LDOS modulations in cuprate superconductors with competing AF order: the temperature effect

Based upon a phenomenological $t-t'-U-V$ model and using Bogoliubov-de Gennes equations, we found that near the optimal doping $\delta=0.15$ at low temperature ($T$), only the pure d-wave superconductivity (dSC) prevails and the antiferromagnetic (AF) order is completely suppressed. However, at higher $T$ the AF order with stripe modulation and the accompanying charge density wave (CDW) emerge, and they could exist even above the superconducting transition temperature. This implies that the existence of the CDW depends critically on the presence of the AF order, not so much on the dSC. The LDOS (local density of states) image indicates that the stripe modulation has an energy independent spacing of $5a/4a$ spreading over a $24a \times 48a$ lattice, corresponding to an average periodicity $4.8a$. This result may be relevant to the recent STM experiment [Vershinin $et al.$, Science {\bf 303}, 1995 (2004)].