Statistical fluctuations of pumping and rectification currents in quantum dots (original) (raw)
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Signatures of chaos in the statistical distribution of conductance peaks in quantum dots
Physical Review B, 1997
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained using random matrix theory and are valid in general for any number of non-equivalent and correlated channels, assuming that the underlying classical dynamic of the electrons in the dot is chaotic or that the dot is weakly disordered. The results are expressed in terms of the channel correlation matrix which for chaotic systems is given in closed form for both point-like contacts and extended leads. We study the dependence of the distributions on the number of channels and their correlations. The theoretical distributions are in good agreement with those computed in a dynamical model of a chaotic billiard.
Parametric correlation of coulomb blockade conductance peaks in chaotic quantum dots
Physica Scripta, 1997
We investigate the autocorrelator of conductance peak heights for quantum dots in the Coulomb blockade regime. Analytical and numerical results based on Random Matrix Theory are presented and compared to exact numerical calculations based on a simple dynamical model. We consider the case of preserved time-reversal symmetry, which is realized experimentally by varying the shape of the quantum dot in the absence of magnetic fields. Upon a proper rescaling, the correlator becomes independent of the details of the system and its form is solely determined by symmetry properties and the number of channels in the leads. The magnitude of the scaling parameter is estimated by a semiclassical approach.
The statistical theory of quantum dots
Reviews of Modern Physics, 2000
A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron's dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between one-body chaos, quantum interference, and electronelectron interactions. The conductance through such dots displays mesoscopic fluctuations as a function of gate voltage, magnetic field, and shape deformation. The techniques used to describe these fluctuations include semiclassical methods, random-matrix theory, and the supersymmetric nonlinear σ model. In open dots, the approximation of noninteracting quasiparticles is justified, and electron-electron interactions contribute indirectly through their effect on the dephasing time at finite temperature. In almost-closed dots, where conductance occurs by tunneling, the charge on the dot is quantized, and electron-electron interactions play an important role. Transport is dominated by Coulomb blockade, leading to peaks in the conductance that at low temperatures provide information on the dot's ground-state properties. Several statistical signatures of electronelectron interactions have been identified, most notably in the dot's addition spectrum. The dot's spin, determined partly by exchange interactions, can also influence the fluctuation properties of the conductance. Other mesoscopic phenomena in quantum dots that are affected by the charging energy include the fluctuations of the cotunneling conductance and mesoscopic Coulomb blockade.
Exponential Sensitivity to Dephasing of Electrical Conduction Through a Quantum Dot
Physical Review Letters, 2004
According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish / = D p when the dephasing time becomes small compared to the mean dwell time D . Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression / expÿ E = when drops below the Ehrenfest time E . We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression / expÿ E = D in the absence of dephasing-which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.
Semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots
Physical Review B, 2001
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate peak height distributions and correlation functions. We demonstrate that corrections to the corresponding results of the standard statistical theory are nonuniversal, and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For nonzero temperature, the correlation function obtained theoretically is consistent with that measured experimentally.
arXiv (Cornell University), 1996
Closed expressions are derived for the resonance widths and Coulomb blockade conductance peak heights in quantum dots for the crossover regime between conserved and broken time-reversal symmetry. The results hold for leads with any number of possibly correlated and inequivalent channels. Our analytic predictions are in good agreement with simulations of both random matrices and a chaotic billiard with a magnetic flux line.
Conductance fluctuations and partially broken spin symmetries in quantum dots
2005
Conductance fluctuations in GaAs quantum dots with spin-orbit and Zeeman coupling are investigated experimentally and compared to a random matrix theory formulation that defines a number of regimes of spin symmetry depending on experimental parameters. Accounting for orbital coupling of the in-plane magnetic field, which can break time-reversal symmetry, yields excellent overall agreement between experiment and theory.
Physical Review B, 1999
We study the combined effect of finite temperature, underlying classical dynamics, and deformations on the statistical properties of Coulomb-blockade conductance peaks in quantum dots. These effects are considered in the context of the single-particle plus constant-interaction theory of the Coulomb blockade. We present numerical studies of two chaotic models, representative of different mean-field potentials: a parametric random Hamiltonian and a smooth stadium. In addition, we study conductance fluctuations for different integrable confining potentials. For temperatures smaller than the mean level spacing, our results indicate that the peakheight distribution is nearly always in good agreement with the available experimental data, irrespective of the confining potential ͑integrable or chaotic͒. We find that the peak bunching effect seen in the experiments is reproduced in the theoretical models under certain special conditions. Although the independent-particle model fails, in general, to explain quantitatively the short-range part of the peak height correlations observed experimentally, we argue that it allows for an understanding of the long-range part. ͓S0163-1829͑99͒10439-9͔