This award supports theoretical research and education to address long-standing fundamental problems concerning the emergent properties of correlated electron fluids using well-controlled methods of theoretical physics. The PI will investigate properties of electronic systems through a careful analysis of the behavior of simplified models of interacting electrons defined at the lattice scale. The PI will explore generic properties of interacting electronic systems and also attempt to gain insights into material specific features of strongly correlated electronic systems through the inclusion of salient features of the electronic structure of interesting materials. The PI will pursue a three-pronged approach:
1. The PI will study the behavior of simplified models of interacting electrons in the weak-coupling limit where controlled, perturbative renormalization group calculations are possible and asymptotically exact results can be obtained. In order to broaden the scope of the physics accessible by these methods, fine-tuned electronic structures will be investigated. This amounts to studying the properties of the phases and phase transitions in the vicinity of quantum multicritical point.
2. Near a quantum critical point, electronic properties can often be described by a quantum field theory. A particularly successful use of quantum field theory in correlated electron systems has been the use of Chern-Simons Landau Ginzberg theory to describe quantum Hall systems. This approach implies a profound analogy between the properties of quantum Hall systems and the properties of superconductors. The PI will study the justification and limits of applicability of the Chern-Simons Landau Ginzberg theory, and further explore the consequences of the implied analogy between superconductors and quantum Hall systems.
3. Specific aspects of the properties of certain correlated materials can be addressed in terms of models that capture some essential feature of their local electronic structure. The goal is mainly to gain insights into the physics of one experimentally interesting material or another. A good example is provided by the newly discovered antiferromagnetic insulating state of Cs3C60; because it is insulating, it can be studied by expanding about a Mott insulating state in which the number of electrons on each C60 molecule is fixed by the effective Hubbard interaction. Understanding which further interactions dominate in this strongly correlated limit, and how they determine the nature of the ordered states may shed light on the interactions that give rise to superconductivity of this material under pressure, and in the broader family of superconducting materials A3C60, where A is any of a number of alkali metals.
Understanding the properties of correlated electron fluids may lead to the ability to exploit novel materials properties to develop new devices and technologies that derive their operating principles from the novel phases and phase competitions that occur in highly correlated electron fluids.
NON TECHNICAL SUMMARY
This award supports research and education with an aim to advance understanding of materials with electrons that interact strongly with each other giving rise to new states of electronic matter with interesting and unusual properties. The broad thrust of this research is to gain insights into the nature of the states of electronic matter that emerge in strongly interacting materials. The PI will use simplified models for electrons in materials to examine the relationship between solutions obtained from controlled theoretical methods that assume that electrons are effectively weakly interacting to results obtained by various other methods.
Superconductivity is one kind of emergent state of matter which is characterized by the ability of conduct electricity without resistance or loss of energy. The PI will explore an interesting connection between the fundamental physics of superconductors and the seemingly very different state of matter known as the quantum Hall effect. The quantum Hall effect arises when a two-dimensional layer of electrons, which can exist in an artificially layered semiconductor material, is exposed to a perpendicular magnetic field. The PI aims to exploit knowledge of superconductivity to gain new insights into the fundamental physics of the quantum Hall effect.
The PI will also investigate the superconducting state that emerges in a material composed of the element cesium and a molecule of carbon containing 60 atoms which exhibits superconductivity under pressure. Experiments reveal properties that are qualitatively similar to those of the high temperature superconductors and other materials with strongly interacting electrons. The PI's study of this recently discovered superconductor may lead to insights into the nature of superconductivity in the high temperature superconductors. Understanding the properties of correlated electron fluids may lead to the ability to exploit novel materials properties to develop new devices and technologies that derive their operating principles from the novel phases and phase competitions that occur in highly correlated electron fluids.
