Three key questions on fractal conductance fluctuations: Dynamics, quantization, and coherence

Micolich, A. P.; Taylor, R. P.; Martin, T. P.; Newbury, R.; Fromhold, T.M.; Davies, A. G.; Linke, Heiner; Tribe, W. R.; Macks, L. D.; Smith, Charles G.; Linfield, E. H.; Ritchie, D. A.

doi:10.1103/physrevb.70.085302

Cited by 15 publications

(27 citation statements)

References 18 publications

(71 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[1]. On the other hand, recent experimental results [6] demonstrate that FCF are hardly affected by the change in the billiard geometry, and consequently by the classical electron trajectories. This experimental fact constitutes an unambiguous evidence that the classical electron dynamics is not as crucial as claimed originally [1] to understand FCF.…”

Section: Introductionmentioning

confidence: 97%

Fractal conductance fluctuations in electron billiards: a random matrix theory approach

Pinheiro

Lewenkopf

2006

Braz. J. Phys.

View full text Add to dashboard Cite

Motivated by recent experiments and theoretical works that contradict the original explanation for fractal conductance fluctuations (FCF) in electron billiards, based on the "mixed" structure of the classical phase space, we propose an alternative approach to investigate FCF using Random Matrix Theory (RMT). By means of a semiclassical estimate for value of the magnetic correlation field B C we conclude that most of the experiments on FCF were performed for magnetic fields around or greater than B C . This strongly suggests that the appropriate explanation for the observed FCF should rely on the absence of long-range correlations and not on the structure of the classical phase space. This idea is supported by a numerical study of parametric variations within the framework of RMT, which validates our surmise that the observed FCF actually reflect a diffusive scenario for electronic transport.

show abstract

Section: Introductionmentioning

confidence: 97%

Fractal conductance fluctuations in electron billiards: a random matrix theory approach

Pinheiro

Lewenkopf

2006

Braz. J. Phys.

View full text Add to dashboard Cite

show abstract

“…Most features of these experiments can be understood semiclassically as a consequence of the phase space topology [3,5,6]. However, the precise origin of the observed fractal conductance fluctuations in these experiments is not yet fully understood [4], and, in fact, various theoretical models [7,8] predict fractal conductance fluctuations for mesoscopic devices. Our aim is to design a concrete experimental scenario in which parametric fractal fluctuations could be measured with high precision cold-atom setups.…”

Section: Introductionmentioning

confidence: 99%

Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?

Tomadin¹,

Mannella²,

Wimberger³

2006

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Abstract. We investigate the parametric fluctuations in the quantum survival probability of an open version of the δ-kicked rotor model in the deep quantum regime. Spectral arguments [Guarneri I and Terraneo M 2001 Phys. Rev. E 65 015203(R)] predict the existence of parametric fractal fluctuations owing to the strong dynamical localisation of the eigenstates of the kicked rotor. We discuss the possibility of observing such dynamically-induced fractality in the quantum survival probability as a function of the kicking period for the atom-optics realisation of the kicked rotor. The influence of the atoms' initial momentum distribution is studied as well as the dependence of the expected fractal dimension on finite-size effects of the experiment, such as finite detection windows and short measurement times. Our results show that clear signatures of fractality could be observed in experiments with cold atoms subjected to periodically flashed optical lattices, which offer an excellent control on interaction times and the initial atomic ensemble.

show abstract

“…These self-similar (or self-affine) structures were also found in many branches of chemistry and physics; prominent examples are crystal growth and fractal surfaces, and transport in gold nanowires and electron "billiards" [3,[8][9][10][11][12][13][14][15]. In contrast with idealized mathematical fractals continuing to infinitely small scales, fractal scaling in nature has a lower and an upper limit.…”

Section: Introductionmentioning

confidence: 94%

Fractal dynamics in chaotic quantum transport

et al. 2013

View full text Add to dashboard Cite

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

show abstract

Three key questions on fractal conductance fluctuations: Dynamics, quantization, and coherence

Cited by 15 publications

References 18 publications

Fractal conductance fluctuations in electron billiards: a random matrix theory approach

Fractal conductance fluctuations in electron billiards: a random matrix theory approach

Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?

Fractal dynamics in chaotic quantum transport

Contact Info

Product

Resources

About