Abstract
In this chapter, the calculation of local electronic structure in the presence of magnetic field is discussed. It starts with the continuum theory for a single vortex and proceeds to the lattice version for the vortex lattices in both conventional s-wave and unconventional d-wave superconductors. A generalization of the BdG formulation for a topological superconductor will be briefly explored. For high-T c cuprates, the local induction of competing order around a magnetic vortex core is examined. Finally, the Zeeman-field induced FFLO superconducting state is also analyzed in depth.
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