Thermoelectric efficiency at maximum power in a quantum dot

We identify the operational conditions for maximum power of a nanothermoelectric engine consisting of a single quantum level embedded between two leads at different temperatures and chemical potentials. The corresponding thermodynamic efficiency agrees with the CurzonAhlborn expression up to quadratic terms in the gradients, supporting the thesis of universality beyond linear response. Copyright c © EPLA, 2009 The purpose of this letter is to present a detailed thermodynamic analysis of electron transport through a single quantum dot connecting two leads at different temperatures and chemical potentials. Of particular interest to us is the efficiency of the thermal motor function, in which electrons are pumped upward in chemical potential under the impetus of a downward temperature gradient. The study of this model addresses several issues of timely interest: nanotechnology, the study of thermodynamic properties of small devices that are prone to fluctuations, the question of universality for thermodynamic properties away from equilibrium, the role of quantum features in this respect, and the promise of thermoelectricity generated by nanodevices. We briefly comment on each of these topics. Spectacular technical and experimental progress in nanoand bio-technology have greatly increased our ability to observe, manipulate, control, and even manufacture systems on a very small scale [1,2]. In parallel, new theoretical tools and concepts have been developed that make it possible to exhibit the deeper relationship between fluctuations, entropy production and work, and the role of stochasticity in small scale non-linear nonequilibrium phenomena. In particular, stochastic thermodynamics formulates the thermodynamics of small entities subject to thermal fluctuations [3–7]. These developments are closely related to the celebrated fluctuation [8] and work theorems [9]. (a)E-mail: [email protected] The concept of Carnot efficiency is a central cornerstone of thermodynamics. According to this principle, the efficiency, defined as the ratio of work output over heat input for a machine operating between two thermal baths at temperatures Tl and Tr (Tr >Tl) is at most equal to