Magnetic flux and gate-voltage dependence of Kondo effect in quantum dot embedded in Aharonov-Bohm ring

The Kondo effect is examined in a quantum dot embedded in an Aharonov-Bohm (AB) ring, based on the Haldane's two-stage scaling theory. In the small limit of the ring size, we derive analytical expressions for the Kondo temperature T_K and conductance at temperatures T ≫ T_K, as functions of the magnetic flux penetrating the ring. The flux dependence of T_K is drastically changed when the energy level in the quantum dot is tuned electrostatically using the gate electrode attached to the dot. T_K hardly depends on the flux at the midpoint in the Kondo valley of the Coulomb oscillation, whereas its flux dependence becomes remarkable apart from the midpoint.