Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall

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We study theoretically a strongly type-II s-wave superconducting state of two-dimensional Dirac fermions in proximity to a ferromagnet having in-plane magnetization. It is shown that a magnetic domain wall can host a chain of equally spaced vortices in the superconducting order parameter, each of which binds a Majorana fermion state. The overlap integral of neighboring Majorana states is sensitive to the position of the chemical potential of the Dirac fermions. This leads to a characteristic V-shaped dependence of thermal conductivity of Majorana fermions on the chemical potential.