Bond Stretching Phonon Softening and Kinks in the Angle-Resolved Photoemission Spectra of Optimally Doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_{1.6}{\mathrm{La}}_{0.4}{\mathrm{Cu}}_2{\mathrm{O}}_{6+\delta }$ Superconductors

We report the first measurement of the Cu-O bond stretching phonon dispersion in optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_{1.6}{\mathrm{La}}_{0.4}{\mathrm{Cu}}_2{\mathrm{O}}_{6+\delta }$ using inelastic x-ray scattering. We found a softening of this phonon at $\mathbf{q}=(\approx 0.25,0,0)$ from 76 to 60 meV, similar to the one reported in other cuprates. A comparison with angle-resolved photoemission data on the same sample revealed an excellent agreement in terms of energy and momentum between the angle-resolved photoemission nodal kink and the soft part of the bond stretching phonon. Indeed, we find that the momentum space where a $63\pm 5\mathrm{meV}$ kink is observed can be connected with a vector $\mathbf{q}=(\xi ,0,0)$ with $\xi \ge 0.22$, corresponding exactly to the soft part of the bond stretching phonon.

Figure 1

IXS phonon spectrum of Bi2201 at 10 K. The markers are the raw data, the dashed line is the resolution function, and the plain line is a fit. (a) Low energy part of the spectrum. (b) High energy part with a smaller $y$ scale.

Figure 2

LO phonons dispersion. (a) IXS spectra for $\mathit{Q}=(3+\xi ,0,0)$ with $\xi$ spanning from the BZ center (top spectrum, $\xi =0.02$) to the BZ face (bottom spectrum, $\xi =0.45$). The spectra are vertically shifted. The plain lines show the fit, the dashed lines show the elastic tail, and the dotted lines show the last two modes used in the fit. (b),(c) Phonon dispersions. The cosine dashed lines are guides for the eyes illustrating the crossing (b) and anticrossing (c) scenarios. (d) FWHM. The error bars are an estimate of the standard deviation of the fit coefficients.

Figure 3

(a) Dispersion of the BS mode for various optimally $p$-doped single layer cuprates in comparison with the Bi2201 data. The frequencies are normalized to their value at $\xi =0$. The error bars are an estimate of the standard deviation of the fit coefficients. The optimally doped LSCO and LaBaCuO data are from 17 and the Hg1201 data are from 1. (b) FWHM when available.

Figure 4

(a) Electron dispersion measured by ARPES for three different momentum cuts. Cut 1 is along the node and was measured with 22.4 eV synchrotron radiation (solid circles) and with 6 eV radiation using a laser setup (open circles). Cuts 2 and 3 are further toward the BZ face, close to the edge of the Fermi arcs reported in pseudogap state [24]. Cuts 2 and 3 were measured with synchrotron light only. The spectra are shifted horizontally and a $\approx 4\mathrm{meV}$ gap for cuts 2 and 3 is subtracted. (b) First derivative of cut 1. (c) Experimental Fermi surface with the momentum location of the three cuts. The apparent finite Fermi arcs are due to the experimental resolution. The solid line shows a constant energy contour at the kink energy, 63 meV. The inset of  (c) shows the IXS dispersion and peak FWHM (error bars) of the BS mode discussed above. The shadow area represents the nodal kink energy and the $\mathit{Q}$ vectors connecting the Fermi surface segments where the nodal kink is observed. Note that $\xi =0.2$ corresponds to $0.4\Delta k_x$ ($\pi /a$).