Magnetic-field dependence of transport in normal and Andreev billiards: A classical interpretation of the averaged quantum behavior

Fytas, Nikolaos G.; Diakonos, F. K.; Schmelcher, Peter; Scheid, Matthias; Lassl, Andreas; Richter, Klaus; Fagas, Giorgos

doi:10.1103/physrevb.72.085336

Cited by 11 publications

(15 citation statements)

References 23 publications

(34 reference statements)

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“…29 The phase difference may even cause a change of the sign of the conductance correction. Furthermore, the magnetic field dependence also inherits a nonmonotonic behavior from the N-S junction 28,31 and again the sign of the conductance correction may be changed by increasing the magnetic field. This has already been found by Whitney and Jacquod 10 in their consideration of the contribution up to second order in N S /N N .…”

Section: Discussionmentioning

confidence: 99%

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Conductance and thermopower of ballistic Andreev cavities

2011

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When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory-based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the quantum correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting and normal conducting leads. In the case of two superconductors with the same chemical potential, we additionally study how the conductance and the sign of quantum corrections are affected by their phase difference. As far as random matrix theory results exist these are reproduced by our calculations. Furthermore, in the case that the chemical potential of the superconductors is the same as that of one of the two normal leads the conductance shows, under certain conditions, similar effects as a normal metal-superconductor junction. The semiclassical framework is also able to treat the thermopower of chaotic Andreev billiards consisting of one chaotic dot, two normal leads, and two superconducting islands and shows it to be antisymmetric in the phase difference of the superconductors.

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Section: Discussionmentioning

confidence: 99%

“…In fact, we did not find values for x where we get a regime not mentioned above such that for large x we again get the same behavior as has been found for the case of one normal conducting lead. 31 Since the diagrammatic rules depend on b …”

Section: Two Superconductors With a Phase Differencementioning

confidence: 99%

Conductance and thermopower of ballistic Andreev cavities

2011

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“…2,3,4,5,6,7,8,9,10,11,12,13,14,15 Also, the effects of Andreev scattering on the conductance through quantum dots whose classical dynamics is integrable or mixed (regular and chaotic) have been investigated. 16,17 On the other hand, random matrix theory (RMT) has been useful to study the statistical properties of many different phenomena in normal metals 18,19,20,21,22 as well as in superconductors. In particular, the effects of NS interfaces on the conductance of disordered and chaotic billiards-quantum dots-have received consider-able attention.…”

Section: Introductionmentioning

confidence: 99%

Effects of Andreev reflection on the conductance of quantum chaotic dots

2009

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We investigate the conductance statistics of a quantum-chaotic dot-a normal-metal grain-with a superconducting lead attached to it. The cases of one and two normal leads additionally attached to the dot are studied. For these two configurations the complete distribution of the conductance is calculated, within the framework of random matrix theory, as a function of the transparency parameter of the Schottky barrier formed at the interface of the normal-metal and superconducting regions. Our predictions are verified by numerical simulations.

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“…This setup has been chosen for simulations in Ref. [14]. The numerical challenge imposed hereby is the exact reproduction of the antidot's circular shape in the continuum limit.…”

Section: Antidot Inside the Scatterermentioning

confidence: 99%

Parallel implementation of the recursive Green’s function method

Drouvelis

Schmelcher

Bastian

2006

Journal of Computational Physics

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A parallel algorithm for the implementation of the recursive Green's function technique, which is extensively applied in the coherent scattering formalism, is developed. The algorithm performs a domain decomposition of the scattering region among the processors participating in the computation and calculates the Schur's complement block in the form of distributed blocks among the processors. If the method is applied recursively, thereby eliminating the processors cyclically, it is possible to arrive at a Schur's complement block of small size and compute the desired block of the Green's function matrix directly. The numerical complexity due to the longitudinal dimension of the scatterer scales linearly with the number of processors, though, the computational cost due to the processors' cyclic reduction, establishes a bottleneck to achieve efficiency 100%. The proposed algorithm is accompanied by a performance analysis for two numerical benchmarks, in which the dominant sources of computational load and parallel overhead as well as their competitive role in the efficiency of the algorithm will be demonstrated.

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Magnetic-field dependence of transport in normal and Andreev billiards: A classical interpretation of the averaged quantum behavior

Cited by 11 publications

References 23 publications

Conductance and thermopower of ballistic Andreev cavities

Conductance and thermopower of ballistic Andreev cavities

Effects of Andreev reflection on the conductance of quantum chaotic dots

Parallel implementation of the recursive Green’s function method

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