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