arXiv subjects

Tomas Novotny

Publications and source records attributed to Tomas Novotny.

28 records · Page 2Linked to original sources

arXiv2005

Full counting statistics of nano-electromechanical systems

We develop a theory for the full counting statistics (FCS) for a class of nanoelectromechanical systems (NEMS), describable by a Markovian generalized master equation. The theory is applied to two specific examples of current interest: vibrating C60 molecules and quantum shuttles. We report a numerical evaluation of the first three cumulants for the C60-setup; for the quantum shuttle we use the third cumulant to substantiate that the giant enhancement in noise observed at the shuttling transition is due to a slow switching between two competing conduction channels. Especially the last example illustrates the power of the FCS.

cond-mat.mes-hall↗

arXiv2004

Current noise spectrum of a quantum shuttle

We present a method for calculating the full current noise spectrum for the class of nano-electromechanical systems (NEMS) that can be described by a Markovian generalized master equation. As a specific example we apply the method to a quantum shuttle. The noise spectrum of the shuttle has peaks at integer multiples of the mechanical frequency, which is slightly renormalized. The renormalization explains a previously observed small deviation of the shuttle current compared to the expected value given by the product of the natural mechanical frequency and the electron charge. For a certain parameter range the quantum shuttle exhibits a coexistence regime, where the charges are transported by two different mechanisms: shuttling and sequential tunneling. In our previous studies we showed that characteristic features in the zero-frequency noise could be quantitatively understood as a slow switching process between the two current channels, and the present study shows that this interpretation holds also qualitatively at finite frequency.

cond-mat.mes-hall↗

arXiv2004

Current and current fluctuations in quantum shuttles

We review the properties of electron shuttles, i.e. nanoelectromechanical devices that transport electrons one-by-one by utilizing a combination of electronic and mechanical degrees of freedom. We focus on the extreme quantum limit, where the mechanical motion is quantized. We introduce the main theoretical tools needed for the analysis, e.g. generalized master equations and Wigner functions, and we outline the methods how the resulting large numerical problems can be handled. Illustrative results are given for current, noise, and full counting statistics for a number of model systems. Throughout the review we focus on the physics behind the various approximations, and some simple examples are given to illustrate the theoretical concepts. We also comment on the experimental situation.

cond-mat.mes-hall↗

arXiv2004

Modeling of quantum electromechanical systems

We discuss methods for numerically solving the generalized Master equation GME which governs the time-evolution of the reduced density matrix of a mechanically movable mesoscopic device in a dissipative environment. As a specific example, we consider the quantum shuttle -- a generic quantum nanoelectromechanical system (NEMS). When expressed in the oscillator basis, the static limit of the GME becomes a large linear non-sparse matrix problem (characteristic size larger than 10^4 by 10^4) which however, as we show, can be treated using the Arnoldi iteration scheme. The numerical results are interpreted with the help of Wigner functions, and we compute the current and the noise in a few representative cases.

cond-mat.mes-hall↗

arXiv2004

Shot Noise of a Quantum Shuttle

We formulate a theory for shot noise in quantum nanoelectromechanical systems. As a specific example, the theory is applied to a quantum shuttle, and the zero-frequency noise, measured by the Fano factor F, is computed. F reaches very low values (F~0.01) in the shuttling regime even in the quantum limit, confirming that shuttling is universally a low noise phenomenon. In approaching the semiclassical limit, the Fano factor shows a giant enhancement (F~100) at the shuttling threshold, consistent with predictions based on phase-space representations of the density matrix.

cond-mat.mes-hall↗

arXiv2004

Current noise in a vibrating quantum dot array

We develop methods for calculating the zero-frequency noise for quantum shuttles, i.e. nanoelectromechanical devices where the mechanical motion is quantized. As a model system we consider a three-dot array, where the internal electronic coherence both complicates and enriches the physics. Two different formulations are presented: (i) quantum regression theorem, and (ii) the counting variable approach. It is demonstrated, both analytically and numerically, that the two formulations yield identical results, when the conditions of their respective applicability are fulfilled. We describe the results of extensive numerical calculations for current and current noise (Fano factor), based on a solution of a Markovian generalized master equation. The results for the current and noise are further analyzed in terms of Wigner functions, which help to distinguish different transport regimes (in particular, shuttling vs. cotunneling). In the case of weak inter-dot coupling, the electron transport proceeds via sequential tunneling between neighboring dots. A simple rate equation with the rates calculated analytically from the P(E)-theory is developed and shown to agree with the full numerics.

cond-mat.mes-hall↗

arXiv2004

Quantum theory of shuttling instability in a movable quantum dot array

We study the shuttling instability in an array of three quantum dots the central one of which is movable. We extend the results by Armour and MacKinnon on this problem to a broader parameter regime. The results obtained by an efficient numerical method are interpreted directly using the Wigner distributions. We emphasize that the instability should be viewed as a crossover phenomenon rather than a clear-cut transition.

cond-mat.mes-hall↗

arXiv2003

Quantum Shuttle in Phase Space

We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from the tunnelling to the shuttling regime, thus extending the previously found classical results to the quantum domain. Further, a new dynamical regime is discovered, where the shuttling is driven exclusively by the quantum noise.

cond-mat.mes-hall↗

arXiv2002

On apparent breaking the second law of thermodynamics in quantum transport studies

We consider a model for stationary electronic transport through a one-dimensional chain of two leads attached to a perturbed central region (quantum dot) in the regime where the theory proposed recently by Capek for a similar model of phonon transport predicts the striking phenomenon of a permanent current between the leads. This result based on a rigorous but asymptotic Davies theory is at variance with the zero current yielded by direct transport calculations which can be carried out in the present model. We find the permanent current to be within the error of the asymptotic expansion for finite couplings, and identify cancelling terms of the same order.

cond-mat.stat-mech↗

arXiv2000

Resonant Activation Phenomenon for Non-Markovian Potential-Fluctuation Processes

We consider a generalization of the model by Doering and Gadoua to non-Markovian potential-switching generated by arbitrary renewal processes. For the Markovian switching process, we extend the original results by Doering and Gadoua by giving a complete description of the absorption process. For all non-Markovian processes having the first moment of the waiting time distributions, we get qualitatively the same results as in the Markovian case. However, for distributions without the first moment, the mean first passage time curves do not exhibit the resonant activation minimum. We thus come to the conjecture that the generic mechanism of the resonant activation fails for fluctuating processes widely deviating from Markovian.

cond-mat.stat-mech↗