Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets

TL;DR

This paper provides a detailed time-dependent simulation and analytical model of electronic Mach-Zehnder interferometers using edge-state wave packets, revealing how carrier localization affects interference patterns and transmission spectra.

Contribution

It introduces an exact numerical approach to simulate single-particle dynamics and develops an analytical model accounting for spatial dispersion effects in edge-state interferometry.

Findings

Damping of Aharonov-Bohm oscillations with arm length difference

Increased mean transmission linked to energy-dependent transmittance

Analytical model reproduces key effects observed in simulations

Abstract

We compute the exact single-particle time-resolved dynamics of electronic Mach-Zehnder interferometers based on Landau edge-states transport, and assess the effect of the spatial localization of carriers on the interference pattern. The exact carrier dynamics is obtained by solving numerically the time-dependent Schroedinger equation with a suitable 2D potential profile reproducing the interferometer design. An external magnetic field, driving the system to the quantum Hall regime with filling factor one, is included. The injected carriers are represented by a superposition of edge states and their interference pattern reproduces the results of Y.Ji et al.[Nature 422, 415 (2003)]. By tuning the system towards different regimes, we find two additional features in the transmission spectra, both related to carrier localization, namely a damping of the Aharonov-Bohm oscillations with increasing difference in the arms length, and an increased mean transmission that we trace to the energy-dependent transmittance of quantum point contacts. Finally, we present an analytical model, also accounting for the finite spatial dispersion of the carriers, able to reproduce the above effects.