Hall Effect and Resistivity in High-Tc Superconductors: The Conserving Approximation

TL;DR

This paper explains the anomalous Hall effect and resistivity in high-Tc superconductors using a conserving approximation that incorporates vertex corrections, aligning theoretical results with experimental observations.

Contribution

It introduces a theoretical framework with vertex corrections within the FLEX approximation to accurately reproduce the Hall coefficient behavior in high-Tc cuprates.

Findings

Reproduces temperature and doping dependence of R_H in high-Tc cuprates.

Provides explanation for sign reversal of R_H between hole- and electron-doped compounds.

Extends the explanation to other nearly AF metals like V2O3 and organic superconductors.

Abstract

The Hall coefficient (R_H) of high-Tc cuprates in the normal state shows the striking non-Fermi liquid behavior: R_H follows a Curie-Weiss type temperature dependence, and |R_H|>>1/|ne| at low temperatures in the under-doped compounds. Moreover, R_H is positive for hole-doped compounds and is negative for electron-doped ones, although each of them has a similar hole-like Fermi surface. In this paper, we give the explanation of this long-standing problem from the standpoint of the nearly antiferromagnetic (AF) Fermi liquid. We consider seriously the vertex corrections for the current which are indispensable to satisfy the conservation laws, which are violated within the conventional Boltzmann transport approximation. The obtained total current J_k takes an enhanced value and is no more perpendicular to the Fermi surface due to the strong AF fluctuations. By virtue of this mechanism, the anomalous behavior of R_H in high-Tc cuprates is neutrally explained. We find that both the temperature and the (electron, or hole) doping dependences of R_H in high-T_c cuprates are reproduced well by numerical calculations based on the fluctuation-exchange (FLEX) approximation, applied to the single-band Hubbard model. We also discuss the temperature dependence of R_H in other nearly AF metals, e.g., V_2O_3, kappa-BEDT-TTF organic superconductors, and heavy fermion systems close to the AF phase boundary.