Fine details of the nodal electronic excitations in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$

Very high energy resolution photoemission experiments on high quality samples of optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ show new features in the low-energy electronic excitations. A marked change in the binding energy and temperature dependence of the near-nodal scattering rates is observed near the superconducting transition temperature, $T_C$. The temperature slope of the scattering rate measured at low energy shows a discontinuity at $T_C$. In the superconducting state, coherent excitations are found with the scattering rates showing a cubic dependence on frequency and temperature. The superconducting gap has a $d$-wave magnitude with negligible contribution from higher harmonics. Further, the bilayer splitting has been found to be finite at the nodal point.

Figure 1

(Color online) (a) High-resolution photoemission spectrum of optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ at $8\mathrm{K}$, along the dashed line in the Brillouin zone, as indicated in (c). (b) MDCs at $\omega =0$ (circles) and at $\omega =-10\mathrm{meV}$ (triangles). (c) Fermi surface reconstructed from a series of spectra along momentum lines parallel to the dashed line. (d) EDC at a fixed momentum $(k-k_F=-0.015{\mathrm{\AA }}^{-1})$. The solid line shows a Lorentzian fit to the near-peak and the high-energy side of the bonding state peak.

Figure 2

(Color online) (a) Momentum width of the Fermi surface as a function of angle $\varphi$ for two optimally doped samples ($\mathbf{A}$ and $\mathbf{B}$). The momentum splitting between bonding and antibonding states for the sample with sharper states $\left(\mathbf{A}\right)$ is also plotted. Components normal to the Fermi surface are shown. (b) Superconducting gap for samples $\mathbf{A}$, $\mathbf{B}$.

Figure 3

(Color online) (a) Width of the MDC peak in the nodal region in the normal and superconducting state recorded with $5\mathrm{meV}$ and $10\mathrm{meV}$ energy resolution, as indicated. (b) The $5\mathrm{meV}$ resolution data from (a), fitted with a cubic fit (solid line). (c) EDC width as a function of binding energy at $8\mathrm{K}$. The straight line indicates the “QP” boundary, $\Gamma \left(\omega \right)=\mid \omega \mid$.

Figure 4

(Color online) (a) The MDC-derived dispersion along the line indicated in Fig. 1c at different temperatures. (b) The corresponding MDC peak widths. (c) The $T$-dependence of MDC width at the Fermi level from two data sets indicated by open and solid circles. The solid line is a cubic fit to all data points below $T_C$.