Thermo-Electric Study of Fermi Surface Reconstruction in YBa$_2$Cu$_3$O$_y$

The Seebeck and Nernst coefficients $S$ and $\nu$ of the high-$T_c$ superconductor YBa$_2$Cu$_3$O$_y$ (YBCO) were measured in a single crystal with a hole concentration $p = 0.12$ in magnetic fields up to $H = 28$ T. For temperatures down to 9 K, $\nu$ becomes independent of field by $H \simeq 30$ T, showing that by then the Nernst signal due to superconducting fluctuations has become negligible. In this field-induced normal state, $S/T$ and $\nu/T$ are both large and negative in the $T \to 0$ limit. The magnitude of $S/T$ is consistent with the small Fermi surface pocket previously detected via quantum oscillations in YBCO at a similar doping and its negative sign confirms that the pocket is electron-like. The normal-state $S(T)$ of YBCO is remarkably similar to that of La$_{2-x}$Ba$_x$CuO$_4$, La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and La$_{2-x-y}$Eu$_y$Sr$_x$CuO$_4$ at $p \simeq 1/8$, all four materials showing a change of sign at $T \simeq 50$ K. Given that in the latter three materials this change of sign is clearly due to the onset of spin/charge density wave (`stripe') order, we infer that a similar density-wave mechanism must cause the Fermi surface reconstruction in YBCO.