This award supports theoretical research and education in strongly correlated electron systems, with a particular focus on quantum criticality in heavy-fermion metals. Electronic properties in conventional solid-state materials are well described by a theory of weakly interacting electrons. However, there are many materials in which electron correlations are important, which give rise to such striking phenomena as high temperature superconductivity and "heavy" electrons with a proton-scale effective mass. In recent years, there is a growing realization that quantum criticality plays an important role in these materials. Heavy-fermion metals represent prototype systems in this context.
The PI will investigate the notion that quantum criticality tends to nucleate new phases. Several specific issues will be explored:
First, the PI plans to investigate the various magnetic phases in a recently proposed global phase diagram, and to study the nature of superconductivity near Kondo-destruction quantum critical points where Fermi surfaces undergo large fluctuations.
Second, the PI intends to go beyond recent work in topological insulators primarily focused on non-interacting systems, to explore the viability of heavy fermions as a setting in which interaction effects can be manifest in topological phases.
Third, the PI will investigate recent experiments on an iridium-based pyrochlore heavy fermion metal to understand the origin of the observed large anomalous Hall effect.
Fourth, in order to elucidate novel excitations near quantum critical points in broader settings, the PI will explore several low-dimensional systems to study the dynamical properties that are influenced by quantum criticality.
Through the proposed research, the PI will engage postdoctoral fellows, graduate students and undergraduate students. The PI will also collaborate with international groups as appropriate, which enrich the research environment of students and junior scientists in the US. Finally, while the proposed research is at the fundamental level, it will contribute to the understanding of advanced materials relevant to future technologies.
NON-TECHNICAL SUMMARY
This award supports theoretical research and education in correlated electron systems. In materials such as the rare-earth-based "heavy-fermion" systems, electrons strongly interact with each other, leading to electronic properties that are highly unusual. A particular focus here is on quantum criticality, the collective behavior of matter undergoing a phase transition at the absolute zero of temperature. Such phase transitions represent the quantum analogue of the familiar phase transitions in daily life, such as water freezing into ice or evaporating into steam. Theoretical methods will be developed to study how quantum criticality gives rise to novel electronic states such as superconductivity, in which electricity flows without experiencing any resistance. Also to be studied is the interplay between magnetism and quantum-mechanical states of the electrons that involve an unusual topology. Finally, novel dynamical properties in quantum critical systems at low dimensions will be explored. The proposed research will engage not only junior scientists but also graduate and undergraduate students. The research will contribute to the understanding of modern electronic materials that may be important for future technologies.
