Nano Express
Analytical expression of Kondo temperature in quantum dot embedded in Aharonov-Bohm ring
Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
Nanoscale Research Letters 2011, 6:604 doi:10.1186/1556-276X-6-604
Published: 23 November 2011Abstract
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
TK are given as a function of magnetic flux Φ penetrating the ring. In this Kondo problem,
there are two characteristic lengths, 
and LK = ħvF = TK, where vF is the Fermi velocity and 
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 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 remarkably modulated by Φ in cases (ii) and (iii), whereas it hardly depends on
Φ in case (i).
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