Transient and finite size effects in transport properties of a quantum wire

TL;DR

This paper investigates how finite length affects the time-dependent backscattered current in a quantum wire with a local barrier, revealing complex temporal patterns and improving the realism of Luttinger parameter estimation.

Contribution

It extends previous models by incorporating finite size effects, showing new temporal behaviors and refining methods to determine the Luttinger parameter K.

Findings

Identification of two regimes based on energy scales

Discovery of temporal steps with relaxation and revivals

Finite size effects modify infinite wire results

Abstract

We study the time-dependent backscattered current produced in a quantum wire when a local barrier is suddenly switched on. Previous investigations are improved by taking into account the finite length of the device. We establish two different regimes in terms of the relationship between the energy scales associated to the voltage and the length of the system. We show how previous results, valid for wires of infinite length, are modified by the finite size of the system. In particular our study reveals a rich pattern of temporal steps within which the current suffers an initial relaxation followed by temporary revivals. By employing both analytical and numerical methods we describe peculiar features of this structure. From this analysis one concludes that our results render a recently proposed approach to the determination of the Luttinger parameter K, more realistic.