Ab Initio Theory of Superconducting Two-Dimensional Crystals

The aim of this research project is to improve the physical understanding of superconductivity in two- dimensional and layered transition metal dichalcogenides and to investigate properties of their superconducting phase from first-principles. Recent studies have shown that the dimensionality of materials is one of the most important factors determining their physical behaviour. This dependence of the physical properties on the dimension is markedly demonstrated in the family of transition metal dichalcogenides. These materials are chemically extremely diverse, resulting in a variety of different compounds ranging from insulators to semiconductors, semimetals and metals. Because of this diversity, they are especially interesting for technological applications in nanoelectronics and optoelectronics, such as monolayer field-effect transistors, flexible electronic devices and energy storage. Additionally, fascinating collective phases like charge density waves, superconductivity and Mott transitions have been observed, making these materials ideal candidates to investigate the effects of reduced dimensionality. With this project, I want to elucidate the atomic-scale mechanisms underpinning superconductivity in two-dimensional and layered transition metal dichalcogenides on a fundamental level. I will investigate the interplay of lattice vibrations and electrons, and quantitatively determine key properties of the superconducting regime from first-principles. To this end, I will employ many-body Green`s function techniques and develop a completely ab initio method to describe the occurring pairing channels leading to superconductivity. This will enable me to study the dependence of the critical superconducting temperature and of the energy gap function on pressure, doping and layer thickness in these materials. Moreover, the availability of a method to describe superconductivity without the need for empirical parameters will permit the ab initio prediction of new superconducting compounds with specifically designed properties. I am confident that the results of this project will be of great interest to the scientific community and that they will help to advance the knowledge on two-dimensional systems and superconductivity in general. Additionally, as the transition metal dichalcogenides are promising for a wide range of future applications, my findings might prove to be of substantial benefit for technological research as well.

In short, it was the aim of this project to describe the superconducting phase of layered bulk materials without the need for phenomenological parameters, i.e., fully ab initio, and as accurately as possible. In order to achieve this, efficient and detailed methods to calculate the interaction between electrons and the materials' lattice, as well as the interaction between the electrons themselves had to be employed. By doing so, we were able to determine key properties of the superconducting phase, like the electron-phonon coupling parameter, the critical superconducting temperature, and the energy distribution of the superconducting gap function. For example, we calculated the superconducting properties of NbS2 and were the first to verify the experimentally observed two-gap behaviour of the superconducting gap function completely from first-principles. In the same study, we also showed that this material is actually much more complex than originally thought, as apart from exhibiting a superconducting phase, it is also very close to a lattice instability. These findings led us to implement a numerical method that is capable of determining the strongly anharmonic corrections of the lattice vibrations close to the lattice instability in NbS2, which we also subsequently employed in a combined experimental and theoretical study on SnSe2. This is another layered bulk material very similar to the transition metal dichalcogenides, and we found that when this material is put under pressure, it develops a similar lattice distortion as observed in transition metal dichalcogenides. This is very surprising considering the fact that applying pressure to such structures usually suppresses the formation of lattice distortions, and in the published paper we explain in detail the origin of this lattice instability. Apart from further work on the superconducting properties of SnSe2 and TaSe2, and encouraged by the success in describing the superconducting properties in these layered crystals, we also applied our approach to the highly topical class of hydride superconductors. These materials exhibit the highest superconducting temperatures ever measured at extreme pressures of around 300 GPa. In the literature it was argued that iron hydrides, i.e., FeHx would be promising new candidates for highest-Tc superconductors, however, as we demonstrate in our work, these materials will not be superconductors with even mediocre Tc due to their electronic structure. On the other hand, we also investigated yttrium hydrides in our latest work, and showed that this class of materials has the potential of setting a new record Tc, potentially above room temperature.