Magnon-mediated Binding between Holes in an Antiferromagnet

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2\phi)/r^2 where r is the distance vector of the holes and \phi is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry. The role of these bound states as potential candidates for the preformed Cooper pairs of high-temperature superconductivity is discussed qualitatively.