Non-universal features in the quasi-particle excitation spectra of Andreev billiards and wires

Ihra, W.; Richter, Klaus

doi:10.1016/s1386-9477(00)00229-0

Cited by 8 publications

(12 citation statements)

References 12 publications

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“…when expanded in powers of r, agrees for a range of values of n with the expansion of (33) derived from the correlation functions obtained from (31 …”

Section: B Density Of Statessupporting

confidence: 77%

“…Removing the magnetic field by setting b = 0 reduces both of these equations (after factorizing) to the previous results (29) and (31 …”

Section: Magnetic Fieldmentioning

confidence: 59%

“…27 The width of this hard gap, also called the minigap, 13 has been calculated as a purely quantum effect by using random matrix theory (RMT) and its value scales with the Thouless energy, E T =h/2τ d , where τ d is the average (classical) dwell time a particle stays in the billiard between successive Andreev reflections. 27 Since the existence of this gap is expected to be related to the chaotic nature of the electronic motion, many attempts have been undertaken to explain this result in semiclassical terms, [28][29][30][31][32][33][34] however this appeared to be rather complicated. Indeed, a traditional semiclassical treatment based on the so-called Bohr-Sommerfeld (BS) approximation yields only an exponential suppression of the DOS.…”

Section: Introductionmentioning

confidence: 99%

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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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“…when expanded in powers of r, agrees for a range of values of n with the expansion of (33) derived from the correlation functions obtained from (31 …”

Section: B Density Of Statessupporting

confidence: 77%

“…Removing the magnetic field by setting b = 0 reduces both of these equations (after factorizing) to the previous results (29) and (31 …”

Section: Magnetic Fieldmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

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Density of states of chaotic Andreev billiards

et al. 2011

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“…36 The effect of these trajectories on the density of states of an Andreev billiard was studied in ref. [37] within semiclassical theory, when the contribution of long trajectories is especially important. We assume that the deviation from the exponential distribution occurs at lengths l longer than either the Ehrenfest time or the mean free time, and we neglected the contribution of anomalously long trajectories to the electron density of states.…”

Section: Discussionmentioning

confidence: 99%

Quantum disorder and quantum chaos in Andreev billiards

Vavilov

Larkin

2003

Phys. Rev. B

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We investigate the crossover from the semiclassical to the quantum description of electron energy states in a chaotic metal grain connected to a superconductor. We consider the influence of scattering off point impurities (quantum disorder) and of quantum diffraction (quantum chaos) on the electron density of states. We show that both the quantum disorder and the quantum chaos open a gap near the Fermi energy. The size of the gap is determined by the mean free time in disordered systems and by the Ehrenfest time in clean chaotic systems. Particularly, if both times become infinitely large, the density of states is gapless, and if either of these times becomes shorter than the electron escape time, the density of states is described by random matrix theory. Using the Usadel equation, we also study the density of states in a grain connected to a superconductor by a diffusive contact.

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“…These billiards are formed when a classically chaotic normal dot is placed in contact with a superconductor [1][2][3][4][5][6][7][8]. Consider a ballistic two-dimensional normal dot of area A, with the mean level spacing of the isolated normal system 2 h 2 mA at the Fermi energy E F .…”

mentioning

confidence: 99%

Proximity-Induced Subgaps in Andreev Billiards

et al. 2002

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We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cutoff in the path length distribution P(s) will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculation for different Andreev billiards gives good agreement with the semiclassical predictions when the energy dependent phase shift for Andreev reflections is properly taken into account. Based on this new semiclassical Bohr-Sommerfeld approximation of the density of states, we derive a simple formula for the energy gap. We show that the energy gap, in units of Thouless energy, may exceed the value predicted earlier from random matrix theory for chaotic billiards.

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Non-universal features in the quasi-particle excitation spectra of Andreev billiards and wires

Cited by 8 publications

References 12 publications

Density of states of chaotic Andreev billiards

Density of states of chaotic Andreev billiards

Quantum disorder and quantum chaos in Andreev billiards

Proximity-Induced Subgaps in Andreev Billiards

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