Friedel Sum Rule for single channel quantum wire

TL;DR

This paper investigates how a point defect influences the Friedel sum rule in a single-channel quantum wire, revealing unique features not observed in higher dimensions, with implications for quantum device design.

Contribution

It demonstrates the distinct effects of a delta impurity on the Friedel sum rule in a quantum wire, highlighting novel scattering features specific to 1D systems.

Findings

Unique scattering features in quantum wires due to point defects

Altered Friedel sum rule behavior in 1D systems

Implications for quantum interference device design

Abstract

Elastic scattering in a quantum wire has several novel features not seen in 1D, 2D or 3D. In this work we consider a single channel quantum wire as its application is inevitable in making devices based on quantum interference effects. We consider a point defect or a single delta function impurity in such a wire and show how some of these novel features affect Friedel-sum-rule (FSR) in a way, that is quite unlike in 1D, 2D and 3D.