Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet

We have constructed a systematic low-energy effective theory for hole- and electron-doped antiferromagnets, where holes reside in momentum space pockets centered at ( ± π / 2 a , ± π / 2 a ) and where electrons live in pockets centered at ( π / a , 0 ) or ( 0 , π / a ) . The effective theory is used to investigate the magnon-mediated binding between two holes or two electrons in an otherwise undoped system. We derive the one-magnon exchange potential from the effective theory and then solve the corresponding two-quasiparticle Schrödinger equation. As a result, we find bound state wave functions that resemble d x 2 - y 2 -like or d xy -like symmetry. We also study possible ground states of lightly doped antiferromagnets.