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arXiv:cond-mat/9509162

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

Ilya V. Krive, P. Sandström, Robert I Shekhter, M. Jonson

Published Sep 26, 1995• 0 citations
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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 $α=v_F/s$, which therefore can be directly measured. We study electrons both with and without spin, taking into account long-range interactions in the ring.

DOI
10.48550/arxiv.cond-mat/9509162

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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 VgV_gVg​ --- both the average ring charge and the persistent current in the ring are step-like functions of VgV_gVg​ at low temperatures. The step positions are determined by the LL parameter α=vF/sα=v_F/sα=vF​/s, which therefore can be directly measured. We study electrons both with and without spin, taking into account long-range interactions in the ring.
We propose a method to detect a Luttinger liquid (LL)-like behavior of a quasione-dimensional ring of electrons that does not depend on a transport measurement.Rather, a Coulomb blockade-induced quantization of the persistent current and excess charge in a ring of interacting electrons are shown to depend on the interaction strength.Both the average ring charge and the persistent current are step-like functions of an applied gate voltage at low temperatures.The step positions are determined by the LL parameter α, which therefore can be directly measured.
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We consider a ring of strongly interacting electrons connected to two external leads by tunnel junctions. By studying the positions of conductance resonances as a function of gate voltage and magnetic flux, the interaction parameter ggg can be determined experimentally. For a finite ring the minimum conductance is strongly influenced by device geometry and electron-electron interactions. In particular, if the tunnel junctions are close to one another, the interaction-related orthogonality catastrophe is suppressed and the valley current is unexpectedly large.
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