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 Haldaneʹs two-stage scaling theory. In the small limit of the ring size, we derive analytical expressions for the Kondo temperature TK and conductance at temperatures T⪢TK, as functions of the magnetic flux penetrating the ring. The flux dependence of TK is drastically changed when the energy level in the quantum dot is tuned electrostatically using the gate electrode attached to the dot. TK 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.