Hierarchies of Hofstadter butterflies in 2D covalent-organic frameworks

The Hofstadter butterfly is one of the first and most fascinating examples of the fractal and self-similar quantum nature of free electrons in a lattice pierced by a perpendicular magnetic field. However, the direct experimental verification of this effect on single-layer materials is still missing as very strong and inaccessible magnetic fields are necessary. For this reason, its indirect experimental verification has only been realized in artificial periodic 2D systems, like moir\'e lattices. The only recently synthesized 2D covalent-organic frameworks might circumvent this limitation: Due to their large pore structures, magnetic fields needed to detect most features of the Hofstadter butterfly are indeed accessible with today's technology. This work opens the door to making this exotic and theoretical issue from the 70s measurable and might solve the quest for the experimental verification of the Hofstadter butterfly in single-layer materials. Moreover, the intrinsic hierarchy of different pore sizes in a 2D covalent-organic framework adds additional complexity and beauty to the original butterflies and leads to a directly accessible playground for new physical observations

Modelling thermo-electric transport and excited states in low dimensional systems

A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in the Faculty of Physics, Chemistry and Materials Science, Department of Materials Physics.The interaction of radiation with matter at the nanoscale has an inexhaustible range of applications in electronics, biotechnology and medicine. At the nanoscale, the length scale where the classical and quantum worlds meet, quantum effects dominate the light–matter interaction and unique phenomena arise. This work addresses fundamental questions on the overlap of quantum theory, non-equilibrium thermodynamics and material science. As the exact description of these quantum phenomena is not feasible, we discuss how the open quantum system approach can be used to study thermal relaxation and thermo-electric transport at the nanoscale. The basic concepts of thermal relaxation are studied from first principles. As the conditions for relaxation are connected with the non-Markovian nature of the equation of motion, we discuss a time-local stochastic Schrödinger equation. Remarkably, this equation can describe thermal relaxation and transport dynamics correctly. Furthermore, this thesis introduces a thermal transport theory where the temperature field is established by radiation of classical blackbodies. The combination of this theory with the techniques of time-dependent current density functional theory provides an ab initio tool to study thermal transport in manybody systems. This approach is general and can be adapted to describe both electron and phonon dynamics. In this way, combined with the time-dependent current DFT, it provides a unified way to investigate ab initio electrical and thermal transport beyond linear response. The observation of thermo-electric transport in macroscopic bodies does not disturb the system or change the flow of energy. However, when moving towards the nanoscale, measurements may influence the system and has to be considered. We demonstrate that the choice of location of these local measurements provides control of the direction of the energy flow and of the particle currents separately. These results seem to violate the second law of thermodynamics. By treating decoherence as a thermodynamic bath we resolve this contradiction. In order to further advance the applications of light–matter interactions for realisable materials, the electronic and optical properties of 2D layered semiconductors are studied. 2D materials have established their place as candidates for the next generation of opto-electronic devices. Specifically, the electronic and optical properties of TiS3 and In2Se3 are theoretically investigated within DFT and many-body perturbation theory. This work constitutes a first step towards exploiting the trichalcogenide family in 2D opto-electronical applications, such as chemical sensors, passive optical polarisers, fast photodetectors, and battery technologies.Peer reviewe

Beyond the State of the Art: Novel Approaches for Thermal and Electrical Transport in Nanoscale Devices

Almost any interaction between two physical entities can be described through the transfer of either charge, spin, momentum, or energy. Therefore, any theory able to describe these transport phenomena can shed light on a variety of physical, chemical, and biological effects, enriching our understanding of complex, yet fundamental, natural processes, e.g., catalysis or photosynthesis. In this review, we will discuss the standard workhorses for transport in nanoscale devices, namely Boltzmann's equation and Landauer's approach. We will emphasize their strengths, but also analyze their limits, proposing theories and models useful to go beyond the state of the art in the investigation of transport in nanoscale devices.This research was funded by the Spanish Ministerio de Economia y Competitividad (MINECO) grant number FIS2016-79464-P (SElecT-DFT) and MINECOG17/A01 (TOWTherm), by the Basque Government (Eusko Jaurlaritza) through the Grupos Consolidados (IT578-13 and IT1249-19). R. B. acknowledges funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 793318. The APC was funded by Dresden University of Technology (TU Dresden)

Switchable Josephson current in junctions with spin-orbit coupling

We study the Josephson current in two types of lateral junctions with spin-orbit coupling and an exchange field. The first system (type 1 junction) consists of superconductors with heavy metal interlayers linked by a ferromagnetic bridge, such that the spin-orbit coupling is finite only at the superconductor/heavy metal interface. In the second type (type 2) of system we assume that the spin-orbit coupling is finite in the bridge region. The length of both junctions is larger than the magnetic decay length such that the Josephson current is carried uniquely by the long-range triplet component of the condensate. The latter is generated by the spin-orbit coupling via two mechanisms, spin precession and inhomogeneous spin relaxation. We show that the current can be controlled by rotating the magnetization of the bridge or by tuning the strength of the spin-orbit coupling in type 2 junctions and also discuss how the ground state of the junction can be tuned from a 0 to a π phase difference between the superconducting electrodes. In leading order in the spin-orbit coupling, the spin precession dominates the behavior of the triplet component and both junctions behave similarly. However, when spin relaxation effects are included the type 2 junction offers a wider parameter range in which 0-π transitions take place.BB and FSB acknowledge funding by the Spanish Ministerio de Ciencia, Innovacin y Universidades (MICINN) under the project FIS2017-82804-P and by the Transnational Common Laboratory QuantumChemPhys. RB acknowledges funding from the European Unions Horizon 2020 research and innovation program under the Marie Skodowska-Curie grant agreement No. 793318.B.B. and F.S.B. acknowledge funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) under the project FIS2017-82804-P and by the Transnational Common Laboratory QuantumChemPhys. R.B. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 793318