The Kondo state in quantum point contacts and the local moment in semiconductor quantum dots - two sides of the same phenomenon

TL;DR

This paper unifies the understanding of the Kondo state in quantum point contacts and local moments in semiconductor quantum dots, explaining experimental phenomena through a virtual Kondo state and a nearly symmetric Anderson model.

Contribution

It introduces a unified theoretical framework linking quantum point contacts and quantum dots via a virtual Kondo state and solves the Anderson model for finite systems.

Findings

Large level spacing $igtriangleup^* o (U\,\Gamma)^{1/2} \,\gg\, \Delta$

Explains 0.7 conductance anomaly in point contacts

Matches experimental observations of level spacing periodicity

Abstract

This is a three step work: i) we explain why quantum point contacts are similar to ballistic quantum dots; ii) we introduce the virtual Kondo state in both systems; iii-1st) this state explains 0.7 structure in point contacts; iii-2nd) formation of the local moment on this state is described by the nearly symmetric Anderson model, we solve it for finite size system having in mind quantum dots. We found one large level spacing $\Delta^\ast \propto (U\Gamma)^{1/2}\gg \Delta$, where $U$ is the charging energy of the virtual state, $\Gamma$ is the spectral width of this state and $\Delta$ is the mean level spacing of whole system. The theory explains periodicity of abnormal level spacing vs gate potential. The theory is in agreement with many experiments.