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We report measurements of the Seebeck effect in both the $ab$ plane ($S_{\rma}$) and along the $c$ axis ($S_{\rm c}$) of the cuprate superconductorLa$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_4$ (Nd-LSCO), performed in magnetic fieldslarge enough to suppress superconductivity down to low temperature. We use theSeebeck coefficient as a probe of the particle-hole asymmetry of the electronicstructure across the pseudogap critical doping $p^{\star} = 0.23$. Outside thepseudogap phase, at $p = 0.24 > p^{\star}$, we observe a positive andessentially isotropic Seebeck coefficient as $T \rightarrow 0$. That $S > 0$ at$p = 0.24$ is at odds with expectations given the electronic band structure ofNd-LSCO above $p^{\star}$ and its known electron-like Fermi surface. We canreconcile this observation by invoking an energy-dependent scattering rate witha particle-hole asymmetry, possibly rooted in the non-Fermi liquid nature ofcuprates just above $p^{\star}$. Inside the pseudogap phase, for $ p <p^{\star}$, $S_{\rm a}$ is seen to rise at low temperature as previouslyreported, consistent with the drop in carrier density $n$ from $n \simeq 1 + p$to $n \simeq p$ across $p^{\star}$ as inferred from other transport properties.In stark contrast, $S_{\rm c}$ at low temperature becomes negative below$p^{\star}$, a novel signature of the pseudogap phase. The sudden drop in$S_{\rm c}$ reveals a change in the electronic structure of Nd-LSCO uponcrossing $p^{\star}$. We can exclude a profound change of the scattering across$p^{\star}$ and conclude that the change in the out-of-plane Seebeckcoefficient originates from a transformation of the Fermi surface.

physical review. x

Seebeck coefficient in a cuprate superconductor: particle-hole asymmetry  in the strange metal phase and Fermi surface transformation in the pseudogap  phase