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ScienceWeek
MATERIALS SCIENCE: SINGLE-ELECTRON-TRANSISTOR KONDO EFFECT
The following points are made by A. Kogan et al (Science 2004 304:1293):
1) The observation of the Kondo effect in nanometer-size semiconductor structures (1,2) has caused a renaissance in the study of this quantum mechanical many-body phenomenon. It has been known since the 1930s (3) that a small concentration of magnetic impurities in a metal radically changes the conductance at low temperatures. However, only with the development of scaling and renormalization group theory techniques could the equilibrium properties of this strongly interacting system be predicted.
2) The Kondo problem involves the coupling between an unpaired electron localized on an impurity and the surrounding delocalized electrons in a metal. The coupling leads to screening of the localized electron's spin by the delocalized electrons with opposite spin, so that a spin-zero singlet is formed below the Kondo temperature (TK). In 1988 it was proposed on the basis of theory (4,5) that a quantum dot containing an unpaired electron coupled to conducting leads would be analogous to a magnetic impurity coupled to its host metal.
3) Such a quantum dot coupled to two leads (the drain and the source), with a gate electrode nearby, is a single-electron transistor (SET). In the absence of the Kondo coupling, the conductance of a SET at zero drain-source bias (Vds = 0) is very small, except for values of the gate voltage at which two charge states of the quantum dot are degenerate. Thus, the zero-bias conductance as a function of gate voltage consists of a series of Coulomb charging peaks, one for each electron added to the dot. The Kondo effect enhances the conductance between these peaks when the dot contains a spin, because the screening of the spin creates a new spin-entangled many-electron quantum state that extends from one lead through the dot into the other lead.
4) SETs provide new ways of studying the Kondo effect that are not possible with magnetic impurities in metals. In particular, the capability of applying a voltage between the two leads of a SET makes it possible to study the Kondo effect out of equilibrium. It has been predicted that one such nonequilibrium phenomenon, photon-assisted Kondo conductance, should provide a new spectroscopy of the Kondo singlet.
5) In summary: The authors measured the differential conductance of a single-electron transistor (SET) irradiated with microwaves. The spin-entangled many-electron Kondo state produces a zero-bias peak in the dc differential conductance if the quantum dot in the SET contains an unpaired electron. When the photon energy (hf) is comparable to the energy width of the Kondo peak and to (e) (the charge on the electron) times the microwave voltage across the dot, satellites appear in the differential conductance shifted in voltage by +- hf/e from the zero-bias resonance. The authors also observe an overall suppression of the Kondo features with increasing microwave voltage.
References (abridged):
1. D. Goldhaber-Gordon et al., Nature 391, 156 (1998)
2. S. M. Cronenwett, T. H. Oosterkamp, L. P. Kouwenhoven, Science 281, 540 (1998)
3. A. C. Hewson, The Kondo Problem to Heavy Fermions, vol. 2 of Cambridge Studies in Magnetism (Cambridge Univ. Press, Cambridge, 1993)
4. L. I. Glazman, M. E. Raikh, JETP Lett. 47, 452 (1988)
5. T. K. Ng, P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988)
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Related Material:
KONDO RESONANCE IN A SINGLE-MOLECULE TRANSISTOR
Notes by ScienceWeek
The "Kondo effect" is a large anomalous increase in the resistance of certain dilute alloys of magnetic materials in nonmagnetic hosts as the temperature is lowered. In general, the Kondo effect occurs when an impurity atom with an unpaired electron is placed in a metal, producing an interaction of localized electrons with delocalized electrons. The "Kondo temperature" is the temperature at which the Kondo effect predominates.
In general, in this context, the term "Coulomb blockade" refers to an effective blockade of quantum mechanical tunneling produced by specific energy barrier constraints.
The following points are made by W. Liang et al (Nature 2002 417:725):
1) When an individual molecule(1), nanocrystal(2-4), nanotube(5), or lithographically defined quantum dot is attached to metallic electrodes via tunnel barriers, electron transport is dominated by single-electron charging and energy-level quantization. As the coupling to the electrodes increases, higher-order tunneling and correlated electron motion give rise to new phenomena, including the Kondo resonance. To date, all of the studies of Kondo phenomena in quantum dots have been performed on systems where precise control over the spin degrees of freedom is difficult. Molecules incorporating transition-metal atoms provide powerful new systems in this regard, because the spin and orbital degrees of freedom can be controlled through well-defined chemistry.
2) The authors prepared devices by an extension of the methods previously used in constructing single-C60 (ref. 1) and single-nanocrystal transistors(3). Using electron-beam lithography, a narrow gold bridge was fabricated on an aluminum pad with a 3-nm oxide layer serving as a gate electrode. The electromigration-induced break-junction technique(1,3) was then used to create two closely spaced gold electrodes. Scanning electron microscope imaging and tunnel current measurements reveal that the narrowest gap between the two electrodes is consistently 1 nm.
3) In summary: The authors report the observation of the Kondo effect in single-molecule transistors, where an individual divanadium molecule serves as a spin impurity. The authors find that the Kondo resonance can be tuned reversibly using the gate voltage to alter the charge and spin state of the molecule. The resonance persists at temperatures up to 30 K and when the energy separation between the molecular state and the Fermi level of the metal exceeds 100 meV. The authors suggest the present study demonstrates that molecules can provide a Kondo system where critical parameters of Kondo physics, such as the spin and orbital degrees of freedom, are defined by chemical synthesis. With the recent advances of synthetic methodology, the preparation of molecular clusters possessing adjustable magnetic properties is becoming feasible. Future investigations of such species are expected to provide detailed insight into electron transport through a molecular system where the spin and orbital degeneracies are precisely controlled.
References (abridged):
1. Park, H. et al. Nano-mechanical oscillations in a single-C60 transistor. Nature 407, 57-60 (2000)
2. Klein, D. L. et al. A single-electron transistor made from a cadmium selenide nanocrystal. Nature 389, 699-701 (1997)
3. Park, H. et al. Fabrication of metallic electrodes with nanometer separation by electromigration. Appl. Phys. Lett. 75, 301-303 (1999)
4. Banin, U., Cao, Y., Katz, D. & Millo, O. Identification of atomic-like electronic states in indium arsenide nanocrystal quantum dots. Nature 400, 542-544 (1999)
5. Tans, S. J. et al. Individual single-wall carbon nanotubes as quantum wires. Nature 386, 474-476 (1997)
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Notes by ScienceWeek
Quantum dots are small electrically conducting regions, typically less than 1 micron in diameter, that contain from one to a few thousand electrons. Because of the small volume, the electron energies within the dot are quantized, and the behavior of the quantum dot is intermediate between that of an atom and that of a classical macroscopic object. Such intermediate systems are called "mesoscopic" systems, and in the past several years great attention has been devoted to the physics of such systems, since they apparently can provide insights into quantum systems in general. The electronic states in quantum dots can be probed by transport when a small *tunnel coupling is allowed between the dot and nearby source and drain leads.
Cronenwett et al (Science 1998 281:540) reported the realization of a tunable Kondo effect in small quantum dots, with the capability of switching a dot from a Kondo system to non-Kondo system as the number of electrons on the dot is changed from odd to even. The Kondo temperature can be tuned by means of a gate voltage as a single-particle energy state nears the Fermi energy. Measurements of the temperature and magnetic field dependence of a Coulomb-blockaded dot show good agreement with prediction of both equilibrium and nonequilibrium Kondo effects.
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