Evidence for a charge collective mode associated with superconductivity in copper oxides from neutron and x-ray scattering measurements of La${}_{2-x}$Sr${}_x$CuO${}_4$

In superconducting copper oxides, some Cu-O bond-stretching phonons around 70 meV show anomalous giant softening and broadening of electronic origin, and electronic dispersions have large renormalization kinks near the same energy. These observations suggest that phonon broadening originates from quasiparticle excitations across the Fermi surface and the electronic dispersion kinks originate from coupling to anomalous phonons. We measured the phonon anomaly in underdoped ($x=0.05$) and overdoped ($x=0.20$ and 0.25) La${}_{2-x}$Sr${}_x$CuO${}_4$ by inelastic neutron and x-ray scattering with high resolution. Combining these and previously published data, we found that doping dependence of the magnitude of the giant phonon anomaly is very different from that of the ARPES kink, i.e., the two phenomena are not connected. We show that these results provide indirect evidence that the phonon anomaly originates from novel collective charge excitations as opposed to interactions with electron-hole pairs. Their amplitude follows the superconducting dome so these charge modes may be important for superconductivity.

Figure 1

(a) INS data of La${}_{2-x}$Sr${}_x$CuO${}_4$ ($x=0.05$) at $Q=(5-h,0,1)$ (top and bottom) and at $Q=(5-h,0,2)$ (middle). $L$ values were chosen to avoid contaminations. See Ref. [20] for details of the fits represented by solid line. (b) and (c) IXS data of La${}_{2-x}$Sr${}_x$CuO${}_4$, (b) $x=0.20$ and (c) $x=0.25$ at $Q=(3+h,0,0)$. Red lines represent the Lorentzian fitting function. (d) and (e) Phonon dispersion in LSCO from $Q=(3.27,0,0)$ (d) and $Q=(3.24,0,0)$ (e) in the [0 1 0] direction, for (d) $x=0.20$ and (e) $x=0.25$. (f) Schematic of the dispersion directions in (a)–(e). (g) Qualitative picture of anomalous phonon broadening distribution.

Figure 2

(a) Longitudinal Cu-O bond stretching phonon dispersions. Solid lines indicate cosine functions. Dashed lines are guides to eye. The data for $x=0.05$, 0.07, 0.15, 0.20, 0.25, and 0.30 are shifted by 10, 20, 30, 40, 50 and 60 meV for clarity, respectively. (b) Resolution-corrected linewidths of the longitudinal Cu-O bond stretching mode. Solid straight lines indicate “background” contributions to linewidths that smoothly increase towards the zone boundary as described in the text. The data for $x=0.07$, 0.15, 0.20, 0.25, and 0.30 are shifted by 5, 10, 20, 30, and 35 meV, respectively. (c) Average linewidths of $h=0.20$, 0.25, 0.30 and 0.35 (diamonds) after subtracting background linewidths [solid lines in Fig. 2] plotted as a function of doping. Dashed line represents $T_c$ of LSCO [23]. Green solid line indicates a plateau of $T_c$ that may originate from competition with another order parameter such as stripes. Inset illustrates strong coupling between the Cu-O bond stretching mode and electronic density fluctuations at $h=0.25$. Black and red lines indicate charge densities with and without atomic displacements (red arrows), respectively. Red arrows indicate atomic displacements of the anomalous phonon.

Figure 3

(a) Fermi surface (FS) of LSCO, $x=0.20$, measured by ARPES. Double sided arrows indicate the wave vector ($h=0.3$) of the giant phonon anomaly. This $q$ vector connects only two points of FS, indicating no FS nesting. (b) Electronic quasiparticle dispersions of LSCO $x=0.20$ and 0.30 along the red line in (a), where Fermi momentum is connected to the Fermi momentum on the other side of the arrow by $h=0.3$. Dashed straight lines represent band velocities from $-$0.2 to $-$0.1 eV for $x=0.20$ and 0.30, respectively. Inset is the Feynman diagram for electronic quasiparticle propagation with electron-phonon coupling. (c) Background-subtracted IXS data of $x=0.20$. Inset is the Feynman diagram for phonon propagation with electron-phonon coupling. (d) INS data of $x=0.30$. Blue horizontal bars inside peaks in (c) and (d) show experimental resolutions. Vertex $g$ in the Feynman diagrams in (b) and (c) is the same.