Temperature crossovers in cuprates

We study the temperature crossovers seen in the magnetic and transport properties of cuprates using a nearly antiferromagnetic Fermi-liquid model (NAFLM). We distinguish between underdoped and overdoped systems on the basis of their low-frequency magnetic behaviour and so classify the optimally doped cuprates as a special case of the underdoped cuprates. For the overdoped cuprates, we find, in agreement with earlier work, mean-field z = 2 behaviour of the magnetic variables associated with the fact that the damping rate of their spin fluctuations is essentially independent of temperature, while the resistivity exhibits a crossover from Fermi-liquid behaviour at low temperature to linear-in-T behaviour above a certain temperature T₀. We demonstrate that above T₀ the proximity of the quasiparticle Fermi surface to the magnetic Brillouin zone boundary brings about the measured linear-in-T resistivity. For the underdoped cuprates we argue that the sequence of crossovers identified by Barzykin and Pines in the low-frequency magnetic behaviour (from mean-field z = 2 behaviour at high temperatures, T > T_cr, to non-universal z = 1 scaling behaviour at intermediate temperatures, T_* < T < T_cr, to pseudogap behaviour below T_*) reflects the development in the electronic structure of a precursor fo a spin-density-wave state. This development begins at T_cr with a thermal evolution of the quasiparticle spectral weight which brings about temperature-dependent spin damping and ends at T_* where the Fermi surface has lost pieces near corners of the magnetic Brillouin zone. For T_* < T < T_cr the resistivity is linear in T because this change in spectral weight does not affect the resistivity significantly; below T_* vertex corrections act to bring about the measured downturn in (ρ(T) - ρ(0))/T and approximately quadratic-in-T resistivity for T ≪ T_*.