Theory of Low-Temperature Hall Effect in Electron-Doped Cuprates

TL;DR

This paper presents a mean field theoretical analysis of the low-temperature Hall effect in electron-doped cuprates, revealing Fermi surface reconstruction and quantum critical behavior with small anomalies.

Contribution

It provides a mean field calculation of the Hall conductance at zero temperature, linking it to density wave ordering and quantum criticality in electron-doped cuprates.

Findings

Fermi surface reconstruction consistent with density wave order

Large density wave gap magnitude

Small quantum critical anomaly in Hall resistance

Abstract

A mean field calculation of the $T\to 0$ limit of the Hall conductance of electron-doped cuprates such as $Pr_{2-x}Ce_xCuO_{4+\delta}$ is presented. The data are found to be qualitatively consistent with the reconstruction of the Fermi surface expected upon density wave ordering. The magnitude of the density wave gap is found to be large. The Hall resistance exhibits a nonanalyticity at the quantum critical point for density wave ordering, but the amplitude of the anomaly is found to be unobservably small. The quantum critical contribution to $R_H(B)$ is determined. Quantitative discrepancies between calculation and data remain, suggesting that the experimental doping is not identical to the $Ce$ concentration $x$.