This project studies an isoelectronic, isostructural set of dense Kondo compounds which display a broad spectrum of ground states of highly correlated electron systems: magnetism, superconductivity and heavy Fermion without other order. Using the variables of temperature, pressure and applied external magnetic field to study both the dense and diluted systems, it is possible to characterize dense Kondo materials in terms of a lattice Kondo scale which evolves at low temperature from the single ion Kondo scale. This characterization provides a classification of correlated electron systems which can provide for the first time a framework for understanding the strong variation of ground states found in correlated electron systems, systems which are closely related in their physics to the less simple transition elements compounds of technological interest. A realistic goal of this study is to give for the first time a precise description of what a "heavy Fermion" is and show how this carries over to d-band elements. High school students, college undergraduates and graduate students will be trained to use the broad phase space of materials as an effective and powerful variable in materials driven condensed matter research. %%%% Metallic materials on the border between magnetism and non-magnetism develop unusual electronic properties, usually at low temperature, and can display a surprising type of superconductivity that appears related to high temperature superconductivity. This research project attempts to answer how this comes about through a study using high pressure and high magnetic field to investigate a closely related set of compounds containing the rare earth element Cerium along with other metals, which display a broad variety of interesting properties at low temperature. The results hold the promise to bring for the first time a clean order to the physics of these materials which can provide new insights and suggest new research directions in the more complicated physics of technologically important transition element compounds. Student from high school to graduate level will be introduced to condensed matter physics through training in the growth of single crystals of new materials, providing a valuable underpinning for really understanding how solids work.
