Tunneling Through A Quantum Dot

Abstract

The recent observation of the Kondo effect in ultra small quantum dots [1, 2, 3, 4] has opened exciting possibilities in the study of the out-of-equilibrium Kondo effect for a single impurity. The theoretical framework for studying the tunneling through a quantum dot is that of the nondegenerate Anderson impurity model [5], described schematically in Fig. 1. This model has three main ingredients: (i) A localized level with energy ɛ _d , corresponding to the dot level closest to the chemical potential of the leads; (ii) An on-site repulsion U ∼ e ²/C, representing the charging energy on the dot (C is the dot capacitance); and (iii) Two hybridization matrix elements t _L and t _R to the left and right leads, respectively. If −ɛ _d , ɛ _d + U ≫ Γ where Γ = πρ ^L t ²_L + πρ ^R t ²_R is the broadening of the level (ρ _α is the conduction-electron density of states in lead α), then a local moment will form on the dot at temperatures T < T _LM ∼ ∣ɛ _d ∣/k _B . In this regime, charge fluctuations are suppressed on the dot, and one is dealing with co-tunneling transport. The Anderson model is then equivalent to the spin-1/2 Kondo model [6]. Upon further lowering the temperature, a many-body screening of the local moment takes place, known as the Kondo effect.