Thermoelectrics of Interacting Nanosystems -- Exploiting Superselection instead of Time-Reversal Symmetry

Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager's results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems -- deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems -- provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.Comment: 38 pages (23 main paper, 15 appendix), 8 figure

Dynamics of open fermionic nano-systems -- a fundamental symmetry and its application to electron transport in interacting quantum dots

The study of electronic transport through strongly confined, interacting open quantum systems has regained considerable interest over the past years. One main motivation behind this concerns the possibility of time-dependently controlled operations on individual electrons, promising applications in, e.g., metrology and electron-based quantum computing. In particular, fundamental questions of quantum thermodynamics and the practical necessity to recover waste heat from nanocircuits have attracted attention towards electronic energy currents.The research articles covered by this thesis contribute to this topic by deriving and exploring a fundamental symmetry relation -- the fermionic duality. This duality applies to the quantum master equation of any locally interacting, fermionic open quantum system tunnel-coupled to non-interacting reservoirs. It yields a crosslink between modes and amplitudes corresponding to the evolution rates in the time-dependent decay of the open-system state. This crosslink involves a mapping between the system of interest and a dual system with inverted environment potentials, local energies, and thus especially inverted interactions. The duality thereby explains many, at first sight unintuitive, transport features and significantly improves their analytic accessability. In particular, we can understand why charge- and energy currents through quantum dots with strong local Coulomb repulsion in fact exhibit features of electron-electron attraction, both in the time-dependent decay after a sudden switch and in the stationary limit.More fundamental insights are obtained by identifying the duality to be rooted in Pauli\u27s exclusion principle and the parity superselection principle. Namely, this implies that the duality is independent of, and hence combinable with many other general symmetries, including particle-hole symmetry, time-reversal symmetry, detailed balance and Onsager reciprocity. Especially the combination with the latter offers a novel perspective on the thermoelectric response of open, locally interacting electronic nanosystems

Thermometry in dual quantum dot set-up with staircase ground state configuration

We propose and investigate thermometry of a setup employing dual quantum dots with staircase ground state configuration. The stair-case ground state configuration actuates thermally controlled inelastic tunnelling, which translates into a temperature sensitive conductance, thereby inducing thermometry. The performance of the set-up is then analyzed employing quantum master equation (QME) for such systems in the sequential tunnelling regime. In particular, it is demonstrated that the system performance, in terms of temperature sensitivity and efficiency, is maximum in the regime of low temperature, making such system suitable for cryogenic thermometry. The proposed set-up can pave the path towards realization of high performance cryogenic nano temperature sensors.Comment: 8 pages, 6 figure

Geometric energy transport and refrigeration with driven quantum dots

We study geometric energy transport in a slowly driven single-level quantum dot weakly coupled to electronic contacts and with strong on-site interaction, which can be either repulsive or attractive. Exploiting a recently discovered fermionic duality for the evolution operator of the master equation, we provide compact and insightful analytic expressions of energy pumping curvatures for any pair of driving parameters. This enables us to systematically identify and explain the pumping mechanisms for different driving schemes, thereby also comparing energy and charge pumping. We determine the concrete impact of many-body interactions and show how particle-hole symmetry and fermionic duality manifest, both individually and in combination, as system-parameter symmetries of the energy pumping curvatures. Building on this transport analysis, we study the driven dot acting as a heat pump or refrigerator, where we find that the sign of the on-site interaction plays a crucial role in the performance of these thermal machines

From 2d-van der Waals magnets to superconductor hybrid devices

This thesis focuses on two distinct topics in different lines of research within mesoscopic physics. The first topic is related tomagnons in 2d-van der Waals magnets. In extension to previous work, we discuss properties of the magnon disperson of abilayer system and uncover an underlying PT-symmetry, which explains the topology of the magnon spectrum and theabsence of a magnon Hall effect in our system. The second topic deals with a quantum dot device (NDS) consisting of aquantum dot proximized by a large gap superconductor and weakly coupled to a normal metal. We study the transientdynamics, including charge and heat transport after distinct switches in gate voltage, which prepare the initial state. Theanalysis makes significantly use of a so called fermionic duality, a novel dissipative symmetry. This way we obtain a detailedmicroscopic understanding of how to control charge and heat currents in this NDS-nanostructure