Nernst effect in the phase-fluctuating superconductor InO$_x$

We present a study of the Nernst effect in the amorphous superconductor InO$_x$. The low carrier density in this system implies a weak superfluid stiffness and consequently, strong phase fluctuations of the superconducting order parameter are expected. Measurements as function of temperature show that the Nernst signal evolves continuously through the superconducting transition as previously observed in underdoped cuprates. This contrasts with the abrupt jump expected at a BCS transition, as observed previously in Nb$_{0.15}$Si$_{0.85}$. In the last system, the Nernst signal due to vortices below T$_{c}$ and by Gaussian fluctuations above are clearly distinct [1]. The behavior of the ghost critical field in InO$_x$ points to a correlation length which does not diverge at the Cooper-pair forming temperature $T_c$, a temperature below which the amplitude fluctuations freeze, but phase fluctuations survive. [1] Pourret et al, Nature Physics 2, 683 (2006)