Projected SO(5) model and its application in high temperature superconductors

A theory based on SO(5) symmetry was developed to understand the physics of high temperature superconductors in 1997 (Science, 275:1089, S. C. Zhang). This theory naturally unifies antiferromagnetism (AFM) and d-wave superconductivity (SC) and explains the complex phase diagram of the material. However, the original SO(5) theory does not consider the Gutzwiller constraints of no-double occupancy. By including this important physics, we develop a new model called Projected SO(5) model (PSO(5)) where all static correlation functions are exactly SO(5) symmetric. We discuss the signature of the projected SO(5) symmetry in dynamical correlation functions and show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high Tc superconductors and account for many of their physical properties.; The PSO(5) model is applied to explain the unusual properties of high temperature superconductors. First, we study the dispersion of pi resonance in the SC state in this model. Away from the commensurate momentum, the propagation of the pi resonance creates phase slips in the SC order parameter. This frustration effect leads to a strong dressing of the pi resonance and a downward dispersion away from the commensurate wave vector. Based on these results, we argue that the commensurate resonance and incommensurate magnetic fluctuations in the cuprates are continuously connected. Secondly, a theory of static and dynamic antiferromagnetic vortices in LSCO superconductors is developed based on PSO(5). It is shown that the AFM region induced by the vortices can be greater than the superconducting coherence length, due to the light effective mass of the dynamic AFM fluctuations at optimal doping, and close proximity to the AFM state in the underdoped regime. Finally, we study hole pair fluctuation around vortex core. A checkerboard pattern is found. We argue this prediction was exactly observed in recent STM experiments. Moreover, a microscopic state for the vortex phase of BSCO superconductors is also proposed and is argued that it can become a static phase at 1/8 doping with strong magnetic field.