Heat control in mesoscopic conductors - exploiting quantum effects and size confinement

This thesis deals with a theoretical analysis of heat currents, their exploitation and their control in nanoscale devices. The motivation for this study is twofold. (i) The development of nanoscale devices sets up the basis of many applications ranging from nanoelectronics to quantum technology. Such nanodevices, typically operated at low temperatures, are highly sensitive to heating effects. Hence the successful performance of these devices relies on controlling and managing this heat. (ii) Nanostructures provide appealing systems to study quantum and nonequilibrium thermodynamics because, at such small scales, the behavior of systems is highly affected by size confinement and quantum effects.The central purpose of this thesis is to investigate the impact of specific characteristics of quantum systems, in particular of quantum size confinement, nonequilibrium effects and phase coherence, on heat transport quantities. A better understanding of this impact can lead to an improved control and exploitation of heat. This can be used for the evacuation of heat from the system, cooling, or producing power using waste heat. We propose different experimentally accessible setups. In these setups, we theoretically study transport quantities using a scattering formalism.We pursue three main study lines in different setups: (i) We investigate phase-dependent heat transport in normal- and superconducting hybrid junctions. We show how disorder influences this, both in simple junctions as well as in a heat circulator. (ii) We analyze thermodynamical machines, which use nonequilibrium states as their resource instead of heat. Such devices show a "demonic behavior" since they seemingly challenge the second law of thermodynamics. (iii) We analyze how to exploit energy filtering of quantum conductors to perform thermoelectric cooling at the example of a quantum spin Hall device in the whole range from linear to nonlinear response

Phase dependent heat transport in superconducting junctions with scattering theory

The operation of nanoscale devices at low temperatures is highly sensitive to heating effects. This motivates current research on controlling heat currents in these devices. A particularly important class of setups are hybrid superconducting devices, since (1) there exist a variety of sensitive applications such as qubits, in which heating is an issue, and (2) because the superconducting energy gap as well as the controllable phase-difference across junctions allow for cooling and heat control.This thesis deals with phase-controllable heat currents through superconducting-normal conducting-superconducting (SNS) Josephson junctions. Elaborate devices containing junctions of this type have in recent years been proposed and partly even experimentally been implemented in heat interferometers, heat switch-es and heat diodes. These complex structures motivate our study on how the properties of an extended, diffusive junction affect the phase-dependent heat conductance of SNS Josephson junctions. In order to analyse the heat conductance of such junctions, in which heat is carried by quasiparticle excitations of the superconducting condensate, we use a scattering matrix formalism for hybrid superconducting systems. The transmission of quasiparticles through the diffusive region takes place via a large number of transmission channels with transmission probabilities characterized by a statistical distribution. We implement these statistical properties using previously obtained results from random-matrix theory. Our main findings are that the channel average of the diffusive conductor leads to a full suppression of the phase-dependence of the heat conductance. In contrast, the weak-localization correction to the heat conductance, as well as the heat conductance fluctuations are still sensitive to the phase. We also find that these heat conductance fluctuations have a similarly universal behavior as the well-known conductance fluctuations of charge currents in normal conductors. However, we identify an additional non-trivial temperature dependence, which is due to the superconducting phase difference

Mesoscopic effects in the heat conductance of superconducting-normal-superconducting and normal-superconducting junctions

We study the heat conductance of hybrid superconducting junctions. Our analysis involves single-channel junctions with arbitrary transmission as well as diffusive connectors and shows the influence of the superconducting gaps and phases of the contacts on the heat conductance. If the junction is diffusive, these effects are completely quenched on average, however, we find that their influence persists in weak-localization corrections and conductance fluctuations. While these statistical properties strongly deviate from the well-known analogues for the charge conductance, we demonstrate that the heat conductance fluctuations maintain a close to universal behavior. We find a generalized Wiedemann-Franz law for Josephson junctions with equal gaps and vanishing phase difference.Comment: 7 pages, 5 figure

Phase-coherent heat circulators with normal or superconducting contacts

We investigate heat circulators where a phase coherent region is contacted by three leads that are either normal- or superconducting. A magnetic field, and potentially the superconducting phases, allow to control the preferential direction of the heat flow between the three-different temperature-biased contacts. The main goal of this study is to analyze the requirements for heat circulation in nonideal devices, in particular focusing on sample-to-sample variations. Quite generally, we find that the circulation performance of the devices is good as long as only a few transport channels are involved. We compare the performance of circulators with normal conducting contacts to those with superconducting contacts and find that the circulation coefficients are essentially unchanged

Quantifying nonequlibrium thermodynamic operations in a multiterminal mesoscopic system

We investigate a multiterminal mesoscopic conductor in the quantum Hall regime, subject to temperature and voltage biases. The device can be considered as a nonequilibrium resource acting on a working substance. We previously showed that cooling and power production can occur in the absence of energy and particle currents from a nonequilibrium resource (calling this an N-demon). Here we allow energy or particle currents from the nonequilibrium resource and find that the device seemingly operates at a better efficiency than a Carnot engine. To overcome this problem, we define free-energy efficiencies which incorporate the fact that a nonequilibrium resource is consumed in addition to heat or power. These efficiencies are well behaved for equilibrium and nonequilibrium resources and have an upper bound imposed by the laws of thermodynamics. We optimize power production and cooling in experimentally relevant parameter regimes.Comment: 22 pages, 12 figure

Detailed study of nonlinear cooling with two-terminal configurations of topological edge states

We study the nonlinear thermoelectric cooling performance of a quantum spin Hall system. The setup consists of a nanomagnet contacting a Kramers' pair of helical edge states, resulting in a transmission probability with a rich structure containing peaks, well-type, and step-type features. We present a detailed analysis of the impact of all these features on the cooling performance, based to a large extent on analytical results. We analyze the cooling power as well as the coefficient of performance of the device. Since the basic features we study may be present in the transmission function of other mesoscopic conductors, our conclusions provide useful insights to analyze the nonlinear thermoelectric behavior of a wide class of quantum devices. The combination of all these properties define the response of the quantum spin Hall setup, for which we provide some realistic estimates for the conditions limiting and optimizing its operation as a cooling device.Comment: 19 pages, 18 figure