Nobel Lecture: Type-II superconductors and the vortex lattice

Antiferromagnetism and superconductivity are both fundamental and common states of matter. In many strongly correlated systems, including the high-Tc cuprates, the heavy-fermion compounds, and the organic superconductors, they occur next to each other in the phase diagram and influence each otherʹs physical properties. The SO(5) theory unifies these two basic states of matter by a symmetry principle and describes their rich phenomenology through a single low-energy effective model. In this paper, the authors review the framework of the SO(5) theory and compare it with numerical and experimental results.