(formula presented) gauge symmetry in high-(formula presented) superconductivity

The square lattice structure of (formula presented) layers and the strongly correlated property of electrons indicate that the high-(formula presented) superconductivity in cuprates can be described by an intrinsic (formula presented) coherent pairing theory in which a (formula presented) gauge symmetry is embedded. Besides the usual charge order, this (formula presented) gauge symmetry is also related to three new magnetic-charge orders-the local AF magnet, the local spin current, and the d-wave charge order. These magnetic-charge orders are completely determined by the (formula presented) coherent pairing state. The magnetic and charge fluctuations that characterize the low-energy excitations in cuprates are then described by this gauge symmetry. Thus, the coexistence of antiferromagnetism and superconductivity can be realized naturally in a unified framework.