Symmetry Analysis of Holes Localized on a Skyrmion in a Doped Antiferromagnet

TL;DR

This paper investigates how holes localize on Skyrmions in a doped antiferromagnet using effective field theory, revealing bound states with quantum numbers similar to hole pairs in high-temperature superconductors.

Contribution

It introduces a theoretical framework for understanding hole localization on Skyrmions and characterizes the quantum states, linking them to phenomena in high-temperature superconductivity.

Findings

Holes form bound states on Skyrmions with specific quantum numbers.

Quantum numbers for p-wave states match those of magnon-mediated hole pairs.

Holes on Skyrmions can have s- or d-wave symmetry, relevant to superconductivity.

Abstract

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.