Full Counting Statistics in Quantum Contacts

Belzig, Wolfgang

doi:10.1007/978-3-540-31533-9_6

Cited by 8 publications

(21 citation statements)

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“…First, it contains the equilibrium occupation probabilities rather than the stationary ones. Second, due to charge conservation the CGF should depend only on the difference of the counting fields λ L − λ R = λ [15], which is also violated. These problems are resolved if we sum up an infinite subclass of diagrams.…”

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confidence: 99%

Full Counting Statistics for a Single-Electron Transistor: Nonequilibrium Effects at Intermediate Conductance

2006

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We evaluate the current distribution for a single-electron transistor with intermediate strength tunnel conductance. Using the Schwinger-Keldysh approach and the drone (Majorana) fermion representation we account for the renormalization of system parameters. Nonequilibrium effects induce a lifetime broadening of the charge-state levels, which suppress large current fluctuations. PACS numbers: 73.23.Hk,72.70.+m The 'Full Counting Statistics' (FCS) of charge transport has proven to be a powerful tool in the description of current fluctuations [1]. The concept had been explored by Levitov and Lesovik [2], who expressed the FCS of an arbitrary mesoscopic structure with non-interacting electrons in terms of its S−matrix. Much less is known about the FCS of interacting mesoscopic systems, a problem which has been addressed only recently [3,4,5,6,7].As a fundamental example of an interacting mesoscopic systems we consider a Single-Electron Transistor (SET). It consists of a metallic island coupled to drain and source (left and right) electrodes via low-capacitance tunnel junctions, with resistances R L and R R , as well as to a gate electrode. The strength of Coulomb interaction is characterized by the charging energy E C = e 2 /2C Σ , which depends on the total capacitance C Σ = C L +C R +C G . A measure for the tunneling strength is the dimensionlessIn Refs. [3,4] the FCS of a similar system -a quantum dot -has been studied, fully accounting for strong electron correlations, however only for a particular setup and parameters, corresponding to the Toulouse point. A renormalization group approach had been developed for the regime α 0 ≫ 1 [5]. In the opposite limit, α 0 → 0, the FCS has been analyzed to lowest order in Ref.[6] and next-to-lowest order (cotunneling) in Ref. [7]. However, effects of quantum fluctuations induced by nonvanishing α 0 are still unknown. The aim of the present paper is to derive the FCS for a SET beyond perturbation theory in the intermediate strength tunneling regime α 0 1.Let us further specify the situation to be considered. At low transport voltages and temperatures, eV, T ≪ E C , due to Coulomb blockade tunneling is suppressed in a SET, everywhere except near specific values of the gate voltage, e.g., near Q G ≡ C G V G = e/2. In the neighborhood of this conductance peak the Coulomb barrier is ∆ 0 = E C (1 − 2Q G /e). For α 0 ≪ 1 electrons tunnel via the island sequentially only when µ R < ∆ 0 < µ L , where µ L/R = κ L/R eV is the voltage drop between the L/R electrode and the island, andWith increasing α 0 , higher order effects such as cotunneling and quantum fluctuations of the charge gain importance [8]. They lead to a renormalization of ∆ 0 and α 0 . The perturbative renormalization group analysis [9] (for eV = 0) predicts a renormalization factor z 0 = 1/{1 + 2α 0 ln(E C /Λ)} to depend logarithmically on the cutoff energy Λ = max{∆ 0 , T }.The model. -We concentrate on the tunneling regime with inverse RC time 1/R T C Σ = 4πα 0 E C smaller than E C , which ensures that the charge...

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confidence: 99%

Full Counting Statistics for a Single-Electron Transistor: Nonequilibrium Effects at Intermediate Conductance

2006

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“…From the basic definition (2), one sees that if only single charges q = 1 (q = e if units are restored) may be transferred between the leads, then F (χ) must be a 2π periodic function. If however one has, for example, a superconductor where only cooper pairs may be transferred with charge q = 2, one will see that F (χ + π) = F (χ) [8]. More interestingly, if one sees a periodicity larger than 2π, then this is an indication that the particles involved in transport are fractionally charged [8,17,35].…”

Section: A Basicsmentioning

confidence: 99%

“…In fact to make the above expressions rigorous in quantum mechanics, one must supplement the definition (2) with a prescription for the appropriate time-ordering of the operator Q = tm 0 dtÎ(t) as the current operator doesn't commute with itself at different times; we refer to the literature [5,6,8,14] for a full discussion on this.…”

Section: A Basicsmentioning

confidence: 99%

“…When one turns to transport through non-equilibrium nano-structures, one finds a similar dichotomy between theory and experiment in the time domain. This is most apparent in the study of full counting statistics (FCS) of charge transfer [5][6][7][8][9][10]. The FCS is the study of the full probability distribution p n (t m ) that n electrons have moved from the source lead to the drain lead in the measuring time t m , typically when driven by a bias voltage V SD .…”

Section: Introductionmentioning

confidence: 99%

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Full counting statistics in the not-so-long-time limit

2015

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The full counting statistics of charge transport is the probability distribution pn(tm) that n electrons have flown through the system in measuring time tm. The cumulant generating function (CGF) of this distribution F (χ, tm) has been well studied in the long time limit tm → ∞, however there are relatively few results on the finite measuring time corrections to this. In this work, we study the leading finite time corrections to the CGF of interacting Fermi systems with a single transmission channel at zero temperature but driven out of equilibrium by a bias voltage. We conjecture that the leading finite time corrections are logarithmic in tm with a coefficient universally related to the long time limit. We provide detailed numerical evidence for this with reference to the self-dual interacting resonant level model. This model further contains a phase transition associated with the fractionalisation of charge at a critical bias voltage. This transition manifests itself technically as branch points in the CGF. We provide numerical results of the dependence of the CGF on measuring time for model parameters in the vicinity of this transition, and thus identify features in the time evolution associated with the phase transition itself.

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“…(2.3). There are basically two strategies to treat multitimes: Either one may regard a time dependent counting field 86,133,134 which involves the Keldysh Green's function method that is usually utilized in semiclassical dynamics, 135,136 or one recovers the time dependence from the master equation, stated above, by a time-local expansion.…”

Section: Frequency Dependent Transportmentioning

confidence: 99%

Noise-induced quantum transport

2005

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Robert Hussein Noise-induced quantum transportPThere is no pleasure more complex than that of thought and we surrendered ourselves to it.(Jorge Luis Borges, El Aleph) ResumenLos puntos cuánticos laterales son heteroestructuras semiconductoras de unos pocos micrómetros de tamaño, los cuales forman un gas bidimensional de electrones a unos nanómetros por de bajo de la superficie. Se definen por puertas metálicas superpuestas que forman barreras de potencial debido a la carga negativa. Los puntos cuánticos son pozos de potencial caracterizados por niveles electrónicos discretos formando circuitos eléctricos cuando se acoplan mediante túnel a contactos. Aplicando diferencias de potencial se logra la realización de experimentos de transporte en puntos cuánticos por los cuales dos sistemas electrónicos aislados próximos pueden interaccionar capacitivamente. En esta tesis, consideramos transporte cuántico en este tipo de circuitos acoplados capacitivamente. Estudiamos teóricamente la influencia entre subsistemas interactuantes en sus propiedades de transporte así como la monitorización del transporte electrónico. Se analizan las corrientes estacionarias y las correlaciones corriente-corriente en términos de full-counting statistics obtenidas mediante la correspondiente ecuación maestra de Bloch-Redfield la cual la usamos también para calcular las correlaciones dependientes de la frecuencia.En concreto, estudiamos un trinquete cuántico formado por un doble punto cuántico sin bias pero con sus niveles fuera de resonancia, el cual está acoplado capacitivamente a otro doble punto cuántico con un bias grande. Este circuito causa una fuerza forzada efectiva mediada por las oscilaciones de túnel en el punto cuántico anterior recordando al efecto de un campo c.a. Esto induce una corriente continua en la ausencia de cualquier bias y clasifica el sistema como un trinquete cuántico.El estudio con full-counting statistics revela que cuando la corriente del trinquete es grande, también aparecen efectos de procesos poissonianos. La eliminación del circuito forzado nos permite obtener una ecuación maestra reducida que proporciona resultados analíticos.En otro sistema, estudiamos un contacto túnel que está acoplado capacitivamente a un doble punto cuántico el cual lo empleamos para monitorizar la carga del doble punto cuántico. Consideramos tanto el régimen cuántico como el límite clásico caracterizado por la ausencia de coherencia cuántica. Generalizando la ya mencionada aproximación de Bloch-Redfield aplicada al contacto de punto cuántico, obtenemos medidas de correlación produciendo enunciados cuantitativos sobre el régimen de parámetros en los cuales el sistema de detección funciona correctamente. Por otra parte, demostramos que no solamente las ocupaciones del doble punto cuántico pueden mostrar fuertes correlaciones con la corriente del detector, sino que también con su propia corriente. La solución mecánica cuántica muestra que la backaction de la medición tiende a localizar los electrones en el doble punto cuántico y por lo vi...

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Full Counting Statistics in Quantum Contacts

Cited by 8 publications

References 50 publications

Full Counting Statistics for a Single-Electron Transistor: Nonequilibrium Effects at Intermediate Conductance

Full Counting Statistics for a Single-Electron Transistor: Nonequilibrium Effects at Intermediate Conductance

Full counting statistics in the not-so-long-time limit

Noise-induced quantum transport

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