Open Access Nano Express

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

Ryosuke Yoshii* and Mikio Eto

Author affiliations

Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

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Citation and License

Nanoscale Research Letters 2011, 6:604  doi:10.1186/1556-276X-6-604

Published: 23 November 2011

Abstract

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, <a onClick="popup('http://www.nanoscalereslett.com/content/6/1/604/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/6/1/604/mathml/M1">View MathML</a> and LK = ħvF = TK, where vF is the Fermi velocity and <a onClick="popup('http://www.nanoscalereslett.com/content/6/1/604/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/6/1/604/mathml/M2">View MathML</a> 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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