Issues in Complex Adaptive Materials
Professor M. Brian Maple
University of California at San Diego
Department of Physics 0319
San Diego, CA 92093-0319
(619) 534-3968
(619) 534-1241 FAX
My main research interests are in strongly correlated electron phenomena in novel d- and f-electron materials. I am primarily interested in two classes of materials, (1) high Tc cuprate superconductors and (2) rare earth and actinide intermetallic compounds in which the f-states are hybridized with the conduction electron states.
The normal and superconducting state properties of the cuprates are both extraordinary. Particularly noteworthy of the anomalous normal state properties of the cuprates are the linear temperature dependence of the electrical resistivity near optimal doping, the unconventional Hall effect, the formation of a pseudogap, which has the same symmetry as the superconducting energy gap, in the underdoped regime, the evolution from insulating to metallic behavior in the range of charge carrier concentration over which superconductivity occurs, the formation of microscopic inhomogeneities ("charge stripes"), and the generalized temperature-charge carrier concentration phase diagram which suggests a relationship between antiferromagnetism and superconductivity in these materials. Many of these features indicate that the normal state properties of these materials may violate the Fermi liquid paradigm, calling for a new theoretical approach. In fact, some models have been proposed that ascribe some of these extraordinary features to the existence of a quantum critical point in the T-x phase diagram. The important issues that pertain to the superconducting state of the cuprates include the superconducting order parameter which currently appears to be predominantly d-wave with a significant s-wave component, the identity of the superconducting pairing mechanism(s), and the physics of vortex phases and dynamics in the mixed state.
Strongly correlated f-electron materials exhibit a variety of unusual phenomena and ground states. These include fluctuating valence phenomena, a heavy fermion ground state that is unstable to the formation of anisotropic superconductivity in which the energy gap has point and/or line nodes on the Fermi surface and small ordered moment antiferromagnetism which sometimes consists with superconductivity over different parts of the Fermi surface, unconventional Kondo phenomena, non-Fermi liquid behavior at low temperatures, and the formation of an insulating state with a small energy gap ~10-3 - 10-2 meV) (the materials in which this occurs are known as "hybridization gap semiconductors" or "Kondo insulators"). There are interesting parallels between the cuprates and the f-electron materials such as the occurrence of antiferromagnetism, anisotropic superconductivity, non-Fermi liquid behavior, and insulating states. Of particular recent interest is the non-Fermi liquid behavior that is observed in chemically-substituted f-electron materials at low temperature where the physical properties exhibit weak power law or logarithmic divergences. Both single ion and interacting ion models have been proposed to account for the non-Fermi liquid behavior that involve the existence of a T = 0 quantum critical point. Recently, the NČel temperature of certain antiferromagnetic cerium-based intermetallic compounds has been suppressed through the application of high pressure, resulting in the occurrence of superconductivity in the vicinity of the antiferromagnetic quantum critical point. The resultant temperature-pressure phase diagram of the cerium-based intermetallics bears an interesting resemblance to the temperature-charge carrier concentration phase diagram in the cuprates and suggests the possibility of a common underlying mechanism for the non-Fermi liquid behavior in the normal state and the superconductivity.
The remarkable phenomena and ground states that are found in the high Tc cuprate superconductors and f-electron intermetallics involves the competition and interplay between several competing interactions of comparable magnitude which results in complex behavior and new types of phenomena such as non-Fermi-liquid states, behavior of physical properties and anisotropic superconductivity involving pairing of electrons with finite orbital angular momentum. In some cases, spatially inhomogeneous states are formed, such as the "charge stripes" in the high Tc cuprates and related materials, and, possibly, the Griffiths' phase that has been proposed recently to account for the non-Fermi liquid behavior in f-electron materials. (The Griffiths' phase is produced by the interplay between atomic disorder, anisotropy, and competing Kondo and RKKY interactions.)