Doping-dependence of nodal quasiparticle properties in high-$T_c$ cuprates studied by laser-excited angle-resolved photoemission spectroscopy

We investigate the doping dependent low-energy, low temperature $(T=5\mathrm{K})$ properties of nodal quasiparticles in the $d$-wave superconductor ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212). By utilizing ultrahigh resolution laser-excited angle-resolved photoemission spectroscopy, we obtain precise band dispersions near $E_F$, mean free paths, and scattering rates $\left(\Gamma \right)$ of quasiparticles. For optimally and overdoped samples, we obtain very sharp quasiparticle peaks of 8 and $6\mathrm{meV}$ full width at half maximum, respectively. The value of $\Gamma$ for optimally doped sample is in good accordance with terahertz conductivity. For all doping levels, we find the energy dependence of $\Gamma \sim \mid \omega \mid$, while $\Gamma (\omega =0)$ shows a monotonic increase from overdoping to underdoping. The doping-dependence suggests the role of electronic inhomogeneity on the nodal quasiparticle scattering at low temperature $(5\mathrm{K}\lesssim 0.07T_c)$ pronounced in the underdoped region. The quasiparticle peak spectra match well with a single Lorentzian function, thus indicating that the nodal carriers can be described as well-defined quasiparticles, even in the underdoped region.

Figure 1

(Color) (a) ARPES intensity image plot from Bi2212 OP90K. The red curve shows the band dispersion as obtained from the MDC peak positions. (b) A schematic of the Brillouin zone of Bi2212. The red line shows the momentum region of the measurement [along $(0,0)\text{−}(\pi ,\pi )$]. (c) $E_B$ dependence of the MDC FWHM obtained from OP90K.

Figure 2

(Color) [(a)–(c)] Ultrahigh resolution ARPES intensity image plot from Bi2212 UN72K, OP90K, and OV73K, respectively. The red curves show the band dispersions obtained from MDC peak positions. (d) EDC taken from ARPES on OV73K (c). (e) $E_B$ dependence of MDC FWHM obtained from (a) UN72K, (b) OP90K, and (c) OV73K, respectively.

Figure 3

(Color online) (a) EDC at $k=k_F$ and (b) that symmetrized at $E_F$ from ARPES on Bi2212 UN72K, OP90K, and OV73K [Figs. 2a, 2b, 2c]. (c) shows the MDC at $E=E_F$ obtained from the same ARPES spectra. The curves in (b) and (c) are the fitting result by using a single Lorentzian function.

Figure 4

(Color online). Doping-dependence of the scattering rate $\Gamma$ estimated from the FWHM of EDC and MDC in Bi2212. The right axis shows the $T_c$ of the measured samples with the relation to hole concentration $p$, $T_c=T_c^{\max }[1-82.6{(0.16-p)}^2]$.