Physical properties of the Hall current

TL;DR

This paper analyzes the stationary state of Hall devices, deriving analytical expressions for currents and showing how power injection efficiency depends on the Hall angle, with implications for device performance.

Contribution

It extends previous work by deriving analytical expressions for currents in Hall devices considering the lateral circuit and magnetic field effects.

Findings

Power injection efficiency is quadratic in the Hall angle.

Main power contribution comes from longitudinal edge currents.

Power transfer obeys the maximum transfer theorem.

Abstract

We study the stationary state of Hall devices composed of a load circuit connected to the lateral edges of a Hall-bar. We follow the approach developed in a previous work (Creff et al. J. Appl. Phys 2020) in which the stationary state of a ideal Hall bar is defined by the minimum power dissipation principle. The presence of both the lateral circuit and the magnetic field induces the injection of a current: the so-called Hall current. Analytical expressions for the longitudinal and the transverse currents are derived. It is shown that the efficiency of the power injection into the lateral circuit is quadratic in the Hall angle and obeys to the maximum transfer theorem. For usual values of the Hall angle, the main contribution of this power injection provides from the longitudinal current flowing along the edges, instead of the transverse current crossing the Hall bar.