Thermal Hall effect in YBCO: Probing Fermi-surface reconstruction inside the superconducting state

The thermal Hall (Righi-Leduc) effect was measured in the cuprate superconductor YBCO at a doping $p$ = 0.11, as a function of magnetic field $H$ up to 29 T. At temperatures well below the zero-field superconducting $T_{c}$, the thermal Hall conductivity \textit{$\kappa $}$_{xy}$ is positive at low field and then turns over to become negative at fields above 15 T. The negative \textit{$\kappa $}$_{xy}$ is consistent with the negative Hall and Seebeck coefficients observed in the normal state above 25 T [1,2]. This further supports our interpretation: the Fermi surface of YBCO contains a small electron-like pocket [3] in that region of the phase diagram, the result of a Fermi-surface reconstruction attributed to stripe order [4]. In the $T $= 0 limit at $H$ = 29 T, we find reasonable agreement with the Wiedemann-Franz law, \textit{$\kappa $}$_{xy}$/$T=L_{0}$\textit{$\sigma $}$_{xy}$. The fact that \textit{$\kappa $}$_{xy}$ changes sign at $H \quad \approx $ 15 T is consistent with a scenario of phase competition whereby stripe order emerges only at finite field, in agreement with recent NMR studies that detect the onset of charge-stripe order above 15 T [5]. \\[4pt] [1] LeBoeuf \textit{et al}., \textit{PRB} \textbf{83}, 054056 (2011); [2] Lalibert\'{e} \textit{et al}., \textit{Nat. Commun.} \textbf{2}, 432 (2011); [3] LeBoeuf \textit{et al}., \textit{Nature} \textbf{450}, 533 (2007); [4] Chang \textit{et al}., \textit{PRL} \textbf{104}, 057005 (2010); [5] Wu \textit{et al., Nature }\textbf{477}$, $191 (2011).