This award supports theoretical research and education in the area of strongly correlated electron materials. The PI will carry out theoretical research to study transport, magnetic and superconducting behavior in highly frustrated lattices. This work is motivated by very recent discoveries of magnetism and unusual superconductivity below ~5 K, and of anomalous transport behavior in the sodium cobalt oxide system Na_xCoO2. These metallic systems display a thermopower as large as some of the best semiconductors; the thermopower is also strongly magnetic field dependent. The Hall effect is most unusual in that there is no saturation with temperature. Extreme type II superconductivity occurs on hydration. Unusual magnetic long-ranged order occurs in the phase diagram. Experimental findings such as these challenge the tenets of the basic theory of metals, suggesting an important role for strong many-body correlations in these systems. The PI will use a combination of analytical and numerical techniques applied to appropriate models to study the transport properties and the occurrence, as well as the nature, of the magnetic and superconducting states. The research will focus on the especially strong many-body renormalizations revealed by recent experiments. Broader impacts: Studying the cobaltates may ultimately improve our understanding of other strongly correlated electron systems, such as the high temperature superconductors, which have proven to be very intellectually challenging. The cobaltates are potentially very important from a technological point of view in their own right - their large thermopower combined with low resistance enables them to achieve the best-known figure of merit at high temperature. They are also related to the lighter alkali atom cobaltate LixCoO2 that is central to lightweight lithium battery technology. Materials such as Liy-xNaxCoO2, that arise as natural possibilities in this study, may catalyze a novel fusion of thermoelectric and battery technologies leading to new technologies. This award also supports graduate level education in advanced theoretical condensed matter physics. %%% This award supports theoretical research and education on strongly correlated electron materials with a focus on understanding the anomalous properties and ordered states revealed in recent experiments on cobaltite compounds, Na_xCoO_2. These experiments show that the cobaltites are unlike ordinary metals. They also show unusual magnetic and superconducting states. It is believed that the inability of the interactions between electron spins to be satisfied because of the geometry of the underlying crystal structure (geometric frustration) combined with strong interactions among electrons, leads to the anomalous properties exhibited by these materials. Some properties of these strongly correlated electron materials, like their combined large thermopower and low resistance, suggest potential technological applications and the potential for new technologies, as suggested above. The study of these materials, like other strongly correlated-electron materials, leads to the discovery of new fundamental condensed matter physics. This award also supports graduate level education in advanced theoretical condensed matter physics. ***
