Anisotropic quasiparticle scattering rates in slightly underdoped to optimally doped high-temperature ${\text{La}}_{2-x}{\text{Sr}}_x{\text{CuO}}_4$ superconductors

An angle-resolved photoemission study of the scattering rate in the superconducting phase of the high-temperature superconductor ${\text{La}}_{2-x}{\text{Sr}}_x{\text{CuO}}_4$ with $x=0.145$ and $x=0.17$, as a function of binding energy and momentum, is presented. We observe that the scattering rate scales linearly with binding energy up to the high-energy scale $E_1\sim 0.4\text{eV}$. The scattering rate is found to be strongly anisotropic, with a minimum along the $\left(0,0\right)–\left(\pi ,\pi \right)$ direction. A possible connection to a quantum-critical point is discussed.

Figure 1

(Color) [(a) and (b)] ARPES intensity, recorded on $x=0.145$, for nodal and antinodal cuts, respectively. The white points are the MDC at $E_F$. The intensity ratio between nodal and antinodal is $\sim 1/3$.

Figure 2

(Color) (a) MDC-normalized ARPES spectra, recorded on $x=0.145$, for the nodal cut shown in the inset. Black squares represent the MDC peak positions. Dashed blue line represents the bare-band dispersion ${\epsilon }_{\mathbf{k}}$. Solid blue line represents the renormalized dispersion obtained from discussions below. (b) MDCs for $\omega$ up to 0.6 eV. The red lines represent fits to the data with a Lorentzian line shape on a sloping background.

Figure 3

(Color) (a) Low-energy dependence of the MDC linewidths for the cuts shown in (b). Dashed lines represent linear fits of the measured scattering rate. [(b) and (c)] Fermi surface of $x=0.145$ and $x=0.17$ samples, respectively. The red lines are tight-binding fit to the data. (d) $\omega$ dependence of MDC linewidth for cuts 1–3 in (b) and the cut in (c). Cut 1 in (b) was measured both in the superconductor (SC) state (circular points) and in the NS (star points) at $T=40\text{K}$. The solid lines are $\text{Im}\Sigma \left(\omega \right)/v_{\varphi }$, where $\text{Im}\Sigma \left(\omega \right)$ and $v_{\varphi }$ are given in the text.

Figure 4

(Color) (a) Momentum dependence of $E_1$. Solid line is obtained from Eq. (1). (b) MDC linewidth ${\Gamma }_0$ as a function of the Fermi-surface (FS) angle ${\varphi }_{\text{FS}}$. (c) Angular dependence of ${\alpha }_{\text{I}}\left(\varphi \right)$ and ${\alpha }_{\text{II}}\left(\varphi \right)$. [(d) and (e)] ${\Gamma }_0\left({\varphi }_{\text{FS}}\right)/{\Gamma }_0\left(\pi /4\right)$, ${\alpha }_{\text{I}}\left({\varphi }_{\text{FS}}\right)/{\alpha }_{\text{I}}\left(\pi /4\right)$, and ${\alpha }_{\text{II}}\left({\varphi }_{\text{WF}}\right)/{\alpha }_{\text{II}}\left(\pi /4\right)$ for $x=0.145$ and $x=0.17$, respectively. Blue, red, and black points are ${\Gamma }_0$, ${\alpha }_{\text{I}}$, and ${\alpha }_{\text{II}}$, respectively. Data have been symmetrized with respect to the nodal direction. Dashed lines are guides for the eyes.