The interplay between electron-electron interactions and impurities in one-dimensional rings

TL;DR

This study uses Monte Carlo simulations to explore how electron-electron interactions and impurities affect persistent current and charge stiffness in one-dimensional rings, revealing a crossover behavior influenced by impurity strength and temperature.

Contribution

It provides a detailed analysis of the interplay between interactions and impurities in 1D rings, highlighting the crossover from impurity enhancement to screening effects.

Findings

Interactions decrease current and stiffness with weak impurities.

Interactions screen impurities at strong impurity potentials.

Persistent current and stiffness peak at a characteristic temperature.

Abstract

The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak and strong impurity limits. For weak impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single impurity study.