This award supports theoretical research and education on quantum correlation phenomena in solids. The long-term goals are to develop new materials and structures with useful functionality not currently available, and to extend the basic scientific framework to understand matter in new regimes and new phases. The research thrusts span bulk materials and heterostructures. In the former, the PI will study (1) frustration and fluctuations, and their consequences and applications; (2) magneto-electric coupling; and (3) orbital fluctuations and ordering. In the heterostructure area, the PI will consider interfaces between correlated electron materials, which are becoming a very exciting subject experimentally. The PI aims to address key outstanding questions raised by experiments in quantum magnets, multiferroics, spin-orbit coupled materials, and more complex Mott insulators. The breadth of topics is an asset to this research program; by viewing one material or structure in a broader context, the PI aims to obtain insights into the relative importance of the very many effects that might be involved. The theoretical techniques ? e.g. statistical mechanics, field theory, renormalization group, numerical methods, constraint counting ? which will be used to study competing interactions and fluctuations are also widely applicable across all these problems. Advances in the past 5 years in growing high quality atomic precision interfaces between transition metal oxides by pulsed laser deposition are remarkable. This is an extremely exciting new venue for correlation phenomena and also eventual applications building semiconductor-style heterostructures from correlated materials with their additional functionalities. The PI will carry out fundamental research aimed at elucidating the new physics occuring at these interfaces and how they differ from semiconductor heterostructures. This award supports the education of graduate students and postdocs in forefront areas of condensed matter theory. New course materials will be developed to convey the excitement of the fields to new students.
NON-TECHNICAL SUMMARY: This award supports theoretical research and education to motivate and explain experiments and properties of materials. The PI will focus on particular areas which he believes are those most likely to lead to revolutionary technological impacts. These areas also advance fundamental science. Experiments reveal materials that have the necessary ingredients to become magnets, but do not exhibit magnetism. On the scale of atoms, there is a competition between the interactions that would favor aligning the fundamental building blocks of magnetism and the geometrical arrangements of the atoms. This frustrates the tendency to magnetic order. Experiments continue to deliver more examples, like the minerals Herbertsmithite and Volborthite, enabling the test of theoretical ideas that new states of matter will arise from failed magnetism. The PI will also study materials where electron charge and magnetism are closely coupled. Multiferroics are an example class of materials; they simultaneously exhibit magnetism and the electric charge analog of magnetism. The PI will also study phenomena that arise from the coupling of spin and charge in a new class of insulating materials, called topological insulators, that are rich with possibilities for new phenomena involving magnetism that arise from the motion of electrons. A recent experimental advance enables the joining of two different oxide materials, analogous to the interfaces between semiconductors that form the basis of modern electronics. In this case the oxide materials have unusual properties that arise from strong interactions between electrons. The interfaces so created are rich with the potential for new phenomena and new materials properties that may have technological impact. The PI will use sophisticated theoretical tools to understand recent experiments and predict new phenomena.
The fundamental tools of advanced quantum mechanics are needed to understand experiments on these systems and to illuminate new possibilities with predictions that motivate further experiment. This work contributes to the foundations of future electronic and information technologies. This award helps provide a quality educational experience for students at the graduate and postdoctoral level.
This project consisted of fundamental theoretical research into the quantum physics of electrons in materials. Electrons pervade solids and determine most of their properties. Though the macroscopic world usually appears classical and familiar, the electrons which comprise it are highly quantum objects, capable of bringing exotic behavior to light under the right conditions. The goals of the research were to understand and design materials and artificial structures where this occurs, and develop techniques to calculate the properties of systems of this type. The two main thrusts of the research are described below. Several smaller studies carried out on problems of current interest in materials physics will not be discussed. A major part of the research dealt with antiferromagnetism, which arises when electrons are bound tightly to individual atoms or molecules, but their spins – the smallest quantum magnets – interact with one another in complex ways. The project showed how these interactions lead to distinct arrangements of the spins, and developed methods to calculate these configurations. Some states are ordered, and capable thereby of storing information; other are disordered, serving instead as a reservoir of entropy useful for thermoelectric cooling. Behavior of both types was found and modeled in several material systems, in which calculations were compared with thermodynamic and scattering experiments by groups from around the world. A third possibility, long sought by physicists, is that spins form a complex quantum superposition of many different possible classical states. Such a system is called a "quantum spin liquid", and physicists characterize this situation by a quantity called "entanglement". Quantum spin liquids have unique properties of interest both fundamentally and for future quantum information applications. One major achievement of this project was to develop a method to calculate the entanglement efficiently for some of the most difficult problems in antiferromagnetism. This provides a smoking gun test for quantum spin liquids in computer studies, and enables prediction and design of these unique states of matter. The second main emphasis of the project was into semimetals, materials which are near the boundary between semiconductors and metals. In these materials, electrons are not tightly bound to atoms, and instead can flow and transport electricity, heat, etc. Substances of this type are of particular practical interest as their conduction properties are very sensitive to applied forces such as electric or magnetic fields, and so can be switched efficiently. Semimetals are particularly interesting when the electrons’ motion is so fast as to become highly relativistic. Then an electron’s spin and its orbital motion become intertwined, with unusual results. Notably, the electron wavefunction, describing the quantum superposition state of both spin and orbital motion, can become "twisted". This twisting is described by the mathematics of topology, and leads to extremely robust properties such as surface electronic bound states. Materials known as topological insulators (discovered simultaneously in 2007 by the PI and a few others) are now famous examples, and subjects of intense physics and materials research. In this project, similar topological properties were uncovered in semimetals which are not insulating. The electronic states discovered and studied in this proposal can emulate for instance neutrinos, nearly undetectable particles that play an important role in high energy physics and cosmology. The research under this project determined specific material systems and general design schemes to construct such topological semimetals, and described the experiments which should be carried out to characterize them in the laboratory.
