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The Seebeck coefficient $S$ of the cuprate superconductor La$ _{2-x} $Sr$_{x}$CuO$ _{4}$ (LSCO) was measured in magnetic fields large enough to access thenormal state at low temperatures, for a range of Sr concentrations from $x =0.07$ to $x = 0.15$. For $x = 0.11$, 0.12, 0.125 and 0.13, $S/T$ decreases uponcooling to become negative at low temperatures. The same behavior is observedin the Hall coefficient $R_{H}(T)$. In analogy with other hole-doped cupratesat similar hole concentrations $p$, the negative $S$ and $R_{H}$ show that theFermi surface of LSCO undergoes a reconstruction caused by the onset ofcharge-density-wave modulations. Such modulations have indeed been detected inLSCO by X-ray diffraction in precisely the same doping range. Our data showthat in LSCO this Fermi-surface reconstruction is confined to $0.085 < p <0.15$. We argue that in the field-induced normal state of LSCO,charge-density-wave order ends at a critical doping $p_{\rm CDW} = 0.15 \pm0.005$, well below the pseudogap critical doping $p^\star \simeq 0.19$.

physical review. x

Critical Doping for the Onset of Fermi-Surface Reconstruction by  Charge-Density-Wave Order in the Cuprate Superconductor La$ _{2-x} $Sr$_{x}  $CuO$ _{4}$