Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Sukhorukov, Eugene V.

doi:10.1016/j.physe.2015.11.018

Cited by 15 publications

(8 citation statements)

References 23 publications

(58 reference statements)

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“…Now focusing on the near ballistic regime 1 − τ L,R ≪ 1, we apply the scattering theory approach developed in Ref. 43,44. The average ⟨I⟩ ≡ Tr(ρI) of the current operator I = v F [ρ R1 (0) − ρ R2 (0)] is evaluated perturbatively in backscattering amplitudes (Eq.…”

Section: Predictions In the Quantum Asymmetric Regimementioning

confidence: 99%

Controlling charge quantization with quantum fluctuations

Jezouin

Iftikhar

Anthore

et al. 2016

Nature

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In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal-semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.

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Section: Predictions In the Quantum Asymmetric Regimementioning

confidence: 99%

Controlling charge quantization with quantum fluctuations

Jezouin

Iftikhar

Anthore

et al. 2016

Nature

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“…Here, the prefactor in the expression for K (t ) can be fixed in the end of calculations by comparing to the equilibrium correlation function for free electrons. Next, we apply the Langevin equation method [13,25] to evaluate electron correlation function K (t ). This method has been successfully used [11,12] to describe experiments on the decay of CB oscillations [11,14,19].…”

Section: Model Of the Quantum Ammetermentioning

confidence: 99%

Quantum ammeter: Measuring full counting statistics of electron currents at quantum timescales

Idrisov

Levkivskyi²,

Sukhorukov

2020

Phys. Rev. B

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We present the theoretical model of the quantum ammeter, a device that is able to measure the full counting statistics of an electron current at quantum timescales. It consists of an Ohmic contact perfectly coupled to chiral quantum Hall channels and of a quantum dot attached to one of the outgoing channels. At energies small compared to its charging energy, the Ohmic contact fractionalizes each incoming electron and redistributes it between outgoing channels. By monitoring the resonant tunneling current through the quantum dot, one gets access to the moment generator of the current in one of the incoming channels at timescales comparable to its correlation time.

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“…We follow the Refs. [22,23] and complement these equations with the boundary conditions in terms of dissipative currents originating from the reservoirs and the metallic island. Fluctuations of these currents are Gaussian, therefore, they can be considered Gaussian sources in the so-arising quantum Langevin equations.…”

Section: A Hamiltonianmentioning

confidence: 99%

“…Using the standard bosonization technique they have made quantitative predictions for the visibility of CB oscillations in the quantum regime T ≪ E C in the case of strong tunneling, where one or both QPCs are close to perfect transmission. Here we extend these predictions to arbitrary temperatures by using an alternative approach to bosonization, 22,23 which is based on the scattering theory for bosons as well as the Langevin equation method. Our quantative predictions fully agree with the experimental data in the whole range of temperatures.…”

Section: Introductionmentioning

confidence: 99%

Thermal decay of Coulomb blockade oscillations

2017

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We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature T and gate voltage. The conductance shows Coulomb blockade (CB) oscillations as a function of the gate voltage that decay with the temperature as a result of thermally activated fluctuations of the charge in the island. The regimes of quantum, T ≪ EC, and thermal, T ≫ EC, fluctuations are considered, where EC is the charging energy of an isolated island. Our predictions for CB oscillations in the quantum regime coincide with previous findings in [A. Furusaki and K. A. Matveev, Phys. Rev. B 52, 16676 (1995)]. In the thermal regime the visibility of Coulomb blockade oscillations decays with the temperature as T /EC exp(−π 2 T /EC), where the exponential dependence originates from the thermal averaging over the instant charge fluctuations, while the prefactor has a quantum origin. This dependence does not depend on the strength of couplings to the leads. The differential capacitance, calculated in the case of a single tunnel junction, shows the same exponential decay, however the prefactor is linear in the temperature. This difference can be attributed to the non-locality of the quantum effects. Our results agree with the recent experiment [S. Jezouin et al., Nature 536, 58 (2016)] in the whole range of the parameter T /EC.

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Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Cited by 15 publications

References 23 publications

Controlling charge quantization with quantum fluctuations

Controlling charge quantization with quantum fluctuations

Quantum ammeter: Measuring full counting statistics of electron currents at quantum timescales

Thermal decay of Coulomb blockade oscillations

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