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

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 the normal 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 upon cooling to become negative at low temperatures. The same behavior is observed in the Hall coefficient \(R_{H}(T)\). In analogy with other hole-doped cuprates at similar hole concentrations \(p\), the negative \(S\) and \(R_{H}\) show that the Fermi surface of LSCO undergoes a reconstruction caused by the onset of charge-density-wave modulations. Such modulations have indeed been detected in LSCO by X-ray diffraction in precisely the same doping range. Our data show that 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 \(p_{\rm CDW} = 0.15 \pm 0.005\), well below the pseudogap critical doping \(p^\star \simeq 0.19\).