This award supports research and education on emergent properties of highly correlated electronic systems. The main thrust of the research undertaken here is the effort at theoretical characterization of qualitatively new behaviors of interacting electrons (i.e. new states of matter) as well as new regimes of parameters in which familiar states of matter behave in new and different ways. In addition, some of the research explores qualitatively the relation between the microscopic interactions between electrons and the effective parameters that control the macroscopic behavior of solids.
The search for new states of matter continues an ongoing effort by the PI in the theory of ''electronic liquid crystals.'' This work is based on an analogy between classical liquid crystals and corresponding phases of strongly interacting electrons. Electronic liquid crystals are quantum states with behaviors intermediate between a Fermi liquid and a Wigner crystal. Examples of such states have recently been observed experimentally: the anisotropic states (quantum Hall nematics) that are seen in high mobility quantum Hall devices and the metamagnetic nematic phase that has recently been identified in Sr3Ru2O7.
The more microscopic issues to be addressed involve the physics of the superconducting Tc. A number of questions are addressed theoretically. What is it about superconductivity that causes transition temperatures, generally, to be so low, while other orders, such as ferromagnetism, frequently onset at much higher temperatures? Why is there, in the cuprate high temperature superconductors, an ''optimal'' doping at which Tc is maximal ? what is there an excess of in ''overdoped'' cuprates? Are there optimal mesoscale structures for superconductivity, structures that enhance the strength of the electron pairing without too strongly suppressing the superfluid stiffness? The research also seeks to interpret the importance of evidence of wide-spread mesoscale inhomogeneities in the cuprates ? both self-organized (i.e. stripes) and nucleated by disorder. The research is motivated by a need to clarify whether these observations are complicating details or essential to the mechanism of high temperature superconductivity.
The effort undertaken has broader impacts with both scientific and educational consequences. Scientifically, there is impact in extending the understanding of the origins of high temperature superconductivity because that opens new theoretical opportunities as well as providing better ability to design materials with this highly desirable property. Involving students and postdoctoral researchers in the diverse problems and theoretical techniques used provides an exceptional training for talented young people. Past students and postdoctoral researchers have gone on to university faculty positions and their own careers in teaching and research and some have found successful positions in high tech companies and a variety of other fields outside of mainstream physics.
NONTECHNICAL SUMMARY: This award supports research and education on exotic properties and unexplained electronic states of unusual materials. The broad thrust of the research undertaken here is the theoretical characterization of qualitatively new behaviors and new states of matter as well as investigating how familiar forms matter can be made to behave in new and different ways. This research explores these unusual states of matter by looking at the behavior of electrons and the microscopic level of the atoms that make up the material and then connecting those behaviors with the large scale properties which are seen in the material as a solid whole.
The search for new states of matter continues an ongoing effort by the PI in the theory of ''electronic liquid crystals.'' This work develops theories of why some materials have electrons that are not just quiescently distributed more or less uniformly but which instead group together in various patterns.
The issues to be addressed also involve the physics of the superconducting materials, those which can conduct electricity with no resistance and thus no waste of energy. The questions are quite basic. What is it about superconductivity that causes working temperatures, generally, to be so low? Why is there, in some high temperature superconductors, an ''optimal'' composition at which the working temperature is highest? Are there optimal ways of creating structures for superconductivity, structures that enhance performance? The research is motivated by a need to clarify which experimental observations are complicating details and which are essential clue to discovering to the mechanism needed to explain high temperature superconductivity.
The effort undertaken has broader impacts with both scientific and educational consequences. Scientifically, there is impact in extending the understanding of the origins of high temperature superconductivity because that opens new theoretical opportunities as well as providing better ability to design materials with this highly desirable property. Involving students and postdoctoral researchers in the diverse problems and theoretical techniques used provides an exceptional training for talented young people. Past students and postdoctoral researchers have gone on to university faculty positions and their own careers in teaching and research and some have found successful positions in high tech companies and a variety of other fields outside of mainstream physics.
Understanding the behavior of electrons in solids is the cornerstone of modern solid state physics and forms the basis of much of our technological advances. Electrons are strongly repulsive to each other due to the Coulomb interaction between them and they arrange their motion in a correlated way in order to minimize this repulsion. This is called "strong correlation physics" and is responsible for phenomena such as magnetism and even superconductivity. In particular, it is now widely recognized that the high temperature superconductors discovered 25 years ago belong to the class of strongly correlated materials. Many in the community also think that magnetic correlation in these materials plays a crucial role. This project aims to understand the root of this magnetic correlation. An exciting recent development is that after years of search, a novel form of this correlated magnetic state, called the "quantum spin liquid" has been discovered experimentally. Work supported by this project provided the theoretical underpinning of this novel state of matter, and proposed new experimental probes to study these new materials. Some of our proposals, such as the prediction that these insulating materials should conduct heat like a metal, have been verified experimentally. Armed with this new knowledge, we are also taking steps to deepen our understanding of the higher temperature superconductors.
