Chiral Fermion and Boundary State Formulation: Resonant Point-Contact Tunneling

TL;DR

This paper models resonant point-contact tunneling in a Luttinger-liquid lead using boundary state formulation, mapping it onto a non-chiral model and analyzing boundary interactions and current correlations.

Contribution

It introduces a boundary state formulation for a simple resonant tunneling model, explicitly constructing the boundary state and analyzing frequency-dependent effects.

Findings

Boundary interaction acts more strongly on lower frequency modes

Explicit boundary state construction for the model

Evaluation of current correlation functions

Abstract

We study a model of resonant point-contact tunneling of a single Luttinger-liquid lead, using the boundary state formulation. The model is described by a single chiral Fermion in one dimensional space with one point contact interaction at the origin. It is the simplest model of this type. By folding the infinite line we map the model onto a non-chiral model on the half infinite line and transcribe the point-contact tunneling interaction into a boundary interaction. The tunneling interaction yields a non-local effective action at the boundary. We explicitly construct the boundary state and evaluate the current correlation functions. The contact interaction is shown to act on the lower frequency modes more strongly.