Inelastic scattering effects and the Hall resistance in a 4-probe ring

TL;DR

This paper introduces a perturbation method within the Landauer-Büttiker formalism to incorporate inelastic scattering effects in mesoscopic systems, demonstrating their impact on Hall resistance and quantum interference phenomena in a 4-probe ring.

Contribution

It presents a novel perturbation approach to include inelastic scattering effects without losing computational efficiency in mesoscopic transport calculations.

Findings

Inelastic scattering influences Hall resistance and Aharonov-Bohm oscillations.

Quantum interference causes Hall effect in the 4-probe ring.

Perturbation method effectively models inelastic effects in mesoscopic systems.

Abstract

Phase randomizing processes in mesoscopic systems can be described in a phenomenological way within the Landauer-B\"{u}ttiker formalism by attaching extra voltage probes to the sample. In this paper, it is shown that a perturbation treatment of this idea allows for the incorporation of such effects without the need of giving up the efficiency of recursive techniques commonly used for calculating the transmission coefficients. The technique is applied to a 4-probe ring, where a Hall effect can be observed that originates from quantum interference rather than a Lorentz force acting on the electrons. The influence of inelastic scattering on both the Hall resistance and the Aharonov-Bohm oscillations in the longitudinal resistance are examined.