The Kondo effect in a single-electron transistor

How localized electrons interact with delocalized electrons is a question central to many of the problems at the forefront of solid state physics. The simplest example, the Kondo effect, occurs when an impurity atom with an unpaired electron is placed in a metal, and the energy of the unpaired electron is far below the Fermi energy. At low temperatures a spin singlet state is formed between the unpaired localized electron and delocalized electrons at the Fermi energy. The consequences of this singlet formation were first observed over 60 years ago in metals with magnetic impurities, but full theoretical understanding was slow to come. Today, the situation is reversed: scaling theories and recent renormalization group calculations (T.A. Costi, A.C. Hewson (1994) J. Phys.: Cond. Mat. 6, 2519) can predict quantitatively the bonding strength of the singlet state, and the singletʹs effect on the conduction electrons at all temperatures. The detailed dependence of these properties on parameters such as the energy of the localized electron cannot be tested experimentally in the classic Kondo systems, since the relevant parameters cannot easily be tuned for impurities in a metal. Recently it has become possible to test these predictions with a new experimental approach — creating an artificial Kondo system by nanofabrication (D. Goldhaber-Gordon et al. (1998), Nature 391, 156). The confined droplet of electrons interacting with the leads of a single electron transistor (SET) is closely analogous to an impurity atom interacting with the delocalized electrons in a metal, as described in the Anderson model (Y. Meir, N.S. Wingreen, P.A. Lee, Phys. Rev. Lett. (1993) 70 2601–2604). We review here measurements on a new generation of SETs that display all the aspects of the Kondo effect: the spin singlet forms and causes an enhancement of the zero-bias conductance when the number of electrons on the artificial atom is odd but not when it is even. The singlet is altered by applying a voltage or magnetic field or by increasing the temperature, all in ways that agree with predictions (N.S. Wingreen, Y. Meir (1994), Phys. Rev. B 49, 11040; T.A. Costi, A.C. Hewson (1994), J. Phys.: Cond. Mat. 6, 2519; W. Izumida, O. Sakai, Y. Shimizu (1998), J. Phys. Soc. Jpn. 67; D. Goldhaber-Gordon et al. (1998), Nature 391, 156; D. Goldhaber-Gordon, J. Göres, M.A. Kastner, H. Shtrikman, D. Mahalu, U. Meirav (1998), Phys. Rev. Lett. 81, 5225).