Generalized waveguide approach to tight-binding wires: Understanding large vortex currents in quantum rings

TL;DR

This paper extends the quantum waveguide method to tight-binding models, enabling analysis of internal currents and vortex phenomena in molecular rings, with a simple formula predicting vortex onset.

Contribution

It introduces a generalized waveguide approach for tight-binding models and derives a Landauer-like formula for internal bond currents in molecular devices.

Findings

Predicts large vortex currents in quantum rings.

Derives a simple formula for vortex regime onset.

Provides a method to analyze internal conductance in molecular systems.

Abstract

We generalize the quantum waveguide approach to H\"uckel or tight-binding models relevant to unsaturated $\p$ molecular devices. A Landauer-like formula for the current density through {\em internal} bonds is also derived which allows for defining a local conductance. The approach is employed to study internal circular currents in two-terminal rings. We show how to predict the occurrence and the nature of large vortex currents in coincidence with vanishingly small currents in the leads. We also prove a remarkably simple formula for the onset of a vortex regime.