Density-functional description of materials for topological qubits and superconducting spintronics

Interfacing superconductors with magnetic or topological materials offers a playground where novel phenomena like topological superconductivity, Majorana zero modes, or superconducting spintronics are emerging. In this work, we discuss recent developments in the Kohn-Sham Bogoliubov-de Gennes method, which allows to perform material-specific simulations of complex superconducting heterostructures on the basis of density functional theory. As a model system we study magnetically-doped Pb. In our analysis we focus on the interplay of magnetism and superconductivity. This combination leads to Yu-Shiba-Rusinov (YSR) in-gap bound states at magnetic defects and the breakdown of superconductivity at larger impurity concentrations. Moreover, the influence of spin-orbit coupling and on orbital splitting of YSR states as well as the appearance of a triplet component in the order parameter is discussed. These effects can be exploited in S/F/S-type devices (S=superconductor, F=ferromagnet) in the field of superconducting spintronics

SiSc Lab 2022, Project 6. A machine learning playground in quantum mechanical simulation.

Density functional theory (DFT) is one of the most widely used simulation techniques. About a third of world supercomputing time is spent each year on such calculations. DFT approximates the solution to the Schrödinger equation, to elucidate the electronic structure of materials and molecules. While it makes quantum many-body problems in a lot of systems of interest tractable, it still is computationally demanding. It typically scales in O(N^3) with the number of electrons in the system, limiting its application to systems with a few thousand atoms at most. Over the last 15 years, the development of surrogate models based on machine learning (ML) has steadily gained momentum in the field of atomistic simulation. In ab initio molecular dynamics for instance, machine-learned interatomic potentials at a fraction of the cost and comparable accuracy of mechanistic methods have already become mainstream. Now these surrogate models also start to increasingly be developed to predict the underlying electronic structure properties of atomic systems directly.In this project, the students will be given the chance to play around with a wide array of state-of-the-art models in this field, from traditional kernel methods to deep graph convolution networks. They will be provided with a computational infrastructure and training datasets from DFT calculations. The challenges ladder they will climb has the rungs a) understanding the electronic structure data, b) understanding the reasoning behind the various surrogate ML modeling approaches, c) discovering common features of the atomic systems to come up with clever optimizations of the model architectures, and d) achieving reasonable prediction accuracy for the targeted electronic structure properties. The project goals will be adjusted, in a reasonable range given the limited time frame, according to the speed of progress and the particular interests of the students.Expected prerequisites: Applied Quantum Mechanics, basic Python skills. Desired, but optional: Physics track, some hands-on ML experience.Advisors : Johannes Wasmer, Philipp Rüßmann , Stefan Blüge