Schematic drawing of the density of states in the lead for the reduced model, in situations (a) Lc ≪ LK ≪ L, (b) Lc ≪ L ≪ LK, and (c) L ≪ Lc ≪ LK, where L is the size of the AB ring, Lc is the screening length of charge fluctuation, and LK is that of spin fluctuation, i.e., size of Kondo screening cloud. The half of band width is D1 ≃ |ε0| in the second stage of scaling. In situation (a), εT ≪ TK ≪ |ε0|. The oscillating part of ν(εk) is averaged out in the integration of scaling equations. In consequence, the Kondo temperature TK does not depend on the ring size nor AB phase ϕ of the magnetic flux penetrating the ring. In situation (b), TK ≪ εT ≪ |ε0|. Then the Thouless energy εT acts as the high energy cut off. ϕ-dependence of TK is determined by the ratio of εT to TK. In situation (c), TK ≪ |ε0| ≪ εT. The density of states is almost constant. In this case, TK reflects the density of states at the Fermi level, ν(0).
Yoshii and Eto Nanoscale Research Letters 2011 6:604 doi:10.1186/1556-276X-6-604