Analytical expression of Kondo temperature in quantum dot embedded in Aharonov-Bohm ring

We theoretically study the Kondo effect in a quantum dot embedded in an Aharonov-Bohm ring, using the "poor man's" scaling method. Analytical expressions of the Kondo temperature T _K are given as a function of magnetic flux F penetrating the ring. In this Kondo problem, there are two characteristic lengths, L _c = h{stroke}v _fF/{pipe}ε̃0{pipe} and L _K = h{stroke}v _F = T _K, where v _F is the Fermi velocity and ε0 is the renormalized energy level in the quantum dot. The former is the screening length of the charge fluctuation and the latter is that of the spin fluctuation, i.e., size of Kondo screening cloud. We obtain diferent expressions of T _K(F) for (i) L _c ≪ L _K ≪ L, (ii) L _c ≪ L ≪ L _K, and (iii) L ≪ L _c ≪ L _K, where L is the size of the ring. T _K is remarkably modulated by F in cases (ii) and (iii), whereas it hardly depends on F in case (i). PACS numbers:.