Symmetry analysis of holes localized on a skyrmion in a doped antiferromagnet

We use the low-energy effective field theory for holes coupled to the staggered magnetization in order to investigate the localization of holes on a skyrmion in a square lattice antiferromagnet. When two holes get localized on the same skyrmion, they form a bound state. The quantum numbers of the bound state are determined by the quantization of the collective modes of the skyrmion. Remarkably, for p-wave states, the quantum numbers are the same as those of a hole pair bound by one-magnon exchange. Two holes localized on a skyrmion with winding number n = 1 or 2 may have s- or d-wave symmetry as well. Possible relations with preformed Cooper pairs of high-temperature superconductors are discussed.