Theory of Hall Effect and Electrical Transport in High-T_cCuprates: Effects of Antiferromagnetic Spin Fluctuations

Abstract

In the normal state of high-Tc cuprates, the Hall coefficient shows remarkable temperature dependence, and its absolute value is enhanced in comparison with that value simply estimated on the basis of band structure. It has been recognized that this temperature dependence of the Hall coefficient is due to highly anisotropic quasiparticle damping rate on the Fermi surface. In this paper we further take account of the vertex correction to the current vertex arising from quasiparticle interactions. Then the transport current is transformed to a large extent from the quasiparticle velocity, and is no longer proportional to the latter. As a consequence some pieces of the Fermi surface outside of the antiferromagnetic Brillouin zone make negative contribution to the Hall conductivity, even if the curvature of the Fermi surface is hole-like. The Hall coefficient is much larger at low temperatures than the estimate made without the vertex correction. Temperature dependence of the antiferromagnetic spin correlation length is also crucial to cause remarkable temperature dependence of the Hall coefficient. In our treatment the Hall coefficient of the electron-doped cuprates can be negative despite hole-like curvature of the Fermi surface.

Pseudogap Phenomena and Superconducting Fluctuations in Hubbard Model for High-TcCuprates

“…The antiferromagnetic spin fluctuations described by χ s (q, iΩ n ) play a dominant role in the FLEX approximation. The characteristic results of the nearly anti-ferromagnetic Fermi liquid theory 17,53,54,55,56,59,60,72,73,75) are qualitatively reproduced within the FLEX approximation. The superconducting critical temperature T c is determined as the temperature below which the linearized Dyson-Gor'kov equation has a non-trivial solution ( Fig.…”

“…The anomalous properties of the Hall coefficient are well explained for not only hole-but also electron-doped cuprates on the basis of the same formalism treating the spin fluctuations. 72,73) Therefore, it is natural to expect the same mechanism for the superconductivity arising from the spin fluctuations. Actually, the instability of the d-wave superconductivity mediated by the spin fluctuations has been reported theoretically.…”

General formula for the magnetoresistance on the basis of Fermi liquid theory

“…[3], which is formally exact of order τ 2 . Then, we find out that the vertex corrections for the current, which are dropped in the RTA, cause the Curie-Weiss like behavior of R H in the presence of AF fluctuations [4][5][6][7].…”

“…As for ∆σ xy , the vertex corrections in J kx also play important roles in strongly correlated systems. In fact, according to recent theoretical studies, the vertex corrections in J kx give rise to the strong enhancement of R H in nearly AF Fermi liquids, like in high-T c superconductors or in κ-(BEDT-TTF) organic superconductors [4][5][6][7]. Noteworthily, R H becomes negative in electron-doped compounds irrespective of the fact that its Fermi surface is hole-like everywhere [11].…”

“…This long-standing mystery, which cannot be explained within the RTA, is naturally reproduced in Refs. [4] and [5] due to the fact that J k is no more parallel to v k .…”