Temperature crossovers in cuprates

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Abstract
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 . We demonstrate that above 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, , to non-universal z = 1 scaling behaviour at intermediate temperatures, , to pseudogap behaviour below ) reflects the development in the electronic structure of a precursor to a spin-density-wave state. This development begins at with a thermal evolution of the quasiparticle spectral weight which brings about temperature-dependent spin damping and ends at where the Fermi surface has lost pieces near corners of the magnetic Brillouin zone. For the resistivity is linear in T because this change in spectral weight does not affect the resistivity significantly; below vertex corrections act to bring about the measured downturn in and approximately quadratic-in-T resistivity for .