Charged vortex structure in high-temperature superconductors

By using a model Hamiltonian with competing antiferromagnetic (AFM) spin density wave (SDW) and d-wave superconductivity orders, the effect of next-nearest-neighbour (nnn) hopping on spin and charge structures in high-temperature superconductors is investigated at finite temperatures. For an optimally doped sample, we find that the AFM order magnitude in the vortex core is firstly enhanced and then suppressed, accompanied with a "positively→negatively→positively" charged vortex structure transition with increasing nnn hopping strength, which implies that the AFM order is unnecessarily bounded to an electron-rich vortex core. In addition, a charge ordering pattern with four negatively charged peaks localized in a small region is also found around the vortex core centre without net charge. Recent scanning-tunneling-microscopy experimental observations of the checkerboard structure are hopefully understood.