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We present a Boltzmann equation analysis of the transport properties of a model of electrons with a lifetime which is short everywhere except near the Brillouin zone diagonals. The anomalous lifetime is directly implied by photoemission and c-axis transport data. We find quantitative agreement between calculations and ac and dc longitudinal and Hall resistivity, but the predicted longitudinal magnetoresistance disagrees with experiment. A possible microscopic origin of the anomalous lifetime is discussed
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In this article, I review progress towards an understanding of the normal state (in-plane) transport properties of high-$T_c$ cuprates in the light of recent developments in both spectroscopic and transport measurement techniques. Against a backdrop of mounting evidence for anisotropic single-particle lifetimes in cuprate superconductors, new results have emerged that advocate similar momentum dependence in the transport decay rate $Gamma$({bf k}). In addition, enhancement of the energy scale (up to the bare bandwidth) over which spectroscopic information on the quasiparticle response can be obtained has led to the discovery of new, unforeseen features that surprisingly, may have a significant bearing on the transport properties at the dc limit. With these two key developments in mind, I consider here whether all the ingredients necessary for a complete phenomenological description of the anomalous normal state transport properties of high-$T_c$ cuprates are now in place.
We present a theoretical framework for understanding recent transverse field muon spin rotation (TF-$mu$SR) experiments on cuprate superconductors in terms of localized regions of phase-coherent pairing correlations above the bulk superconducting transition temperature $T_c$. The local regions of phase coherence are associated with a tendency toward charge ordering, a phenomenon found recently in hole-doped cuprates. We simulate the appearance of these regions by a conserved order parameter dynamics, and perform self-consistent superconducting calculations using the Bogoliubov-deGennes method. Within this context we explore two possible scenarios: (i) The magnetic field is diamagnetically screened by the sum of varying shielding currents of isolated small-sized superconducting domains. (ii) These domains become increasingly correlated by Josephson coupling as the temperature is lowered and the main response to the applied magnetic field is from the sum of all varying tunneling currents. The results indicate that these two approaches may be used to simulate the TF-$mu$SR data but case (ii) yields better agreement.
A random lattice model with dilute interlayer bonds of density $p$ is proposed to describe the underdoped high--$T_c$ cuprates. We show analytically via an appropriate perturbation expansion and verify independently by numerical scaling of the conductance that for any finite $p$ the states remain extended in all directions, despite the presence of interlayer disorder. However, the obtained electronic transport is highly anisotropic with violent conductance fluctuations occuring in the layering direction, which can be responsible for the experimentally observed metallic in-plane and semiconducting out-of-plane resistivity of the cuprates.
Combining (1) the universal correlations between $T_{c}$ and $n_{s}/m^{*}$ (superconducting carrier density / effective mass) and (2) the pseudo-gap behavior in the underdoped region, we obtain a picture to describe superconductivity in cuprate systems in evolution from Bose-Einstein to BCS condensation. Overdoped and Zn-substituted cuprate systems show signatures of reduced superfluid density in a microscopic phase separation. Scaling of $T_{c}$ to the superfluid volume density $n_{s}$ in all these cases indicate importance of Bose condensation.
We report that planar CuO_2 hole densities in high-T_c cuprates are consistently determined by the Cu-NMR Knight shift. In single- and bi-layered cuprates, it is demonstrated that the spin part of the Knight shift K_s(300 K) at room temperature monotonically increases with the hole density $p$ from underdoped to overdoped regions, suggesting that the relationship of K_s(300 K) vs. p is a reliable measure to determine p. The validity of this K_s(300 K)-p relationship is confirmed by the investigation of the p-dependencies of hyperfine magnetic fields and of spin susceptibility for single- and bi-layered cuprates with tetragonal symmetry. Moreover, the analyses are compared with the NMR data on three-layered Ba_2Ca_2Cu_3O_6(F,O)_2, HgBa_2Ca_2Cu_3O_{8+delta}, and five-layered HgBa_2Ca_4Cu_5O_{12+delta}, which suggests the general applicability of the K_s(300 K)-p relationship to multilayered compounds with more than three CuO_2 planes. We remark that the measurement of K_s(300 K) enables us to separately estimate p for each CuO_2 plane in multilayered compounds, where doped hole carriers are inequivalent between outer CuO_2 planes and inner CuO_2 planes.
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