Thermoelectric efficiency at maximum power in a quantum dot

Esposito, Massimiliano; Lindenberg, Katja; Broeck, C. Van den

doi:10.1209/0295-5075/85/60010

Cited by 326 publications

(409 citation statements)

References 32 publications

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“…The first is made of the second term of (50) and the first term of (51). It has the exact same form as the entropy flow at the microstates level (20) with (21).…”

Section: A Single Reservoirmentioning

confidence: 99%

“…They coincided with an unprecedented development in the experimental techniques used to manipulate small systems and triggered a great deal of experimental studies in a variety of contexts, such as single molecule stretching experiments [35,[38][39][40], nanomechanical oscillator work measurements [41], spectroscopic measurement of trajectory entropies [42,43], and electronic current fluctuations in full counting statistics experiments [44]. Since stochastic thermodynamics combines kinetics and thermodynamics, it has also proved extremely useful to describe the finite-time thermodynamics (e.g., efficiency at finite power) of various nanodevices operating as thermodynamic machines [45][46][47][48][49][50][51][52][53][54]. Overall, this theory is becoming a fundamental tool for the study of nanosciences.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic thermodynamics under coarse graining

2012

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A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "mesostates" (e.g., sets of "microstates"), the consequence on the thermodynamic description of the system is studied in detail. When microstates within mesostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the mesostate level. This is not the case when these microstates remain out of equilibrium, leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots.

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“…The first is made of the second term of (50) and the first term of (51). It has the exact same form as the entropy flow at the microstates level (20) with (21).…”

Section: A Single Reservoirmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic thermodynamics under coarse graining

2012

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“…The procedure is identical to that of Ref. [2]. The resulting transcendental equation can easily be solved numerically and leads to the efficiency at maximum power displayed in Fig.…”

Section: Refrigerator and Heat Enginementioning

confidence: 95%

“…Parallel to spectacular developments in bio-and nanotechnology, there has been great theoretical interest in the study of small-scale machines. A well-documented case is the small-scale Carnot engine, in which the operational unit is subject to thermal fluctuations [1][2][3][4]. Of greater biological relevance are machines that convert one form of work to another, and yet these have received far less attention [5].…”

mentioning

confidence: 99%

Stochastically driven single-level quantum dot: A nanoscale finite-time thermodynamic machine and its various operational modes

et al. 2012

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We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two values. In the isothermal regime, it can operate as a rechargeable battery by generating an electric current against the applied bias in response to the stochastic driving and then redelivering work in the reverse cycle. This behavior is reminiscent of the Parrondo paradox. If there is a thermal gradient the device can function as a work-generating thermal engine or as a refrigerator that extracts heat from the cold reservoir via the work input of the stochastic driving. The efficiency of the machine at maximum power output is investigated for each mode of operation, and universal features are identified. Parallel to spectacular developments in bio-and nanotechnology, there has been great theoretical interest in the study of small-scale machines. A well-documented case is the small-scale Carnot engine, in which the operational unit is subject to thermal fluctuations [1][2][3][4]. Of greater biological relevance are machines that convert one form of work to another, and yet these have received far less attention [5]. In this article we introduce an electronic nanodevice that allows several modes of operation. The device is a single-level quantum dot subject to stochastic driving while in contact with two reservoirs that may be at different temperatures and chemical potentials. Its properties can be derived from a stochastic thermodynamic description [6]. We investigate in analytic detail various operational regimes. When operating under tight coupling conditions, familiar features are recovered in appropriate limits: Carnot efficiency for reversible operation when the reservoirs are at different temperatures, universal features of efficiency at maximum power [3,7], and efficiency at maximum power close to the Curzon-Ahlborn efficiency [8]. When the reservoirs are at the same temperature, the work done on the dot by the switching can reverse the "normal" direction (from high to low chemical potential) of the current. Thus, the engine can be seen as a technologically relevant implementation of the Parrondo paradox [9] in that the switching can induce an electron flow against the chemical gradient. When operating under tight coupling, the efficiency at maximum power starts from the universal value of 1/2 close to equilibrium and increases monotonically to 1 as one moves further into the nonequilibrium regime and can thus be much higher than in the traditional implementations of the Parrondo paradox [10]. The same efficiency is observed when the engine works in the reverse mode. I. MODEL AND DYNAMICSWe consider a single-level quantum dot whose energy is stochastically switched between an upper and a lower value, ε j , with j = u or d (Fig. 1). The upward and downward rates are k + and k − . The dot is in contact with a left and a right lead, ν = L or R, at chemical potentials μ ν and temperatures T ν . The transition r...

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“…Various layouts for such heat engines have been discussed, most of them based on quantum dots. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] In particular, for the heat engine proposed in Ref. 4 two quantum dots with a single energy-level are used as energy filters in order to generate a directed charge current.…”

Section: Introductionmentioning

confidence: 99%

Implementation of transmission functions for an optimized three-terminal quantum dot heat engine

Schiegg

Dzierzawa

Eckern

2017

J. Phys.: Condens. Matter

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We consider two modifications of a recently proposed three-terminal quantum dot heat engine. First, we investigate the necessity of the thermalization assumption, namely that electrons are always thermalized by inelastic processes when traveling across the cavity where the heat is supplied. Second, we analyze various arrangements of tunneling-coupled quantum dots in order to implement a transmission function that is superior to the Lorentzian transmission function of a single quantum dot. We show that the maximum power of the heat engine can be improved by about a factor of two, even for a small number of dots, by choosing an optimal structure.

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Thermoelectric efficiency at maximum power in a quantum dot

Cited by 326 publications

References 32 publications

Stochastic thermodynamics under coarse graining

Stochastic thermodynamics under coarse graining

Stochastically driven single-level quantum dot: A nanoscale finite-time thermodynamic machine and its various operational modes

Implementation of transmission functions for an optimized three-terminal quantum dot heat engine

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