The onset of the vortex-like Nernst signal above Tc in La_{2-x}Sr_xCuO_4 and Bi_2Sr_{2-y}La_yCuO_6

The diffusion of vortices down a thermal gradient produces a Josephson signal which is detected as the vortex Nernst effect. In a recent report, Xu et al., Nature 406, 486 (2000), an enhanced Nernst signal identified with vortex-like excitations was observed in a series of La_{2-x}Sr_xCuO_4 (LSCO) crystals at temperatures 50-100 K above T_c. To pin down the onset temperature T_{\nu} of the vortex-like signal in the lightly doped regime (0.03 < x < 0.07), we have re-analyzed in detail the carrier contribution to the Nernst signal. By supplementing new Nernst measurements with thermopower and Hall-angle data, we isolate the off-diagonal Peltier conductivity \alpha_{xy} and show that its profile provides an objective determination of T_{\nu}. With the new results, we revise the phase diagram for the fluctuation regime in LSCO to accomodate the lightly doped regime. In the cuprate Bi_2Sr_{2-y}La_yCuO_6, we find that the carrier contribution is virtually negligible for y in the range 0.4-0.6. The evidence for an extended temperature interval with vortex-like excitations is even stronger in this system. Finally, we discuss how T_{\nu} relates to the pseudogap temperature T* and the implications of strong fluctuations between the pseudogap state and the d-wave superconducting state.