Coulomb Blockade-Effects on Quantization of Charge and Persistent Current in a Luttinger-Liquid Ring

TL;DR

This paper investigates how Coulomb blockade effects influence charge quantization and persistent currents in a Luttinger Liquid ring, revealing step-like behaviors in charge and current related to the LL parameter, which can be experimentally measured.

Contribution

It introduces a detailed analysis of Coulomb blockade effects on charge and current quantization in a Luttinger Liquid ring, including spin and long-range interactions.

Findings

Charge and persistent current exhibit step-like dependence on gate voltage.

Step positions are determined by the Luttinger Liquid parameter lpha.

The LL parameter lpha can be directly measured from these steps.

Abstract

We show that in a ring-shaped Luttinger Liquid (LL) in contact with an electron reservoir --- the chemical potential in the ring being controlled by a gate voltage $V_g$ --- both the average ring charge and the persistent current in the ring are step-like functions of $V_g$ at low temperatures. The step positions are determined by the LL parameter $\alpha=v_F/s$, which therefore can be directly measured. We study electrons both with and without spin, taking into account long-range interactions in the ring.