Electron Transport Through Quantum Dots: An Unusual Kondo Effect

Abstract

Quantum-dot devices consist of a small electronic island connected by tunnel barriers to source and drain electrodes [1]. Due to on-site Coulomb repulsion, the addition of an electron to the island implies an energy change U=e ²/C, where C is the total capacitance of the island. Hence the number of confined electrons is a well-defined integer, N, that can be controlled by varying the voltage on a nearby gate electrode. Transport of electrons through the dot is allowed only at the transition points where the N- and (N+1)-states are both energetically accessible. Otherwise, N is constant and current transport is strongly suppressed. As a result, the linear conductance as a function of gate voltage exhibits a sequence of narrow resonances located at the transitions between consecutive electron numbers. This is known as Coulomb blockade [2,3]. If the tunnel conductance of the barriers, G _t is much smaller than the quantum conductance, e ²/h, transport can be well described in terms of single-electron processes, which are first-order in G _t . As Gt approaches ∼ e ²/h, however, higher-order tunneling events need to be taken into account. These are commonly known as co-tunneling events since they involve the simultaneous coherent tunneling of two or more electrons [4]. In the case of spin-less electrons, the co-tunneling contribution to conductance can be evaluated by perturbation theory. The leading term is a second-order in G _t. A more complicated scenario occurs when the spin degree of freedom is taken into account. If the total spin of the quantum dot is non-zero, the coherent superposition of virtual tunnel events can result in a strong correlation between the localised electrons and the free electrons in the leads. The physics of a quantum dot becomes similar to the physics of a magnetic impurity in a metal host, i.e. the Kondo effect.