Mode-Matching Technique for Transmission Calculations in Electron Waveguides at High Magnetic Fields

TL;DR

This paper introduces a mode-matching technique to analyze electron transmission in waveguides under high magnetic fields, addressing challenges and applying it to quantum boxes and meandering wires to study various quantum phenomena.

Contribution

A novel mode-matching method tailored for high magnetic field conditions in mesoscopic electron waveguides, enabling detailed transmission analysis in complex geometries.

Findings

Effective calculation of transmission coefficients at high magnetic fields.

Insights into Coulomb blockade and Aharonov-Bohm regimes.

Analysis of electron transport in bent quantum wires.

Abstract

In this paper we present a mode-matching technique to study the transmission coefficient of mesoscopic devices such as electron waveguides in the presence of high magnetic fields for different situations. A detailed study of the difficulties rising due to the presence of the magnetic field is given and the differences with the zero magnetic field case are stressed. We apply this technique to calculate the transmission at non-zero magnetic field of two completely different systems: a) a quantum box built up on a quantum wire (or electron waveguide) by means of two barriers and b) a meandering quantum wire, {\em i.e.}, a wire with changes in the guiding direction. In the former case we analyze the so-called {\em Coulomb Blockade} and {\em Aharanov-Bohm} regimes and in the latter one we focus on the realistic case of soft, circular bends joining the different sections of the wire.