Resonant Tunneling and Persistent Current of a Non-interacting and Weakly Interacting One-dimensional Electron Gas

TL;DR

This paper investigates the behavior of persistent current in a one-dimensional ring with two tunnel barriers, revealing conditions for true and semi-resonance phenomena influenced by electron interactions and temperature effects.

Contribution

It introduces a detailed analysis of resonant behaviors in a weakly interacting 1D electron ring with two barriers, highlighting the impact of geometry and interactions on resonance types.

Findings

True resonance is independent of barrier transparency.

Semi-resonance is favored by repulsive interactions.

Temperature can suppress semi-resonance peaks.

Abstract

The persistent current for a one-dimensional ring with two tunnel barriers is considered in the limit of weakly interacting electrons. In addition to a small off-resonance current, there are two kinds of resonant behavior; (i) a current independent of the barrier transparency (true resonance) and (ii) a current analogous to the one for a ring with only a single barrier (``semi''-resonance). For a given barrier transparency one or the other type of resonant behavior is realized depending on a geometric factor (ratio of interbarrier distance to ring circumference) and on the strength of the electron-electron interaction. It is shown that a repulsive interaction favours the``semi''-resonance behavior. For a small barrier transparency the ``semi''-resonance peaks are easily washed out by temperature whereas the true resonance peaks survive.