Resonant Multilead Point-Contact Tunneling: Boundary State Formulation

TL;DR

This paper models resonant multilead point-contact tunneling using boundary state formulation, explicitly constructs boundary states for two and three leads, and analyzes electron transport with group theoretical insights.

Contribution

It introduces a boundary state approach to analyze multilead tunneling, extending previous single-lead models and providing exact correlation functions for complex lead configurations.

Findings

Electron transport is dominated by resonant tunneling at low frequencies.

Explicit boundary states are constructed for two and three leads.

Group structures like SU(2) and SU(3) are identified in the model.

Abstract

We study a model of resonant multilead point-contact tunneling by using the boundary state formulation. At a critical point the model is described by multi-flavor chiral fermions on an infinite line with a point contact interaction at the origin. By applying the folding procedure, previously developed for the model of resonant point-contact tunneling of a single lead, we map the model onto a non-chiral fermion model defined on the half line. The resonant point-contact tunneling interaction is transcribed into a non-local effective boundary interaction in the folded setup, where the boundary state formulation is applicable. We construct the boundary states for the models with two and three leads explicitly and evaluate the correlation functions of currents operators exactly. The electron transport between the leads is dominated by the resonant point-contact tunneling in the low frequency regime. We observe some $SU(2)$ and $SU(3)$ group theoretical structures, which may be useful to analyze more complex models.