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Density-Functional Theory for Thermoelectric Phenomena

Periodic Reporting for period 1 - ThermalDFT (Density-Functional Theory for Thermoelectric Phenomena)

Reporting period: 2016-10-15 to 2018-10-14

The development of sustainable energy sources is one of the greatest challenges for our society, because natural resources are scarce. Hence it is of crucial importance to optimize the efficiency of our energy production, for example, by recovering useful energy from waste heat, an unavoidable by-product of energy production processes. Thermoelectric phenomena describe how a heat flow can be converted into an electric current. Hence, if we are able to identify materials which possess good thermoelectric properties they can be potentially used to harness electricity from waste heat. In order to identify suitable materials there are broadly speaking two complementary approaches: 1) We can synthesize various materials and measure their thermoelectric properties. 2) Alternatively we can perform numerical calculations, based on the natural laws of quantum physics, in order to predict thermoelectric properties of candidate materials. Experimental synthesis and characterization is an expensive endeavor. Accordingly, it is of great importance to steer the experimental efforts by scouting out materials using numerical simulations. The goal of this project was to provide the necessary tools for a description of thermoelectric devices based on their microscopic structure. We pushed forward the development and implementation of a theoretical framework dubbed thermal DFT. The core idea of thermal DFT is to address charge and energy (or heat) degree of freedoms on the same footing, which is crucial for addressing thermoelectric phenomena. Two important aspects had to be considered for the numerical implementation of the thermal DFT framework: 1) The construction of physically sound approximations which take the electron-electron interaction into account. 2) The conception of efficient computer codes. Both aspects have been addressed within this project.
"The interaction between electrons renders a direct solution of the fundamental equation of quantum mechanics, the Schrödinger equation, a formidable task, which can only be achieved for systems comprised of just a few degrees of freedom. In order to numerically describe systems which are comparable in size to actual experiments approximations are unavoidable. Within thermal DFT these approximations manifest themselves in the form of effective potentials shaping the charge and energy distribution of the electrons. Within this project we tackled the construction of approximations for these effective potentials along two research lines: 1) Approximations based on the uniform electron gas, a paradigm for interacting electrons. 2) Approximations based on impurity models, which have recently attracted a lot of attention, because they showed some promise in describing strongly interacting electrons. Based on the electron gas we constructed a so-called adiabatic local-density approximation. However, we realized that the required input, the free energy of the interacting electron gas, is, at least for the moment, not available in the required accuracy. Using impurity models we were able to devise novel approximation which take retardation effects into account. Furthermore, we understood how the effective potentials from impurity models can be generalized to study transport devices at experimentally relevant scales. In order to perform such large scale simulations, we derived (semi-)analytic methods to simulate the dynamics of electrons exposed to a temperature gradient and a potential bias.
In the course of this project we presented our findings at various national and international conferences and workshops. The ER presented contributed talks at both the DPG spring meeting and APS March meeting in 2017 and 2018 respectively:
• 2017 „Charge and energy transport at the Nanoscale: A DFT perspective “
• 2018 „Transient charge and energy flow in the wide-band limit “
Furthermore, results were presented at specialized workshops in Europa and USA in form of invited and contributed talks.
• 2016 Workshop: Time-Dependent Density-Functional Theory: Prospects and Applications in Benasque, Spain; „Thermal density-functional theory: Towards the ab-initio description of thermoelectric transport at the nano scale “(invited talk)
• 2017 Workshop: Excited States: Electronic Structure and Dynamics in Telluride, U.S.A.; „Charge and Energy Transport at the Nanoscale: A Density-Functional Theory Perspective “(invited talk)
• 2018 ETSF Workshop 2018, Milano, Italy; „Time-dependent charge and energy transport in nanoscale devices “(contributed talk)

We also addressed the general public during the ""Open Door Day 2017"" with a popular science talk titled “The Beautiful Invisible” at the hosting institution in an effort to underline the importance and promote the fascination for fundamental research.
In this project we have made progress in pushing forward the boundaries of a theoretical description of thermoelectric properties in quantum materials. Specifically, we were able to construct so-called non-adiabatic approximations for the effective potentials in thermal DFT, which take retardation effects due to electron-electron interactions into account. The importance of these non-adiabatic effects for quantum transport has been known for some time, but progress in the construction of non-adiabatic approximation has been slow. We believe that with the work carried out during this research project, we provide an innovative route to implement non-adiabatic approximation tailored for the description of charge and energy transport in nano- and meso-scale system, going beyond the current state-of-the-art. The numerical tools and approximations developed in the course of this project will further our understanding of thermoelectric transport in the near future. Moreover, they put us in an excellent position to theoretically assess exciting new experiments, carried out recently, on the so-called hydrodynamical regime of quantum transport, where electron-electron interactions play a pivotal role. The research performed under this Marie-Curie action brings us one step closer to an understanding of thermoelectric properties based on a microscopic description of quantum system, opening new pathways for harnessing thermoelectric devices to improve the efficiency of our energy production.
Artistc rendering of thermoelectric transport through a molecular junction