Aharonov-Bohm effect and resonances in the circular quantum billiard with two leads

TL;DR

This paper investigates how magnetic flux and lead geometry influence conductance in a circular quantum billiard, revealing Aharonov-Bohm effects through conductance fluctuations and suppression at specific flux values.

Contribution

It introduces a detailed analysis of the Aharonov-Bohm effect in a circular quantum billiard with different lead shapes and positions, highlighting flux-induced conductance modifications.

Findings

Conductance is affected by lead shape, position, and magnetic flux.

Aharonov-Bohm effect causes shifts and splittings in conductance fluctuations.

Conductance is suppressed to zero at flux = h/2e with 180° lead angle.

Abstract

We calculate the conductance through a circular quantum billiard with two leads and a point magnetic flux at the center. The boundary element method is used to solve the Schrodinger equation of the scattering problem, and the Landauer formula is used to calculate the conductance from the transmission coefficients. We use two different shapes of leads, straight and conic, and find that the conductance is affected by lead geometry, the relative positions of the leads and the magnetic flux. The Aharonov-Bohm effect can be seen from shifts and splittings of fluctuations. When the flux is equal to (h/2e) and the angle between leads is 180 degree, the conductance tends to be suppressed to zero in the low energy range due to the Aharonov-Bohm effect.