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ScienceWeek
NANOTECHNOLOGY: ON CORRELATED ELECTRONS
The following points are made by R.M. Potok and D. Goldhaber-Gordon (Nature 2005 434:451):
1) The behavior of electrons is difficult to predict. Undergraduates routinely calculate the quantum states of a hydrogen atom, but even a helium atom with only two electrons displays complex dynamics. How much more complex are solids, with electrons in the billions. Nanotechnology now enables researchers to create controlled, or tunable, models of electronic behavior in solids. Recent work[1] presents perhaps the most sophisticated example of this approach to date, studying the flow of electrons through a carbon nanotube that is made to act like an exotic magnetic atom.
2) In attempting to explain the electronic properties of materials, theorists often construct "microscopic" models, comprising electrons that can move freely (become delocalized), sit on localized sites, and make transitions between these states. Such models offer powerful insights but also have drawbacks when applied to conventional bulk materials. In particular, electrons on many sites can interact with each other, making complete calculations impractical; and parameters such as an electron's tunnelling rate and interaction strength are not tunable, and can be difficult to measure precisely. Nanotechnology can remedy these limitations: by building submicrometer-sized structures in which one or a few electrons are isolated, researchers can know everything about the relevant electronic states, and can study electrons at a single site. Perhaps most importantly, nearly all of the significant parameters can be designed, measured and often tuned in situ.
3) The interaction of mobile electrons with magnetic impurities -- atoms or ions with a non-zero magnetic moment -- in a host metal has been a theme in solid-state physics for decades. In 1961, Anderson proposed that a magnetic impurity could be modelled as an electronic quantum state localized at a single site within a crystal. According to the Pauli exclusion principle, the site can be occupied by up to two electrons (with opposite spins), but Coulomb repulsion can make it energetically favorable for only one electron with arbitrary spin to reside there. If its spin opposes that of a nearby delocalized electron, the localized electron can lower its energy by tunnelling off the site and back on again. At low temperature, the electron ensures that it can tunnel by pairing with a single delocalized electron of opposite spin to form a state of zero total spin (a "singlet") -- a phenomenon known as the "Kondo effect". In Anderson's microscopic model, the stability of the singlet ground state (and hence its temperature-dependent effect on electrical resistance) can be calculated in terms of basic parameters such as the binding energy of the localized electron and its rate of tunnelling between localized and delocalized states[2].
4) Now, however, experimental physicists can design and fabricate single artificial magnetic impurities, such as semiconductor quantum dots[3], molecules[4,5] and nanotubes with substantial control over the basic parameters of Anderson's model. In each of these systems, conducting leads attached to the artificial impurity play the same role as the host metal of a traditional magnetic impurity. Electron flow from one lead to the other through the artificial impurity serves as a powerful probe of local electronic states. The tunability of such nanostructures, and their amenability to electrical measurement, have allowed highly quantitative studies of the Kondo effect, and have spurred the construction of new Kondo systems not described by the minimal Anderson or Kondo model.
References (abridged):
1. Jarillo-Herrero, P. et al. Nature 434, 484-488 (2005)
2. Haldane, F. D. M. Phys. Rev. Lett. 40, 416-419 (1978)
3. Goldhaber-Gordon, D. et al. Nature 391, 156-159 (1998)
4. Liang, W. et al. Nature 417, 725-729 (2002)
5. Park, J. et al. Nature 417, 722-725 (2002)
Nature http://www.nature.com/nature
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Related Material:
MATERIALS SCIENCE: ON CORRELATIONS IN MATERIALS
The following points are made by G. Kotliar and D. Vollhardt (Physics Today 2004 March):
1) Modern solid-state physics explains the physical properties of numerous materials, such as simple metals and some semiconductors and insulators. But materials with open d and f electron shells, where electrons occupy narrow orbitals, have properties that are harder to explain. In transition metals, such as vanadium, iron, and their oxides, for example, electrons experience strong Coulombic repulsion because of their spatial confinement in those orbitals. Such strongly interacting or "correlated" electrons cannot be described as embedded in a static mean field generated by the other electrons.(1) The influence of an electron on the others is simply too pronounced for each to be treated independently.
2) The effect of correlations on materials properties is often profound. The interplay of the d and f electron internal degrees of freedom -- spin, charge, and orbital moment -- can exhibit a whole zoo of exotic ordering phenomena at low temperatures. That interplay makes strongly correlated electron systems extremely sensitive to small changes in external parameters, such as temperature, pressure, or doping.
3) The dramatic effects can range from huge changes in the resistivity across the metal-insulator transition in vanadium oxide and considerable volume changes across phase transitions in actinides and lanthanides, to exceptionally high transition temperatures (above liquid-nitrogen temperatures) in superconductors with copper-oxygen planes. In materials called "heavy fermion systems", mobile electrons at low temperature behave as if their masses were a thousand times the mass of a free electron in a simple metal. Some strongly correlated materials display a very large thermoelectric response; others, a great sensitivity to changes in an applied magnetic field -- an effect dubbed "colossal magnetoresistance". Such properties make the prospects for developing applications from correlated-electron materials exciting. But the richness of the phenomena, and the marked sensitivity to microscopic details, makes their experimental and analytical study all the more difficult.
4) To understand materials made up of weakly correlated electrons -- silicon or aluminum, for example -- band theory, which imagines electrons behaving like extended plane waves, is a good starting point. That theory helps capture the delocalized nature of electrons in metals. Fermi liquid theory describes the transport of conduction electrons in momentum space and provides a simple but rigorous conceptual picture of the spectrum of excitations in a solid. In that description, excited states consist of independent quasiparticles that exist in a one-to-one correspondence to states in a reference system of noninteracting Fermi particles plus some additional collective modes. To calculate the various microscopic properties of such solids, we have accurate quantitative techniques at our disposal. Density functional theory (DFT),(2) for example, allows us to compute the total energy of some materials with remarkable accuracy, starting merely from the atomic positions and charges of the atoms.
5) However, the independent-electron model and the DFT method are not accurate enough when applied to strongly correlated materials. The failure of band theory was first noticed in insulators such as nickel oxide and manganese oxide, which have relatively low magnetic-ordering temperatures but large insulating gaps. Band theory incorrectly predicts them to be metallic when magnetic long-range order is absent.(3-5)
References (abridged):
1. For a recent review of the electronic correlation problem, see M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998); for an early review of fermionic correlations, see D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984)
2. R. O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)
3. W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)
4. E. Mueller-Hartmann, Z. Phys. B: Condens. Matter 74, 507 (1989); U. Brandt, C. Mielsch, Z. Phys. B: Condens. Matter 75, 365 (1989); V. Jani , Z. Phys. B: Condens. Matter 83, 227 (1991)
5. A. Georges, G. Kotliar, Phys. Rev. B 45, 6479 (1992)
Physics Today http://www.physicstoday.org
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CONDENSED MATTER PHYSICS: ON CORRELATED ELECTRONS
Notes by ScienceWeek:
One sure thing in science is that whenever the prevailing authorities in a field announce that nearly all problems have been solved and that everyone ought to pack up and go home, that is the time you need to bet all your capital that within a short time an important discovery or technological innovation will suddenly open an entire reservoir of new problems that make the field young again. In science, "maturity" in a field is usually doomed to be ephemeral, and every scientist knows examples of this in his own domain.
An instance was the so-called "maturity" of solid-state physics in the 1970s, when independent electron approximations worked well for most semiconductors and metals, the phase transition problem seemed solved, and the fundamentals of magnetism, ferroelectricity, and superconductivity appeared to be known. Within a short time, however, as if to slam the authorities who had pronounced solid-state physics a closed book, there came discoveries of a variety of new materials whose behavior could not be understood at all with traditional ideas.
These materials have in common the apparent dominant role played by electron-electron interaction effects, and such systems are categorized under the general rubric of "highly correlated electron systems". Examples of such systems are transition metal oxides, including copper oxide high-temperature superconductors, heavy fermion metals, organic charge transfer compounds, and one-and two-dimensional electron gas systems. In addition to intriguing possible technological applications, the behaviors of these systems appear to present profound challenges in fundamental physics.
The following points are made by Yoshinori Tokura (Physics Today 2003 July):
1) As with any other quantum particle, an electron exhibits wave-like and particle-like characteristics. Which aspect predominates in a solid depends on how an electron interacts with its neighbors. According to the *Bloch theorem, for instance, an electron placed in a periodic lattice behaves like an extended plane wave. However, when the number of free electrons in a solid becomes comparable to the number of the constituent atoms and the mutual electron-electron interaction becomes strong, electrons may lose their mobility.
2) The dual nature is most apparent in correlated-electron systems, such as the transition-metal oxides in which electron interactions strongly determine electronic properties. In the transition-metal ions, for example, /d/ electrons experience competing forces: Coulombic repulsion tends to localize individual electrons at atomic lattice sites, while hybridization with the oxygen /p/ electron states tends to delocalize the electrons. The subtle balance makes many of the transition-metal oxides excellent resources for studying and taking advantage of the metal-insulator transition that can accompany dramatic changes in a system's electronic properties.
3) An electron in a solid has three attributes that determine its behavior: charge, *spin, and orbital symmetry. One can imagine an orbital, which represents the electron's probability-density distribution, as the shape of an electron cloud in a solid. The charge, spin, and orbital degrees of freedom -- and their coupled dynamics -- can produce complex phases such as liquid-like, crystal-like, and liquid-crystal-like states of electrons, and phenomena such as electronic phase separation and pattern formation.
4) The correlation of electrons in a solid produces a rich variety of states, typically through the interplay between magnetism and electrical conductance. That interplay has itself been a long-standing research topic among condensed matter physicists. But since the discovery of copper-oxide high-temperature *superconductors in 1986, a more general interest in the *Mott transition -- the metal-insulator transition in a correlated-electron system -- has been emerging. The high-temperature copper oxides are composed of CuO2 sheets that are separated from each other by ionic "blocking layers". Although it has one conduction electron (or hole) per Cu site, each CuO2 sheet is originally insulating because of the large electron correlation. That behavior is typical of the Mott insulator state, in which all the conduction electrons are tied to the atomic sites. The superconducting state emerges when holes from the blocking layers dope the CuO2 layers in a way that alters the number of conduction electrons and triggers the Mott transition. Researchers believe that the strong *antiferromagnetic correlation, which originates in the Mott-insulating CuO2 sheets and persists into the metallic state, is most responsible for the mechanism of high-temperature superconductivity.
Physics Today http://www.physicstoday.org
ScienceWeek http://scienceweek.com
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