Semiclassical approach to chaotic quantum transport

Müller, Sebastian; Heusler, Stefan; Braun, P. A.; Haake, Fritz

doi:10.1088/1367-2630/9/1/012

Cited by 89 publications

(195 citation statements)

References 63 publications

(147 reference statements)

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“…2) and the trajectory stretches involve many bounces at the normal boundary of the cavity. We draw such topological sketches as the semiclassical methods were first developed for transport, 47,55,57 where typically we have S † (complex conjugate transpose) instead of S * (complex conjugate) in (16), restricted to the transmission subblocks, so that all the trajectories would travel to the right in our sketches. Without the magnetic field, the billiard has time-reversal symmetry and S is symmetric, but this difference plays a role when we turn the magnetic field on later.…”

Section: Semiclassical Diagramsmentioning

confidence: 99%

Density of states of chaotic Andreev billiards

et al. 2011

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Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice versa). Using a semiclassical framework for systems with chaotic dynamics, we show how this reflection, along with the interference due to subtle correlations between the classical paths of electrons and holes inside the system, is ultimately responsible for the gap formation. The treatment can be extended to include the effects of a symmetry-breaking magnetic field in the normal part of the billiard or an Andreev billiard connected to two phase-shifted superconductors. Therefore, we are able to see how these effects can remold and eventually suppress the gap. Furthermore, the semiclassical framework is able to cover the effect of a finite Ehrenfest time, which also causes the gap to shrink. However, for intermediate values this leads to the appearance of a second hard gap-a clear signature of the Ehrenfest time.

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Section: Semiclassical Diagramsmentioning

confidence: 99%

Density of states of chaotic Andreev billiards

et al. 2011

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“…A path pair or an l-encounter hitting the superconductor S i , i.e. l path pairs hitting S i at the same channel, contributes a factor N Si [6]. The density of states is related to the correlation functions C(ǫ, n, φ) = (N S ) −1 Tr e −iφ S * − ǫ 2τ D e iφ S ǫ 2τ D n of n scattering matrices.…”

Section: Andreev Reflection and Andreev Billiardsmentioning

confidence: 99%

Semiclassics of Andreev billiards

Engl

Kuipers

Berkolaiko

et al. 2010

Mesoscopic Physics in Complex Media

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“…10,27,28 However, it has been demonstrated by Aigner et al 29 and by some of us, 17 by means of numerical simulations, that a Fano factor of 1/4, corresponding to the RMT result for a symmetric cavity, is achieved also in a cavity with a perfectly regular shape, such as a rectangle, with a completely flat potential inside, as long as the conditions on symmetry and on the width of the constrictions (which must be narrow enough to guarantee the presence of sufficiently strong diffraction and a long enough dwell time for the electrons) are satisfied. In a rectangular cavity diffraction originates from the apertures and from the corners.…”

Section: Introductionmentioning

confidence: 99%

Effect of potential fluctuations on shot noise suppression in mesoscopic cavities

et al. 2013

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We perform a numerical investigation of the effect of the disorder associated with randomly located impurities on shot noise in mesoscopic cavities. We show that such a disorder becomes dominant in determining the noise behavior when the amplitude of the potential fluctuations is comparable to the value of the Fermi energy and for a large enough density of impurities. In contrast to existing conjectures, random potential fluctuations are shown not to contribute to achieving the chaotic regime whose signature is a Fano factor of 1/4, but, rather, to the diffusive behavior typical of disordered conductors. In particular, the 1/4 suppression factor expected for a symmetric cavity can be achieved only in high-quality material, with a very low density of impurities. As the disorder strength is increased, a relatively rapid transition of the suppression factor from 1/4 to values typical of diffusive or quasi-diffusive transport is observed. Finally, on the basis of a comparison between a hard-wall and a realistic model of the cavity, we conclude that the specific details of the confinement potential have a minor influence on noise. C

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Semiclassical approach to chaotic quantum transport

Cited by 89 publications

References 63 publications

Density of states of chaotic Andreev billiards

Density of states of chaotic Andreev billiards

Semiclassics of Andreev billiards

Effect of potential fluctuations on shot noise suppression in mesoscopic cavities

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