Two-lifetime model for the cuprates revisited

Abstract

Several models of the strange-metal state of the cuprate superconductors postulate the existence of strong inelastic forward scattering of the electrons, but direct evidence of such scattering is missing. Here we show that angle-resolved photoemission spectroscopy (ARPES) provides a unique tool which can address this issue. We propose a two-lifetime phenomenological model of the superconducting state of the cuprates and we show that it explains several salient low-energy features of the measured ARPES spectra. The model enables discrimination between forward- and large-angle scattering and, in addition, gives access to the magnitude of the gap function away from the Fermi surface.

Figures (9)

• Figure 1: (a-d): Momentum maps of $A({\bf k},\omega)$ predicted by MRDP for model superconductors with momentum-independent scattering rates $\Gamma$ and $\Gamma_s$. (a,b) shows data at the chemical potential $\omega=0$ for $\Gamma_s=16$ meV. (a): $\Delta_d=30$ meV and $\Gamma=3$ meV. (b): $\Delta_d=6$ meV and $\Gamma=6$ meV. (c,d) shows data at finite energy $\omega=-14$ meV for $\Delta_d=30$ meV. (c): $\Gamma=10$ meV and $\Gamma_s=0$. (d): $\Gamma=2$ meV and $\Gamma_s=80$ meV. (e): Definition of the angle $\theta$. Also shown is the banana-shaped line where $E_{\bf k}=-\omega$ (blue line) and the gap arcs where $|\Delta_{\bf k}|=-\omega$ (red lines) for the same parameters as in (c,d). (f): Momentum map of the logarithm of the second derivative of the data in (d) with respect to energy, $\log[-A"({\bf k},\omega)]$. Only points where $A"({\bf k},\omega)<0$ are shown. White dashed lines show the gap arcs.
• Figure 2: (a,c): Tomographic maps of $A(k,\omega)$ predicted by MRDP along the path indicated in the inset for a superconductor with $\Delta_d=30$ meV. (b,d): Logarithm of the second derivatives with respect to energy $\log[-A"(k,\omega)]$ of the same data. Only points where $A"(k,\omega)<0$ are shown. (a,b): $\Gamma=15$ meV and $\Gamma_s=0$ meV. (c,d): $\Gamma=3$ meV and $\Gamma_s=15$ meV. White dashed line in (d): the function $\omega=-\Delta_{\bf k}$ along the tomographic cut.
• Figure 3: (a): Temperature dependence of the MRDP parameters obtained by fitting the spectral functions at $k=k_F$ and $\theta=24^\circ$ in optimally doped Bi2212, taken from Ref. Kondo15. In agreement with Refs. Reber12Kondo15Chen22Li18, the gap and the scattering rates are continuous across the critical temperature $T_c=92$ K. (b): Spectral functions (symbols) and their MRDP fits (lines) for selected temperatures.
• Figure 4: (a): Angular dependence of the MRDP parameters for spectral functions at $k=k_F$ and $T=10$ K in optimally doped Bi2212, taken from Ref. Kondo15. The line is a fit to $\Delta_{\bf k}=\Delta_d(\cos k_ya-\cos k_xa)/2$ with $\Delta_d=34.8$ meV. For $\theta=0^\circ$ we can determine only $\Gamma_{\rm tot}=\Gamma_s+\Gamma=7$ meV; individual values of $\Gamma$ and $\Gamma_s$ are assigned by hand. (b): Spectral functions (symbols) and their MRDP fits (lines) for selected angles.
• Figure S1: Dependence of the Fermi-surface spectral function $A(k_F,\omega)$ for $\Delta=25$ meV on the scattering rates. (a): Fixed $\Gamma_s=20$ meV. Increasing $\Gamma$ symmetrically broadens the peaks. (b): Fixed $\Gamma=4$ meV. Increasing $\Gamma_s$ generates asymmetric shape of the peaks, shifting weight from $|\omega|<\omega_\ast$ to $|\omega|>\omega_\ast$.