| The interplay between superconductivity and antiferromagnetism has been investigated by using a phenomenological t-t'-U-V model defined in a two dimensional lattice. The Coulomb repulsion U is responsible for the antiferromagnetism and the nearest neighbor attraction V is responsible for the d-wave pairing. The ratio of U/V determines the competition between superconductivity and an antiferromagnetic order. In intermediate U/V, superconductivity and antiferromagnetism coexist to a certain extent.; At high temperatures, antiferromagnetism emerges and coexists with superconductivity. When the antiferromagnetism appears, both local density of states (LDOS) and local differential tunneling conductance (LDTC) exhibit the same charge density wave (CDW)-like modulations along the x-axis with the average periodicity of 4.8a. The LDTC at higher temperatures shows that the "gap" of the quasiparticles obtained directly from STM experiments does not correspond to the real gap of the system in cuprate superconductors. Under an applied magnetic field, LDOS maps show stripe-like modulations along the x-axis with the periodicity of 4a. At low energies, the modulation appears inside the vortex core. At vortex core states, the modulation spreads away from the vortex core. At high energies, the modulation is the same as those at vortex core states, but the intensities inside the vortex core are lower than those outside the vortex core. The superposition of the degenerate eigenfunctions that describe the stripe modulations along the x- and y-directions is able to explain the checkerboard pattern observed by STM experiments. |
