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Chiral $p$-wave superconductors in applied magnetic field can exhibit morecomplex topological defects than just conventional superconducting vortices,due to the two-component order parameter (OP) and the broken time-reversalsymmetry. We investigate the electronic properties of those exotic states, someof which contain clusters of one-component vortices in chiral components of theOP and/or exhibit skyrmionic character in the \textit{relative} OP space, allobtained as a self-consistent solution of the microscopic Bogoliubov-de Gennesequations. We reveal the link between the local density of states (LDOS) of thenovel topological states and the behavior of the chiral domain wall between theOP components, enabling direct identification of those states in scanningtunneling microscopy. For example, a skyrmion always contains a closed chiraldomain wall, which is found to be mapped exactly by zero-bias peaks in LDOS.Moreover, the LDOS exhibits electron-hole asymmetry, which is different fromthe LDOS of conventional vortex states with the same vorticity. Finally, wepresent the magnetic field and temperature dependence of the properties of askyrmion, indicating that this topological defect can be surprisingly large insize, and can be pinned by an artificially indented non-superconducting closedpath in the sample. These features are expected to facilitate the experimentalobservation of skyrmionic states, thereby enabling experimental verification ofchirality in emerging superconducting materials.

Electronic properties of emergent topological defects in chiral $p$-wave superconductivity