Conductance of a Finite Quantum Wire Connected to Reservoirs

TL;DR

This paper investigates how the conductance of a finite quantum wire connected to reservoirs varies with wire length, impurity position, and temperature, revealing different behaviors in short and long wires.

Contribution

It provides a detailed analysis of conductance dependence on wire length, impurity position, and temperature, highlighting differences between short and long quantum wires.

Findings

Long wires exhibit conductance similar to infinite wires above a small energy scale.

Short wires have conductance independent of electron-electron interactions at higher temperatures.

At lower temperatures, short wires show conductance behavior akin to infinite wires.

Abstract

We study a finite quantum wire connected to external leads, and show that the conductance of the system significantly depends upon the length of the quantum wire and the position of the impurity in it. For a very long quantum wire and the impurity far away from its two ends, the conductance has the same behavior as that for an infinity quantum wire above some very little energy scale. However, for a very short quantum wire, the conductance is independent of the electron-electron interactions in it and closing to $e^{2}/(2\pi\hbar)$ in a higher temperature range. While, in a lower temperature range, the conductance shows the same property as that for an infinity quantum wire.