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

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 for the Kondo temperature T_K as a function of the Aharonov-Bohm phase 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=_F/ |ε₀|, where v_F is the Fermi velocity and ε₀ is the energy level in the quantum dot. The other is the screening length of the spin fluctuation, i.e., the size of the Kondo screening cloud, L_K=_F/T_K. We obtain different expressions for T_K for (i) L_cL_KL, (ii) L _cLL_K, and (iii) LL_cL_K, where L is the size of the ring. T_K is markedly modulated by in cases (ii) and (iii), whereas it hardly depends on in case (i). We also derive logarithmic corrections to the conductance at temperature TT_K and an analytical expression for the conductance at TT_K, on the basis of the scaling analysis.