Variation of Vortex Charges in Hole Over-Doped High-Temperature Superconductors with Competing Anti-Ferromagnetic and d-Wave Superconducting Order

Vortex charges in copper oxide high-temperature superconductor (HTS) with hole over-doping are investigated by Bogoliubov-de Gennes (BdG) equations based on a model Hamiltonian with competing anti-ferromagnetic (AF) and d-wave superconducting order (DSC) with variation of temperature T. For the DSC, the spin density wave (SDW) and the charge density wave (CDW), the transition from stripe to checkerboard pattern and to 2D-structure may occur with variation of temperature T. Especially, the vortex core will be negatively charged for hole over-doped HTS at the lower temperature where the AF and DSC orders coexist, whereas positive core charges are expected for relatively large temperature (still below Superconducting critical temperature Tc) where AF order vanishes.