Weak localization and integrability in ballistic cavities

We construct a trajectory-based semiclassical theory of shot noise in clean chaotic cavities. In the universal regime of vanishing Ehrenfest time τE, we reproduce the random matrix theory result, and show that the Fano factor is exponentially suppressed as τE increases. We demonstrate how our theory preserves the unitarity of the scattering matrix even in the regime of finite τE. We discuss the range of validity of our semiclassical approach and point out subtleties relevant to the recent semiclassical treatment of shot noise in the universal regime by Braun et al. [cond-mat/0511292]. 74.40.+k, 05.45.Mt Introduction. Quantum transport through chaotic ballistic cavities is often well described by Random Matrix Theory (RMT) [1]. Despite its many successes, or should we say, because of these successes, one might wonder what is the origin of this RMT universality, and under what conditions do system specificities modify the RMT of transport. System specific contributions to transport originate from the underlying classical dynamics, which suggests that one employs semiclassical methods based on classical trajectories [2]. Indeed, the semiclassical program toward a microscopic foundation for the RMT of transport, including explicit bounds for its regime of applicability, is currently on its way to being completed successfully [3,4,5,6,7,8,9].Here we contribute to this program by deriving the zero-frequency shot noise power S for quantum chaotic systems. The interest in shot-noise, the intrinsically quantum part of the fluctuations of a non-equilibrium electronic current, is that it often contains information on the system that cannot be obtained through conductance measurements. For instance, shot-noise experiments have determined the charge and statistics of the charge carriers in superconducting heterostructures or in the fractional quantum hall effect [10]. In this paper, we consider an open ballistic quantum dot [11] carrying a large number of conducting channels and accordingly neglect electron-electron interactions. We reproduce the RMT result, and show how shot noise deviates from RMT predictions in the semiclassical limit. We calculate the Fano factor F = S/S p , given by the ratio of S to the Poissonian noise S p = 2e I that would be generated by a current flow of uncorrelated electrons. According to the scattering theory of transport one has. If one makes the RMT assumption that the transmission matrix t is the , 10], in term of the number of quantum channels N L and N R carried by the contacts to the left and right leads. Ref. [5] carried out the first semiclassical calculation of F for the specific case of quantum graphs. The difficulty is to calculate Tr[t † tt † t] = i,j,q |t j,i | 2 |t q,i | 2 +

show abstract

“…(7), we change integration variables using p F cos θ 03 dY 03 = dr 0⊥ dp 0⊥ [15], and then definep 0 ≡ p 0⊥ + mλr 0⊥ . In the regime of interest…”

mentioning

confidence: 99%

Shot Noise in Semiclassical Chaotic Cavities

2006

View full text Add to dashboard Cite

show abstract

“…Unless designed otherwise for a specific purpose (such as measuring the weak localization lineshape [13]) an odd-shaped, smooth potential generically exhibits soft chaos, i.e. significant contributions of both stable and unstable motion.…”

mentioning

confidence: 99%

Quantum-Dot Ground-State Energies and Spin Polarizations: Soft versus Hard Chaos

Ullmo

Nagano²,

Tomsovic³

2003

Phys. Rev. Lett.

View full text Add to dashboard Cite

We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that "mesoscopic Stoner fluctuations", that arise from the residual screened Coulomb interaction, are very sensitive to the degree of chaos. It leads to ground state energies and spin-polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.Our interest in this letter lies in microstructures fabricated using electrostatic gates or etching that pattern a two dimensional electron gas in a semiconductor heterostructure, for example, GaAs/AlGaAs. Typically, the electronic transport mean free path is significantly larger than the dimensions of the device, and the electrons essentially travel ballistically across the microstructure. Their motion is governed by the shape of a smooth, self-consistent, steep-walled, confining potential which is often conceptualized as a quantum billiard.For many physical properties, the simplifying assumption that the dots' underlying classical dynamics are fully chaotic (hard chaos) has provided a good description of the experimental data [1,2,3,4]. It has been used to justify various hypotheses from the applicability of random matrix theory (RMT) and random plane wave modeling (RPW) to statistical assumptions applied within semiclassical mechanics [5,6,7]. Indeed, chaotic systems manifest a large variety of universal behaviors. Furthermore, chaotic quantum dots are often qualitatively very similar to diffusive ones provided the Thouless energy E T H is defined ashv F /L, where v F is the Fermi velocity and L is a typical dimension of the dot (as opposed tō hD/L 2 with D the diffusion constant). Consequently, most techniques, developed much earlier to study disordered metals (diagrammatic approaches [8], nonlinear sigma model [9]) and applied to disordered quantum dots [10,11,12], are applicable to ballistic quantum dots.Nevertheless, unlike billiards, there are no known smooth potentials which are truly, fully chaotic. Unless designed otherwise for a specific purpose (such as measuring the weak localization lineshape [13]) an odd-shaped, smooth potential generically exhibits soft chaos, i.e. significant contributions of both stable and unstable motion. The general assumption of hard chaos is unfounded.As opposed to a genuine belief that the electrons' dynamics are strongly chaotic, the implicit assumption is that for many properties the distinctions between soft and hard chaos are more subtle than spectacular. This has been shown explicitly, for instance, for the fluctuation properties of Coulomb blockade (CB) peak heights [14], or for their correlations [15]. In such circumstances, using a chaotic model allows for simpler analytic derivations without drastically altering the results.Our purpose here is to demonstrate that even this weaker assumption may, in some cases, be problematic; and that for some proper...

show abstract

“…As in disordered systems, certain transport properties are found to be universal, like conductance fluctuations and weak localization properties of transport through cavities. [6][7][8][9][10][11] In contrast, if the dynamics is integrable, these features are in general not universal but depend on the specific system. Semiclassical methods have been applied to explain universal properties of chaotic transport as well as the nongeneric behavior of integrable cavities.…”

Section: Introductionmentioning

confidence: 94%

“…Semiclassical methods have been applied to explain universal properties of chaotic transport as well as the nongeneric behavior of integrable cavities. 6,7,9,12,13 Other experiments have been concerned with revealing signatures of classical periodic orbits in quantum phenomena. Examples are orbital magnetism in ballistic microstructures 14 and transport through antidot superlattices.…”

Section: Introductionmentioning

confidence: 99%

Universal quantum signature of mixed dynamics in antidot lattices

2005

View full text Add to dashboard Cite

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.

show abstract

Weak localization and integrability in ballistic cavities

Cited by 258 publications

References 18 publications

Shot Noise in Semiclassical Chaotic Cavities

Shot Noise in Semiclassical Chaotic Cavities

Quantum-Dot Ground-State Energies and Spin Polarizations: Soft versus Hard Chaos

Universal quantum signature of mixed dynamics in antidot lattices

Contact Info

Product

Resources

About