Self-consistent calculation of electric potentials in Hall devices

TL;DR

This paper uses a first-principles classical many-body simulation to investigate the formation of the Hall potential, emphasizing the roles of contacts, interactions, and confinement, and linking the Hall effect to boundary conditions.

Contribution

It provides a microscopic, self-consistent simulation approach to understanding the conditions necessary for the Hall potential formation.

Findings

Hall potential build-up resembles conformal-mapping results

Hall effect linked to boundary conditions at reservoirs

Simulation captures electron interactions and confinement effects

Abstract

Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii) confinement to a finite system. By propagating thousands of interacting electrons over million time-steps we capture the build-up of the self-consistent potential, which resembles results obtained by conformal-mapping methods. As shown by a microscopic model of the current injection, the Hall effect is linked to specific boundary conditions at the particle reservoirs.