Effects of charge inhomogeneities on elementary excitations in ${\mathbf{La}}_{2-x}{\mathbf{Sr}}_x{\mathbf{CuO}}_4$

Purely local experimental probes of many copper oxide superconductors show that their electronic states are inhomogeneous in real space. For example, scanning tunneling spectroscopic imaging shows strong variations in real space, and according to nuclear quadrupole resonance (NQR) studies, the charge distribution in the bulk varies on the nanoscale. However, the analysis of the experimental results utilizing spatially averaged probes often ignores this fact. We have performed a detailed investigation of the doping dependence of the energy and linewidth of the zone-boundary Cu-O bond-stretching vibration in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ by inelastic neutron scattering. Both our results as well as previously reported angle-dependent momentum widths of the electronic spectral function detected by angle-resolved photoemission can be reproduced by including the same distribution of local environments extracted from the NQR analysis.

Figure 1

Doping dependence of the Cu-O bond-stretching mode energy. (a) Dispersion in the [100] direction at different doping levels. (b) Zone-boundary half-breathing ($h=0.5$) mode energy as a function of doping ($x$).

Figure 2

Inelastic neutron-scattering data of half-breathing zone-boundary bond-stretching modes in LSCO. (a) $x=0$, (b) $x=0.05$, (c) $x=0.07$, (d) $x=0.15$ at 10 K, and (e) $x=0.05$ at 500 K. Red (solid) lines on raw data are composed of a linear background and two Gaussian peaks for (a) and (b) and a linear background and a single Gaussian peak for (c)–(e). Large Gaussian peaks on the bottom represent longitudinal bond-stretching modes; small Gaussian peaks at 87 meV represent the suspect artifact (see text). Full widths at half maximum (FWHM) of the main peaks of $x=0,x=0.05,x=0.07$, and $x=0.15$ are 4.5, 10.5, 8, and 5 meV, respectively. Two Gaussian peaks of $x=0.0$ data and a small Gaussian peak of $x=0.05$ data are resolution limited (4.5 meV). Dotted blue line on $x=0.0$ raw data is composed of a linear background and a Gaussian peak with 6.5-meV FWHM. (f) Doping dependence of the zone boundary ($h=0.5$) and zone center ($h=0.0$) longitudinal bond-stretching mode linewidths after deconvolving the resolution function.

Figure 3

Doping distributions for (a) and (g) $x=0.05$, (b) $x=0.074$, and (c) $x=0.15$ based on the NQR data.[17] Inelastic neutron-scattering data from the half-breathing mode for (d) $x=0.05$, (e) $x=0.07$, (f) $x=0.15$ at 10 K, and (h) $x=0.05$ at 500 K. Dotted red curves and solid blue curves over data points show results calculated from the inhomogeneous doping effect at high temperatures and at 10 K, respectively. Red curve in (h) shows the simulated results at 500 K.

Figure 4

Simulated Fermi surfaces for (a) $x=0.07$ and (b) $x=0.15$. (c) Doping-dependent Fermi surface evolution extracted from the ARPES data.[31] (d) Momentum distribution curve (MDC) widths at Fermi energy from the experiment[37] and simulation from antinodes to nodes.