Doping Dependence of the Mass Enhancement in $(\mathrm{P}\mathrm{b},\mathrm{B}\mathrm{i}{)}_2{\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{u}}_2{\mathrm{O}}_8$ at the Antinodal Point in the Superconducting and Normal States

Angle-resolved photoemission spectroscopy is used to study the mass renormalization of the charge carriers in the high-$T_c$ superconductor $(\mathrm{P}\mathrm{b},\mathrm{B}\mathrm{i}{)}_2{\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{u}}_2{\mathrm{O}}_8$ in the vicinity of the $(\pi ,0)$ point in the superconducting and the normal states. Using matrix element effects at different photon energies and due to a high momentum and energy resolution the bonding and the antibonding bands could be separated in the whole dopant range. A huge coupling to a bosonic collective mode is observed below $T_c$ for both bands, in particular, for the underdoped case. Above $T_c$, a weaker coupling to a continuous spectrum of modes is detected.

Figure 1

ARPES intensity plots as a function of energy and wave vectors along the $(\pi ,\pi )-(\pi ,-\pi )$ direction of overdoped (OD), optimally doped (OP), and underdoped (UD) Pb-Bi2212 superconductors taken at $T=30\mathrm{K}$ (upper three rows). Zero corresponds to the $(\pi ,0)$ point. Bottom row: data for an UD sample taken at $T=120\mathrm{K}$. Left column: data taken with a photon energy $h\nu =38\mathrm{e}\mathrm{V}$, at which the signal from the bonding band is maximal. Middle column: data taken at $h\nu =50\mathrm{e}\mathrm{V}$ (or 55 eV), where the signal from the antibonding band is dominant. Right column: subtraction of the latter from the former yielding the spectral weight of the bonding band (see text for details).

Figure 2

Top row: dispersion of the bonding band near the antinodal point in an underdoped Pb-Bi2212 sample at $T=30\mathrm{K}$ (left) and at $T=120\mathrm{K}$ (right) as derived from EDCs (blue points) and MDCs (red points) together with the bare electron dispersion (black points). Middle row: the same data for the antibonding band. Bottom row: MDCs (left panel) at 30 meV and EDCs (right panel) of the bonding band at $k_F$ including fits to obtain the maximum.

Figure 3

The coupling strength parameter $\lambda$ as a function of dopant concentration. Squares: superconducting state; circles: normal state; open (solid) symbols: bonding (antibonding) band. The dashed lines are fits to the data using a straight line. Horizontal bar: experimental error in the dopant concentration.

Figure 4

Top row: imaginary part of self-energy ${\Sigma }^{\prime \prime }$ as derived from MDC fits. Open (solid) symbols: bonding (antibonding) band. Bottom row: MDC fits for OD and UD samples at energies of 15 and 35 meV, respectively.