Interplay Between Superconductivity and Charge Order in Near-Critical Metals

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NONTECHNICAL SUMMARYThis award supports theoretical research and education in condensed matter physics, in the subfield of high temperature superconductivity. At sufficiently low temperature, high temperature superconductors become superconducting, a cooperative state of electrons that exhibits distinctly different properties from those of ordinary conductors like copper. Among them is the ability to conduct electricity without dissipation. This theoretical investigation is inspired by experimental discoveries over the last few years indicating that the highest temperature at which superconductivity appears is often the largest near a boundary between other kinds of electronic states for which the electrons self organize to display periodic arrangements of either electron magnetism or electron charges. The understanding of how the competition among distinctly different tendencies for electrons to self-organize might enhance the tendency for superconductivity is important in developing a fundamental understanding of the origin of high temperature superconductivity. It may also contribute to developing the capability to design new superconducting materials which exhibit superconductivity at higher temperatures and have properties that make them suitable for practical applications. This award supports a detailed study of what causes charge and magnetic orders to compete and how superconductivity gains from this competition. This project supports specialized training of graduate students and postdoctoral researchers in an active area of research, as well as community discussions of the science that enables high temperature superconductivity.TECHNICAL SUMMARYThis project supports theoretical research and education in the field of strongly correlated electron systems. The research is focused on two fundamental issues related to the pseudo gap in systems of fermions tuned to a quantum-critical point: 1. the competition between d-wave superconductivity and competing non-superconducting orders, and 2. the analysis of superconducting fluctuations when superconductivity emerges from a quantum-critical regime and the normal state is very different from that of a Fermi liquid. The PI will investigate two competing orders: incommensurate charge density wave order and incommensurate pair density wave order. The latter can be considered as superconductivity with a non-zero total momentum of a pair. The PI and his research team will analyze the stability of competing orders, ordering patterns, and whether critical fluctuations of competing orders give an additional boost to superconductivity leading to transition temperatures above the corresponding quantum-critical points. In the analysis of superconducting fluctuations, the PI and his team will study in detail the effects of longitudinal fluctuations of a superconducting order parameter in a situation when superconductivity emerges from a quantum-critical regime in which a pairing potential couples incoherent fermions. The goal of this study is to go beyond conventional Eliashberg-type theories to obtain the full Luttinger-Ward functional, and analyze the profile of fluctuations away from the minimum and check the existence of an intermediate temperature range where the gap is already developed, but gap fluctuations keep fermions incoherent and prevent a true superconducting order to develop. In this temperature range the system will display the pseudogap behavior. The interplay between superconductivity and competing orders is a pervasive theme in the study of classes of exotic superconductors, such as the heavy fermion, cuprate, ruthenate, Fe-pnictide, organic and molecular superconductors. Magnetism and superconductivity are antithetical in elemental superconductors, but in exotic superconductors magnetism may enhance the tendency toward superconductivity. The analysis of the full phase diagram of quantum-critical metals may help advance understanding of the key ingredients required for high- temperature superconductivity in correlated electron systems.