A Unified Theory Based on SO (5) Symmetry of Superconductivity and Antiferromagnetism

Abstract

The complex phase diagram of high-critical temperature ( T c ) superconductors can be deduced from an SO (5) symmetry principle that unifies antiferromagnetism and d -wave superconductivity. The approximate SO (5) symmetry has been derived from the microscopic Hamiltonian, and it becomes exact under renormalization group flow toward a bicritical point. This symmetry enables the construction of a SO (5) quantum nonlinear σ model that describes the phase diagram and the effective low-energy dynamics of the system. This model naturally explains the basic phenomenology of the high- T c superconductors from the insulating to the underdoped and the optimally doped region.