Weak-field Hall effect and static polarizability of Bloch electrons

TL;DR

This paper develops a theoretical framework for the weak-field Hall effect in Bloch electrons, highlighting the roles of electric and demagnetization currents, and analyzes how Hall resistance varies with electron concentration in different lattice models.

Contribution

It introduces a force-based theory of the weak-field Hall effect and details the Hall resistance behavior in specific lattice structures, including effects of strong magnetic fields.

Findings

Hall resistance varies with electron concentration in tight-binding models

Electric current has two components: driven by electric field and demagnetization currents

Comparison of weak and strong magnetic field effects on Hall phenomena

Abstract

A theory of the weak field Hall effect of Bloch electrons based on the analysis of the forces acting on electrons is presented. It is argued that the electric current is composed of two contributions, that driven by the electric field along current flow and the non-dissipative contribution originated in demagnetization currents. The Hall resistance as a function of the electron concentration for the tight-binding model of a crystal with square lattice and body-centered cubic lattice is described in detail. For comparison the effect of strong magnetic fields is also discussed.