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BOX 1.6 Kondo Effect in an Artificial Atom

The analogy of a quantum dot to an artificial atom has been extended with the demonstration that a quantum dot interacts with nearby metallic leads in much the same way that a single magnetic impurity interacts with a surrounding metal—in the phenomenon known as the Kondo effect. Kondo behavior was found recently in a single-electron transistor, which consists of a semiconductor quantum dot sandwiched between two metallic leads. This miniature device turns on and off as individual electrons controlled by a nearby gate flow on and off the dot.

The theory of the Kondo effect was developed in the early 1960s to explain a long-standing puzzle about the resistance of some metals: Why does the resistance start to increase as the metal is cooled below a certain temperature? According to the picture that has emerged, the increased resistance comes from magnetic impurities whose local magnetic moments couple antiferromagnetically to those of the conduction electrons. The coupling becomes stronger and increasingly impedes the flow of current as the temperature is decreased.

The concept of the Kondo effect is intriguing because it involves the pairing of a localized electron with an electron in an extended state in the metal. Its manifestation in a quantum dot is no less compelling. Although interactions between electrons in quantum dots are known to be important, the Kondo phenomenon is a true many-body effect requiring a coherent state resulting from the coupling of the localized electrons in the dot and a continuum of electron states outside the dot.

Experimenters have tried to see a manifestation of the Kondo effect in quantum dots ever since its presence was predicted in the late 1980s, but succeeded only recently. Kondo behavior for a single spin had been observed in resonant tunneling through a charge trap created unintentionally in a point contact. A collaborative experiment involving the Massachusetts Institute of Technology (MIT) and the Weizmann Institute in Israel has attracted additional interest because it shows the Kondo effect in a way that will allow one to explore the phenomenon in a system with many tunable parameters.

Kondo-like effects in quantum dots are observable only under a very narrow set of conditions. To see the effects of coupling between the dot and the leads, one needs to make the rate for tunneling of electrons between the dot and the leads as high as possible. The higher this rate, the higher the temperature at which the Kondo effect survives. However, if one makes the rate too high, the electrons on the dot become completely delocalized. With a smaller dot, the electrons are more localized to begin with, and a higher rate is possible.

To make a semiconductor quantum dot, one starts with a two-dimensional electron gas of electrons confined in a plane at the boundary between two semiconducting materials. Additional semiconductor layers go on top of this boundary region. At the top of the structure, one lays down electrical gates; the electrical potentials created by these gates confine the electrons in the plane below the gates to a very small region. Typically the quantum dots lie 100 nm below the surface. The MIT-Weizmann team made a much smaller artificial atom by forming the two-dimensional electron gas closer to the surface.

The conductance of a single electron transistor displays a peak when the sum of the voltage (Vg), on one of the gates and of the voltage (Vds) between the two leads on either side of the dot, each multiplied by the appropriate capacitance, is large enough to add an electron to the dot. A gray-scale plot of the conductance

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