Kramer, Tobias and Krueckl, Viktor and Heller, Eric J. and Parrott, Robert E.
Self-consistent calculation of electric potentials in Hall devices.
Phys. Rev. B 81, p. 205306.
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.