Determination of doped charge density in superconducting cuprates from NMR or stripes

Abstract

Independent investigations of nuclear quadrupole resonance (NQR) and of stripes in high-$T_c$ cuprates find a small deviation of doped-hole density $h$ from the doping level of $La_{2-x}Sr_xCuO_4$. The value observed with NQR, $ x - h \approx 0.02$, agrees closely with the density of itinerant holes, $\tilde{p}$, responsible for suppression of 3D-AFM, as obtained from stripe incommensurability. The stripe model's assumption that doped holes in $La_{2-x}Sr_xCuO_4$ reside at oxygen sites, and that doped electrons in $Ln_{2-x}Ce_xCuO_4$ ($Ln = Pr, Nd$) reside at copper sites, is (to a large degree) confirmed with NQR. The NQR finding of doped-hole probabilities in oxygen and copper orbitals of $HgBa_2CuO_{4+\delta}$ and other oxygen-enriched high-$T_c$ cuprates, $P_p \simeq P_d \simeq 1/2$, as well as of oxygen-doped $YBa_2Cu_3O_{6+y}$, $P_p \simeq 2P_d \simeq 2/3$, is interpreted with the stripe model in terms of excess oxygen atoms in the $CuO_2$ planes and $CuO$ chains.