Stripe Formation by Long Range Interactions within SO(5) Theory

We study the formation of stripe order within the SO(5) theory of high- $T_c$ superconductivity. Spin and charge modulations arise as a result of the competition between a local tendency to phase separate and the long-range Coulomb interaction. This frustrated phase separation leads to hole-rich and hole-poor regions which are, respectively, superconducting and antiferromagnetic. A rich variety of microstructures ranging from droplet and striped to inverted-droplet phases are stabilized, depending on the charge carrier concentration. We show that the SO(5) energy functional favors nontopological stripes.