Nodal quasiparticle lifetimes in cuprate superconductors

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 omega, which arises from elastic scattering processes. The inelastic spin-fluctuation scattering leads to a low-energy omega(3) dependence, which, for omega greater than or similar to 3 Delta(0), crosses over to a quasilinear behavior.