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ScienceWeek
MATERIALS SCIENCE: ON ELECTRON GEOMETRICAL FRUSTRATION
The following points are made by N.P. Ong and R.J. Cava (Science 2004 305:52):
1) For electrons on a triangular lattice, the concept of "geometrical frustration" in the face of strong electric (Coulomb) mutual repulsion is a crucial, decisive factor that shapes their behavior. In an insulating material, the Coulomb repulsion force is relieved if each electron can point its spin antiparallel to that of its nearest neighbors. On most lattices, this is readily implemented and leads to a state in which spins alternate up and down along each bond direction (the Neel state). On a triangular lattice, however, the geometric arrangement frustrates such ideal regularity. Two of the three electrons in each triangle must share the same spin orientation. At a temperature of 0 K, the spins remain in a disordered quantum state with no discernible pattern, often called a "spin liquid."
2) Understanding the spin-liquid state is a major goal of the science of strongly correlated materials (materials in which the Coulomb force is very large relative to familiar metals such as gold). Further, the problem is greatly enriched if the electrons are free to hop between sites and carry an electrical current. Does this electron itinerancy relieve the geometrical frustration? Does the disordered quantum spin state leave its imprint on the conductivity? Can these electrons form "Cooper" pairs to produce superconductivity?
3) These theoretical questions are relevant to recent experiments (1-5) on the cobalt oxide NaxCoO2 in which the Co ions define a layered triangular lattice (and the Na ions are sandwiched between CoO2 layers). Initial results (1) obtained on as-grown materials with x close to 2/3 showed that the material is an excellent, if unremarkable, electrical conductor. However, its magnetic susceptibility -- a measure of how well a magnetic field aligns the electron spins -- is decidedly odd. In a metal, the fraction of electron spins that can be field-aligned is very small and steadily shrinks to zero with decreasing temperature. By contrast, in NaxCoO2, the susceptible spin population just equals the population of carriers with positive charge ("holes") and stays unchanged with falling temperature (2,3). The susceptibility resembles that of an insulator that is frustrated from attaining the ordered Neel state as described above. This Janus-like ambivalence -- metallic in charge conduction but insulator-like in spin alignment -- has been dubbed a "Curie-Weiss metal" (4).
4) Equally puzzling was the finding that NaxCoO2 has an enhanced thermopower.(1) In metals, an electrical (or charge) current involves the flow of electrons, but because electrons carry entropy, the charge current is accompanied by an electronic heat current. The thermopower measures the ratio of the heat to the charge current. As a rule, the thermopower in metals is very small because in an electric field, nearly equal populations of electrons and holes flow in opposite directions. A recent experiment (3) has unearthed a vital clue to the large thermopower in NaxCoO2. At 2 K, a magnetic field completely suppresses the thermopower to zero (this is possibly the first such observation in any solid). Quantitative estimates confirm that the vanishing of the thermopower coincides with the complete alignment of the spins by the field (3). By inference, this implies that the thermopower derives mostly from the spin entropy carried by the holes in the Curie-Weiss phase.
References (abridged):
1. I. Terasaki, Y. Sasago, K. Uchinokura, Phys. Rev. B 56, 12685 (1997)
2. R. Ray, A. Ghoshray, K. Ghoshray, S. Nakamura, Phys. Rev. B 59, 9454 (1999)
3. Y. Wang, N. S. Rogado, R. J. Cava, N. P. Ong, Nature 423, 425 (2003)
4. M.-L. Foo et al., Phys. Rev. Lett. 92, 247001 (2004)
5. K. Takada et al., Nature 422, 53 (2003)
Science http://www.sciencemag.org
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CHEMICAL PHYSICS: ON QUANTUM ORDER IN METALS
The following points are made by H.Q. Yuan et al (Science 2003 302:2104):
1) Quantum order in metals, of which the phenomenon of superconductivity provides one of the most explicit examples, can involve subtle and often unforeseen collective mechanisms. In strongly correlated electron systems, the strength of the local electrostatic Coulomb repulsion present between the charge carriers, when compared to the width of their often-narrow energy bands, precludes the most common kind of superconductivity, which is based on bound electron pairs coupled by deformations of the lattice. However, superconductivity of more subtle origins is observed in many of these complex metals, and the quest for understanding its structure and origin is of interest to a wide community.
2) The phase diagrams that arise when ordering temperatures (magnetic, superconducting, or otherwise) are plotted against external control parameters (such as pressure, magnetic field, or composition) are important tools for recognizing the patterns that emerge in correlated electron systems. Numerous materials, including many organic, cuprate, and heavy fermion superconductors, follow very similar phase diagrams, in which superconductivity is closely linked to magnetism. In particular, in a number of studies in f-electron compounds, which have tracked magnetism and superconductivity as functions of lattice density through the application of hydrostatic pressure, unconventional superconductivity in very pure samples has been tied clearly to the threshold of magnetism (1-3).
3) These findings suggest that the mechanism that forms Cooper pairs can be of magnetic origin: On the verge of magnetic order, the magnetically soft electron liquid can mediate spin-dependent attractive interactions between the charge carriers. The resulting phase diagram has been observed in several heavy fermion compounds, such as CePd2Si2, CeIn3, and CeRh2Si2, and roughly similar behavior has been found in the recently discovered Ce 1-1-5 compounds. The material which started the field, however, the archetypal heavy fermion superconductor CeCu2Si2 (4), has so far escaped a similar explanation. Although an analogous magnetic quantum critical point has been demonstrated in CeCu2Si2 (5), the associated superconducting region extends to much higher densities than in the other materials, and the transition temperature (Tc) reaches its maximum far away from the magnetic quantum phase transition.
4) In summary: The authors report the presence of two disconnected superconducting domes in the pressure-temperature phase diagram of partially germanium-substituted CeCu2Si2. The lower density superconducting dome lies on the threshold of antiferromagnetic order, indicating magnetically mediated pairing, whereas the higher density superconducting regime straddles a weakly first-order volume collapse, suggesting a pairing interaction based on spatially extended density fluctuations. Two distinct pairing mechanisms thus appear to operate in the single, wide, superconducting range of stoichiometric CeCu2Si2, both of which might apply more generally to other classes of correlated electron systems.
References (abridged):
1. N. D. Mathur et al., Nature 394, 39 (1998)
2. R. Movshovich et al., Phys. Rev. B 53, 8241 (1996)
3. H. Hegger et al., Phys. Rev. Lett. 84, 4986 (2000)
4. F. Steglich et al., Phys. Rev. Lett. 43, 1892 (1979)
5. P. Gegenwart et al., Phys. Rev. Lett. 81, 1501 (1998)
Science http://www.sciencemag.org
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CONDENSED MATTER: SUPERCONDUCTIVITY AND COOPER PAIRS
The following points are made by Piers Coleman (Nature 2003 424:625):
1) One of the outstanding mysteries in condensed-matter physics is that the most perfect conductors so far discovered -- the high-temperature superconductors -- are more like insulators than metals. Superconductivity, the flow without resistance of current through some materials, usually only occurs at very low temperatures. Conventional superconductivity develops in metals, but high-temperature superconductivity (at about 90 K) occurs in insulating copper oxide ceramics when small amounts of charge are injected by chemical doping.
2) The quantum physicist Paul Dirac (1902-1984) once remarked that the equations needed to understand most of physics are known, but are far too complicated to solve. Lurking in this complexity lies the astounding ability of matter to develop new types of collective behavior, such as superconductivity and magnetism. The equation that accurately describes all of this behavior is the many-body Schroedinger equation. This involves two essential elements: the wavefunction, which is related to the probability of finding the electrons (or other particles) of a system in a given spatial configuration; and the Hamiltonian, a function that determines the energy of a system from its wavefunction. In a typical material, the number of particles tracked by the wavefunction is of the order of Avogadro's number -- 6 x 10^(23). This level of complexity means that understanding collective behavior, such as that of electrons in a superconductor, depends on the creative abstraction of both the Hamiltonian and the wavefunction into a much simpler model that captures the essence of the physics.
3) Conventionally, superconductivity develops in a conducting metal when the electrons bind together to form "Cooper pairs". Each electron spins like a tiny top, and in a Cooper pair the electron spins are aligned in an antiparallel configuration. Soon after high-temperature superconductivity was discovered, it was noted that the insulating state from which high-temperature superconductivity arises is a special kind of insulator, called a "Mott insulator". The mobile electrons in a high-temperature superconductor hop from one copper atom to the next, but repel one another because of their negative charges. When these repulsive forces are large enough, the electrons are prevented from ever doubly occupying a given copper atom.
4) In undoped copper oxide superconductors, there is precisely one mobile electron per copper atom, so the restriction on double occupancy causes the electrons to remain localized, at one electron per site. Strong magnetic forces between the localized electrons at different sites cause their spins to orient together in oppositely aligned pairs. According to the "resonating valence bond" (RVB) model of high-temperature superconductivity, these pairs form a fluid that resonates between the sites in a fashion reminiscent of the Cooper pairs inside a superconductor. When charge is introduced into this insulating background of pairs (through doping with impurity atoms), the RVB state evolves directly from insulator to superconductor.
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