture of QPC. A very recent measurement of the reflection phase [17] is based on the Fabry Perot electron interferometry. The Ref. [17] again claims observation of some correlation effects in the reflection phase. However, some preliminary results obtained in Master Thesis of Greg Vionnet [18] indicate that analysis of Fabry Perot interferometry is not quite straightforward and might be the interpretation developed in Ref. [17] is not correct.

The goal of the present project is to develop the theory of the Fabry Perot electron interferometry experiments with QPCs. On technical side the project will require both analytical and numerical calculations.

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