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The Seebeck coefficient (thermopower) $S$ of the cuprate superconductorLa$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ was measured across its doping phasediagram (from $p = 0.12$ to $p = 0.25$), at various temperatures down to $T\simeq 2$ K, in the normal state accessed by suppressing superconductivity witha magnetic field up to $H = 37.5$ T. The magnitude of $S/T$ in the $T=0$ limitis found to suddenly increase, by a factor $\simeq 5$, when the doping isreduced below $p^{\star} = 0.23$, the critical doping for the onset of thepseudogap phase. This confirms that the pseudogap phase causes a largereduction of the carrier density $n$, consistent with a drop from $n = 1 + p$above $p^{\star}$ to $n = p$ below $p^{\star}$, as previously inferred frommeasurements of the Hall coefficient, resistivity and thermal conductivity.When the doping is reduced below $p = 0.19$, a qualitative change is observedwhereby $S/T$ decreases as $T \to 0$, eventually to reach negative values at$T=0$. In prior work on other cuprates, negative values of $S/T$ at $T \to 0$were shown to result from a reconstruction of the Fermi surface caused bycharge-density-wave (CDW) order. We therefore identify $p_{\rm CDW} \simeq0.19$ as the critical doping beyond which there is no CDW-induced Fermi surfacereconstruction. The fact that $p_{\rm CDW}$ is well separated from $p^{\star}$reveals that there is a doping range below $p^{\star}$ where the transportsignatures of the pseudogap phase are unaffected by CDW correlations, aspreviously found in YBa$_2$Cu$_3$O$_y$ and La$_{2-x}$Sr$_x$CuO$_4$.

Thermopower across the phase diagram of the cuprate La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ : signatures of the pseudogap and charge-density-wave phases