Scaling analysis of Kondo screening cloud in a mesoscopic ring with an embedded quantum dot

TL;DR

This paper analyzes how the Kondo screening cloud in a mesoscopic ring with an embedded quantum dot is affected by magnetic flux, deriving analytical expressions for the Kondo temperature and conductance modulations.

Contribution

It provides analytical expressions for the Kondo temperature as a function of magnetic flux and different screening length regimes, advancing understanding of Kondo physics in mesoscopic rings.

Findings

T_K is modulated by magnetic flux in certain length regimes.

Different expressions of T_K() are derived for various length scale hierarchies.

Conductance behavior is characterized at temperatures above and below T_K.

Abstract

The Kondo effect is theoretically studied in a quantum dot embedded in a mesoscopic ring. The ring is connected to two external leads, which enables the transport measurement. Using the "poor man's" scaling method, we obtain analytical expressions of the Kondo temperature T_K as a function of the Aharonov-Bohm phase \phi by the magnetic flux penetrating the ring. In this Kondo problem, there are two characteristic lengths. One is the screening length of the charge fluctuation, L_c=\hbar v_F/ |\epsilon_0|, where v_F is the Fermi velocity and \epsilon_0 is the energy level in the quantum dot. The other is the screening length of spin fluctuation, i.e., size of Kondo screening cloud, L_K=\hbar v_F/ T_K. We obtain different expressions of T_K(\phi) for (i) L_c \ll L_K \ll L, (ii) L_c \ll L \ll L_K, and (iii) L \ll L_c \ll L_K, where L is the size of the ring. T_K is markedly modulated by \phi in cases (ii) and (iii), whereas it hardly depends on \phi in case (i). We also derive logarithmic corrections to the conductance at temperature T\gg T_K and an analytical expression of the conductance at T\ll T_K, on the basis of the scaling analysis.