The interplay between correlations and topology is an open question in condensed matter physics. In this project I will set up a framework with which to study this question, using the iron-based superconductors as a platform. Experimentally, vortex cores in these materials have been shown to host bound states under certain conditions. I will design a feasible experimental setup to probe the exchange statistics of the observed bound states. To complement this endeavor, I will develop a minimal model for these materials and establish whether the observed states are expected to be topological in nature. The iron-based superconductors exhibit two strong signatures of correlations, namely a multitude of ordered phases coexisting in the phase diagram, and the tendency towards orbital selectivity. I will establish how these two phenomena affect the topological properties of these materials. The research will be carried out in the group of Professor Karsten Flensberg of the Niels Bohr Institute (NBI) at the University of Copenhagen. Professor Flensberg leads the Center of Quantum Devices at NBI which brings together a host of theorists and experimentalists working in the field of topological systems. The center has a tradition for close collaborations between experiment and theory, making it an ideal place to carry out the proposed research. While carrying out the research, I will receive training in methods from topology and device physics, in addition to more specific technical skills. Furthermore, I will attend courses on teaching, science communication, and grant writing. These skills will make me more attractive to prospective employers and will help me attain a job at the end of the fellowship.
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