The subject of this thesis is the development of theoretical and computational methods to allow for the search of new superconductors via High-Throughput Methods (HTMs)
HTMs test thousands of materials for a desired property. Each test on a material is performed by computational simulation; hence the computational cost of each individual simulation has a strong impact on the global performance of a HTM. While first-principle methods exist and allow for in-depth studies of single superconducting materials, such methods are far too expensive to be applied directly in HTMs.
In order to predict superconductors, one needs to address primarily three challenges, namely the accelerated prediction (i) of new crystalline systems that are thermodynamically or at least dynamically stable and are yet to be synthesized, (ii) of basic electronic properties such as the metallicity and absence of magnetic instabilities, (iii) of the strength of the pairing interaction and hence the possibility of having a high superconducting transition temperature Tc within this work, we consider conventional electron-phonon superconductivity.}
At the core of this work, we focus on challenge (iii) by introducing Descriptors of Superconductivity, that, while accessible at low computational cost, convey sufficient information to select candidate materials for in-depth investigation. Our approach to develop such descriptors is based both on theoretical knowledge and on empirical data, while connections between the former and the latter are demonstrated by models. We implement the Descriptors numerically on the basis of Kohn-Sham Density Functional Theory (DFT). We perform a high-throughput search, evaluating our Descriptors of Superconductivity on a library of known materials, and identify promising candidate superconductors. For a subset sample of those candidates, we perform expensive full-scale ab initio calculations, validating our Descriptors.
We address challenge (ii) by developing machine learning (ML) methods with the goal to further accelerate the process by predicting electronic properties directly from the crystal structure of a given material. For this purpose, we introduce a new representation of crystal structures for ML, which takes important symmetries of periodic systems into account. These ML methods are evaluated with the help of the data generated in our high-throughput search.
Finally, we develop a strategy for challenge (i), which allows to predict new crystalline systems via element substitution. By means of statistical analysis performed on a large library of materials, we introduce a new measure for the similarity between chemical elements.
