Nodal quasiparticle lifetimes in cuprate superconductors

Abstract

A new generation of angular-resolved photoemission spectroscopy (ARPES) measurements on the cuprate superconductors offers the promise of enhanced momentum and energy resolution. In particular, the energy and temperature dependence of the on-shell nodal $({k}_{x}={k}_{y})$ quasiparticle scattering rate can be studied. In the superconducting state, low-temperature transport measurements suggest that one can describe nodal quasiparticles within the framework of a BCS $d$-wave model by including forward elastic scattering and spin-fluctuation inelastic scattering. Here, using this model, we calculate the temperature and frequency dependence of the on-shell nodal quasiparticle scattering rate in the superconducting state, which determines the momentum width of the ARPES momentum distribution curves. For a zero-energy quasiparticle at the nodal momentum ${k}_{N}$, both the elastic and inelastic scattering rate show a sudden decrease as the temperature drops below ${T}_{c}$, reflecting the onset of the gap amplitude. At low temperatures the scattering rate decreases as ${T}^{3}$ and approaches a zero-temperature value determined by the elastic impurity scattering. For $T>{T}_{c}$, we find a quasilinear dependence on $T$. At low reduced temperatures, the elastic scattering rate for the nodal quasiparticles exhibits a quasilinear increase at low energy $\ensuremath{\omega}$, which arises from elastic scattering processes. The inelastic spin-fluctuation scattering leads to a low-energy ${\ensuremath{\omega}}^{3}$ dependence, which, for $\ensuremath{\omega}\ensuremath{\gtrsim}3{\ensuremath{\Delta}}_{0}$, crosses over to a quasilinear behavior.