Quasiparticle States at ad-Wave Vortex Core in High-TcSuperconductors: Induction of Local Spin Density Wave Order

The local density of states (LDOS) at the vortex lattice cores in a high- $T_c$ superconductor is studied by using a self-consistent mean-field theory including interactions for both antiferromagnetism (AF) and $d$-wave superconductivity (DSC). In a zero-field optimally doped sample the AF order is completely suppressed while DSC prevails. In the mixed state, we show that the local AF-like spin density wave order appears near the vortex core and acts as an effective local magnetic field on electrons via Zeeman coupling. As a result, the LDOS at the core exhibits a double-peak structure near the Fermi level that is in good agreement with recent scanning tunneling microscopy observations.