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

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 ϕby 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/ |ε_0|, where v_F is the Fermi velocity and ε_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(ϕ) 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 ϕin cases (ii) and (iii), whereas it hardly depends on ϕin 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.