Heat, molecular vibrations, and adiabatic driving in non‐equilibrium transport through interacting quantum dots

Haupt, Federica; Leijnse, Martin; Calvo, Hernán L.; Claßen, Laura; Splettstoesser, Janine; Wegewijs, M. R.

doi:10.1002/pssb.201349219

Cited by 37 publications

(47 citation statements)

References 148 publications

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“…[31] gives a less mathematical overview of the work on quantum dots discussed in this review, other related issues are reviewed in Ref. [32]. The thermodynamics of systems modelled by Markovian quantum master equations (Lindblad master equations) is reviewed in Ref.…”

Section: Further Reading: Textbooks and Reviewsmentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without interaction effects, (v) stochastic thermodynamic for fluctuating small systems. In all cases, we place particular emphasis on the fundamental questions about the bounds on ideal machines. Can magnetic-fields change the bounds on power or efficiency? What is the relationship between quantum theories of transport and the laws of thermodynamics? Does quantum mechanics place fundamental bounds on heat to work conversion which are absent in the thermodynamics of classical systems?

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Section: Further Reading: Textbooks and Reviewsmentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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“…[17,18,36,37,54,[67][68][69][70][71], see Refs. [2][3][4] for recent reviews. However, here we do not ask what is the efficiency of a given system, we ask what is the system that would achieve the highest efficiency, and what is this efficiency?…”

Section: Nonlinear Scattering Theorymentioning

confidence: 99%

Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output

2015

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We investigate the nonlinear scattering theory for quantum systems with strong Seebeck and Peltier effects, and consider their use as heat-engines and refrigerators with finite power outputs. This article gives detailed derivations of the results summarized in Phys. Rev. Lett. 112, 130601 (2014). It shows how to use the scattering theory to find (i) the quantum thermoelectric with maximum possible power output, and (ii) the quantum thermoelectric with maximum efficiency at given power output. The latter corresponds to a minimal entropy production at that power output. These quantities are of quantum origin since they depend on system size over electronic wavelength, and so have no analogue in classical thermodynamics. The maximal efficiency coincides with Carnot efficiency at zero power output, but decreases with increasing power output. This gives a fundamental lower bound on entropy production, which means that reversibility (in the thermodynamic sense) is impossible for finite power output. The suppression of efficiency by (nonlinear) phonon and photon effects is addressed in detail; when these effects are strong, maximum efficiency coincides with maximum power. Finally, we show in particular limits (typically without magnetic fields) that relaxation within the quantum system does not allow the system to exceed the bounds derived for relaxation-free systems, however, a general proof of this remains elusive.

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“…Furthermore, when operated under strong nonequilibrium conditions in which linear-response theory breaks down, a theoretical treatment taking into account the * nicwall@nanotech.dtu.dk † kkaa@nanotech.dtu.dk full nonlinear properties is needed [16][17][18][19]. Only recently have these issues been discussed in strongly interacting QD systems [9,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings

2017

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We study thermoelectric effects in Coulomb-coupled quantum-dot (CCQD) systems beyond lowest-order tunneling processes and the often applied wide-band approximation. To this end, we present a master-equation (ME) approach based on a perturbative T -matrix calculation of the charge and heat tunneling rates and transport currents. Applying the method to transport through a noninteracting single-level QD, we demonstrate excellent agreement with the Landauer-Büttiker theory when higher-order (cotunneling) processes are included in the ME. Next, we study the effect of cotunneling and energy-dependent lead couplings on the heat currents in a system of two CCQDs. We find that cotunneling processes (i) can dominate the off-resonant heat currents at low temperature and bias compared to the interdot interaction, and (ii) give rise to a pronounced reduction of the cooling power achievable with the recently demonstrated Maxwell's demon cooling mechanism. Furthermore, we demonstrate that the cooling power can be boosted significantly by carefully engineering the energy dependence of the lead couplings to filter out undesired transport processes. Our findings emphasize the importance of higher-order cotunneling processes as well as engineered energy-dependent lead couplings in the optimization of the thermoelectric performance of CCQD systems.

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Heat, molecular vibrations, and adiabatic driving in non‐equilibrium transport through interacting quantum dots

Cited by 37 publications

References 148 publications

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output

Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings

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