Theories of Metals with Correlated Electrons

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NONTECHNICAL SUMMARYThis award supports theoretical research and education to investigate unusual metallic states that arise in quantum materials and the interesting states of matter composed of electrons that emerge from these 'strange metals.' In familiar metals like copper or silver, electrical conduction occurs via the motion of a liquid of electrons through the crystal of atoms, with the quantum motion of each electron largely independent of the other electrons. However, in many modern quantum materials, and especially in the cuprate compounds which display high temperature superconductivity, the motion of an electron is correlated with that of other electrons. This correlation is of a subtle non-local quantum variety, often referred to as quantum entanglement, in which observation of one electron can determine the state of other well-separated electrons. In this project, the PI will focus on studying and classifying states of electrons with complex varieties of long-range quantum entanglement. Understanding such metallic states is required to predict the critical temperature for high temperature superconductivity, as superconductivity emerges from such a `strange' metal upon lowering the temperature. Superconductors exhibit the ability to conduct electricity without resistance when the temperature is lowered through the superconducting transition temperature. With transition temperatures near the temperature where liquid oxygen boils, high temperature superconductors still exhibit superconductivity at much higher temperatures than traditional superconductors but still very much below room temperature. More fundamentally, theoretical research in combination with experimental observations, is expected to lead to a deeper understanding of the structure of quantum matter. The research supported by this award will be coupled with public lectures, articles in popular science journals, lectures at schools for advanced students. The research will be conducted by a group of students and postdoctoral fellows drawn from institutions around the world.TECHNICAL SUMMARYThis award supports theoretical research and education to investigate the interplay of topological order, quantum criticality, and broken symmetry in interesting metallic materials. Lattice models will be developed that are amenable to analytical study and quantum Monte Carlo simulations. The PI aims to describe the transition between metallic states with and without quantum entanglement, and the role of topological order. The theory of the interplay of topological order, quantum criticality, and broken symmetry is fairly well-developed in insulators; the PI proposes a program to extend such theories to metals. Reliable analytic and numerical tools will lead to a description of the phase diagrams of such metals, and of quantum phase transitions involving changes in Fermi surface size linked to the development of topological order. The effect of disorder on correlated metallic states will be examined, building upon the solvable Sachdev-Ye-Kitaev model of a strange metal that had been originally proposed by the PI. Disorder plays a crucial role in the electrical and thermal conductivities of metals, and these conductivities will be computed in correlated states. New analytic tools will be developed to analyze the dynamics of metals without quasiparticle excitations. Collaborations with a number of experimental groups will allow comparison of theories to observations in the cuprate and pnictide superconductors and closely related materials, graphene, and other modern materials.