One of the most dynamically developing field of condensed matter physics is related to the implementation of quantum computers. At the heart of the problem is the engineering of a qubit, or rather an array of qubits, which has a decoherence time exceeding the time to perform a calculation. Current implementations are still suffering from this problem, and one possible solution is to implement qubits based on so called Majorana fermions. Their main advantage is that they are topologically protected, therefore, a long coherence time is expected. It has been shown that Majorana fermions can develop at the edge states of magnetic nanostructures on the surface of conventional superconductors. Because of their topological properties, such states might be the building blocks of future quantum computers.
To study superconducting heterostructures with and without magnetic surfaces, our group developed and successfully applied a new method by solving the Kohn-Sham-Dirac-Bogoliubov-de Gennes (KSDBdG) equations. This computer code allows the study of normal metal – superconductor interfaces and heterostructures. The goal of the PhD work is to extend this theory and the corresponding computer code for finite sized surface nanostructures, which would then allow the theoretical studies of such materials.
The first step along this route would be the implementation of the already existing KSDBdG solver in the also existing nanostructure code. The second step will be to use the resulting new code to study real systems in a first principles approach, in order to systematically understand the Yu-Shiba-Rusinov and Majorana states in them. The research will be performed in a collaboration between the Wigner Research Centre for Physics and the Theoretical Physics Department of the BUTE, and is supported by national research grants.
The project requires very good knowledge in theoretical physics and also high-level programing skills. It is absolutely necessary to understand current, rather involved and parallelized computer codes in order to further develop them and extend their functionality. Because the project will require numerically highly intensive computations, it will be necessary to use national and international supercomputer systems as well.