Isotopic Fingerprint of Electron-Phonon Coupling in High-$T_c$ Cuprates

Angle-resolved photoemission spectroscopy with low-energy tunable photons along the nodal direction of oxygen isotope substituted ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ reveals a distinct oxygen isotope shift near the electron-boson coupling “kink” in the electronic dispersion. The magnitude (a few meV) and direction of the kink shift are as expected due to the measured isotopic shift of phonon frequency, and are also in agreement with theoretical expectations. This demonstrates the participation of the phonons as dominant players, as well as pinpointing the most relevant of the phonon branches.

Figure 1

(a),(c) Fermi surface maps taken with 7.5 and 7.0 eV photons, respectively. (b),(d),(f) Energy-momentum distribution maps taken with 7.5, 7.0, and 24.0 eV along the nodal direction, indicated by the gray (red) line in (a) and (c). MDCs at the Fermi level ($E_F$) are also shown by the white line, where the $BB$ and $AB$ denote bonding band and antibonding band, respectively. The Fermi momentum is set to the momentum of the $AB$ crossing $E_F$. (e) Comparison of MDCs at $E_F$ between 7.0 eV (blue line) and 24.0 eV (red line). Note that ARPES data using a conventional photon-energy of 24.0 eV were taken at BL5-4 of the Stanford Synchrotron Radiation Laboratory.

Figure 2

(a) Energy-momentum dispersions near the nodal region both for ${}^{16}\mathrm{O}$ (blue lines) and ${}^{18}\mathrm{O}$ (red lines) from optimally doped Bi2212. Those measured cuts are labeled $-5$ to $+5$, displayed in the inset. Gray shaded area roughly indicates the kink in all the dispersions. (b) Real parts of the self-energy both for ${}^{16}\mathrm{O}$ [blue (lower) lines] and ${}^{18}\mathrm{O}$ [red (upper) lines], showing an isotope shift of $\sim 70\mathrm{meV}$ peak. Blue dashed lines and red dashed lines indicates the kink energy, averaged from cut $-5$ to cut $+5$, for ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$, respectively. Positive and negative cuts are represented by solid lines and dashed lines, respectively.

Figure 3

(a) Real part of the self-energy $\mathrm{Re}\Sigma (\omega )$ from five samples both for ${}^{16}\mathrm{O}$ (blue lines) and ${}^{18}\mathrm{O}$ (red lines) along the nodal direction indicated by the gray (red) line in Fig. 1c. All $\mathrm{Re}\Sigma (\omega )$ are deduced by subtracting a bare band dispersion from the experimental one, where $\omega$ is the energy relative to the Fermi energy, and normalized by the peak maximum, and are also offset for clarity. (b) Imaginary part of the self-energy $\mathrm{Im}\Sigma (\omega )$ determined from MDC full widths. An impurity scattering term at $\omega =0$ is subtracted as an energy independent constant background. (c),(d) Obtained kink energy as a function of sample numbers both for ${}^{16}\mathrm{O}$ (blue line) and ${}^{18}\mathrm{O}$ (red line) from $\mathrm{Re}\Sigma (\omega )$ and $\mathrm{Im}\Sigma (\omega )$, respectively.