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arXiv:0912.0382 · Journal of Physics A Mathematical and Theoretical

Ballistic electron quantum transport in the presence of a disordered background

Valentin V Sokolov

Published Jun 4, 2010• 6 citations
arXivHTMLPDF

Abstract

The effect of a complicated many-body environment is analyzed on the electron random scattering by a 2D mesoscopic open ballistic structure. A new mechanism of decoherence is proposed. The temperature of the environment is supposed to be zero, whereas the energy of the incoming particle E in can be close to or somewhat above the Fermi surface in the environment. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of escape through such channels but also due to the ulterior population of the long-lived environmental states. Transmission of an electron with a given incoming E in through the structure turns out to be an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted into the structure by the environment. Though the number of particles is conserved in each individual event of transmission, there exists a probability that some part of the electron's energy can be absorbed due to environmental many-body effects. In such a case the electron can disappear from the resonance energy interval and elude observation at the fixed transmission energy E in thus resulting in the seeming loss of particles, violation of the time-reversal symmetry and, as a consequence, suppression of the weak localization. Both decoherence and absorption phenomena are treated within the framework of a unit microscopic model based on the general theory of the resonance scattering. All the effects discussed are controlled by the only parameter: the spreading width of the doorway resonances that uniquely determines the decoherence rate.

DOI
10.1088/1751-8113/43/26/265102

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The effect of a complicated many-body environment is analyzed on the electron random scattering by a 2D mesoscopic open ballistic structure. A new mechanism of decoherence is proposed. The temperature of the environment is supposed to be zero, whereas the energy of the incoming particle E in can be close to or somewhat above the Fermi surface in the environment. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of escape through such channels but also due to the ulterior population of the long-lived environmental states. Transmission of an electron with a given incoming E in through the structure turns out to be an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted into the structure by the environment. Though the number of particles is conserved in each individual event of transmission, there exists a probability that some part of the electron's energy can be absorbed due to environmental many-body effects. In such a case the electron can disappear from the resonance energy interval and elude observation at the fixed transmission energy E in thus resulting in the seeming loss of particles, violation of the time-reversal symmetry and, as a consequence, suppression of the weak localization. Both decoherence and absorption phenomena are treated within the framework of a unit microscopic model based on the general theory of the resonance scattering. All the effects discussed are controlled by the only parameter: the spreading width of the doorway resonances that uniquely determines the decoherence rate.
Effect of a complicated many-body environment is analyzed on the chaotic motion of a quantum particle in a mesoscopic ballistic structure. The dephasing and absorption phenomena are treated on the same footing in the framework of a model which is free of the ambiguities inherent to earlier models. The single-particle doorway resonance states excited via an external channel are damped not only because of the escape onto such channels but also due to ulterior population of long-lived background states, the resulting internal damping being uniquely characterized by the spreading width. On the other hand, the formation of the fine-structure resonances strongly enhances the delay time fluctuations thus broadening the delay time distribution.
Effect of a complicated many-body environment is analyzed on the chaotic motion of a quantum particle in a mesoscopic ballistic structure. The dephasing and absorption phenomena are treated on the same footing in the framework of a schematic microscopic model. The single-particle doorway resonance states excited in the structure via an external channel are damped not only because of the escape onto such channels but also due to ulterior population of the long-lived background states. The transmission through the structure is presented as an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles reemitted by the environment. The resulting internal damping as well as the dephasing rate are uniquely expressed in terms of the spreading width which controls the coupling to the background. The formation of the long-lived fine-structure resonances strongly enhances delay time fluctuations thus broadening the delay time distribution.
Anderson localization1 in a random system is sensitive to a distance dependence of the excitation transfer amplitude V(r). If V(r) decreases with the distance r slower than 1/r^d in a d-dimensional system then all excitations are delocalized at arbitrarily strong disordering, due to the resonant interaction of far separated quantum states (Fig. 1). At finite temperature T>0 the density of excitations is finite and they can influence each other by means of their interaction. Many body excitations involving simultaneous transitions of several single particle excitations create additional channels for energy delocalization and transport. Here we show that if the interaction of excitations decreases with the distance slower than 1/R^(2d) then excitations are delocalized at finite temperature irrespectively to disordering. This delocalization results in the finite decoherence rate in the ensemble of interacting spins 1/2 representing the model of quantum computer, thus restricting the quantum hardware performance. It also leads to the energy and particle delocalization and transport at finite temperature in various physical systems including doped semiconductors, despite of the full localization of electrons at zero temperature.
The destruction of quantum-mechanical phase coherence by a fluctuating quantum bath has been investigated mostly for a single particle. However, for electronic transport through disordered samples and mesoscopic interference setups, we have to treat a many-fermion system subject to a quantum bath. Here, we review a novel technique for treating this situation in the case of ballistic interferometers, and discuss its application to the electronic Mach-Zehnder setup. We use the results to bring out the main features of decoherence in a many-fermion system and briefly discuss the same ideas in the context of weak localization.
We point out that even at the absolute zero of temperature environmental decoherence limits the destructive interference between time-reversed paths for an electron in a disordered metal, and thus causes the leading (`weak localization') quantum correction to the conductivity to saturate at T=0. Our calculation, which is intended to be illustrative rather than complete, uses a model in which an electron interacts with the fluctuations of the mean voltage in the sample. The average of the fluctuations produces the steady damping well known in Brownian motion, introduces a direction of time, ensures that arbitrarily long time-reversed electron paths lose phase coherence, and is consistent with the experimental observation of a finite low temperature phase-breaking lifetime.
We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy ET{E}_{T}ET​ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi-liquid parameters. When g, the Thouless number (also the dimensionless conductance when it has strong coupling to leads) of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $\stackrel{\ensuremath{\rightarrow}}{g}\ensuremath{\infty}$ (as in a $\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\ensuremath{-}N$ theory). The infinite g theory has two phases as a function of the Landau parameter um{u}_{m}um​ in a channel with angular momentum m: A weak-coupling phase where constant charging and exchange interactions dominate the low-energy physics, as in previous ``universal Hamiltonian'' treatments, and a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi-surface distortion), but smeared and pinned by disorder. Thus, both interactions and disorder are crucial to the existence of these phases. At finite g, the two phases and critical point evolve into three regimes in the ${u}_{m}\ensuremath{-}1/g$ plane---weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum-critical point. In this, the first of a two part series, we focus on the consequences of this picture for Coulomb Blockade experiments. We employ analytical and numerical methods to predict the statistics of single-particle levels, Coulomb Blockade peak spacings, conductance peak heights, and quasiparticle widths. We show that in the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\ensuremath{\Delta}$ within a few $\ensuremath{\Delta}\mathrm{'}\mathrm{s}$ of the Fermi energy due to coupling to collective excitations. In the strong-coupling regime if m is odd, the dot will (if isolated) crossover from the orthogonal to unitary ensemble for an exponentially small external flux or will (if strongly coupled to leads) break time-reversal symmetry spontaneously. For any m, the peak-spacing distribution becomes broader than expected in previous works and even has support at negative values, which in turn is correlated with small peak heights. Ballistic/chaotic quantum dots afford us unrivalled theoretical and experimental control over the problem of simultaneous disorder and interactions due to the 1/g1/g1/g expansion and our ability to vary disorder and interaction much more readily than in the bulk.