sound knowledge in quantum mechanics and solid state physics, motivation for computational research
Many bulk magnets and magnetic thin films exhibit helical or spin-spiral ground states. In the presence of magnetic field, spin spirals can transform to topologically protected whirling textures called magnetic skyrmions, while in nanowires deposited on top of superconductors Majorana bound states can be formed, both of which being prospective hardware elements of quantum information technology. Quantum mechanical (first principles) calculation of the electronic structure of spin-spiral states is possible via the generalized Bloch theorem in case of simultaneous translational and spin-rotational symmetry. Self-consistent calculation of the spin-spiral state is possible only in the non-relativistic limit, while effects of spin-orbit coupling can be accounted for by using perturbation techniques. The student will aquire the use of the spin-spiral code developed in our research group in terms of the multiple scattering Green's-function formalism. As first application, the magnetic ground state of an Fe monolayer on top of Ta(110) will be determined for which both recent experiments and previous spin-model studies explored a rather long wave-length spin spiral. A particular goal of the diploma work is to extend the code to infinite on-dimensional wires and perform calculations for magnetic wires in connection to topological superconductivity as proposed in Fe wires on Re(0001) or Mn wires on Nb(110). In addition, it is desirable to combine this code with the solution of the Bogoliubov - de Gennes equations which would enable to study proximity-induced superconductivity in these systems.