Interplay Between non-Fermi Liquid, Superconductivity, and Pseudogap Behavior in Quantum-Critical Metals

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education to examine superconductivity in the strong coupling regime. Superconductivity, the ability of electrons to conduct electric current without dissipation below a certain temperature called Tc, is not only one of the most remarkable phenomena emerging from the quantum physics of many interacting electrons but is also of great technological importance. Metrology, lossless energy transmission, and quantum computation are important examples. Earlier theoretical studies of superconductivity were based on the Bardeen-Cooper-Schrieffer (BCS) model, which assumed that electrons are weakly interacting. This approach was questioned after the discovery of high-temperature superconductivity first in cuprate oxides and then in other series of compounds, including, most recently, graphene-based systems. Experiments revealed that these materials display behavior, which differs fundamentally from that expected for ordinary superconductors both above Tc and below Tc. These discoveries called for a qualitatively new theory of superconductivity in the regime of strong interactions between electrons. In this project, the PI and his students will work to understand the mechanism of superconductivity in these unusual materials and the competition between superconductivity and other ordered states of interacting electrons, such as magnetism. This is a problem with no easy answer because strong interaction makes it more difficult to establish a dissipation-less current flow, required for superconductivity. At the same time, the stronger the interaction the higher Tc is expected. Understanding the dual role of strong interactions also the interplay between superconductivity and other possible ordered states is the main goal of the proposed work. Theoretical advances resulting from this project may guide the identification of materials with higher superconducting transition temperatures and desirable properties, which should have a revolutionary impact on society. This project will contribute to the development of the scientific workforce by training two graduate students. The PI will continue running conferences and lecturing at schools for graduate students and junior faculty. TECHNICAL SUMMARY This award supports theoretical research and education which will examine superconductivity in the strong coupling regime. This is a central problem in experimental and theoretical condensed-matter physics. In addition to incipient practical applications, the interest in this field is driven by the fascinating variety of observed effects and universality of underlying theoretical ideas. The PI will focus on several fundamental issues related to a system behavior near a quantum-critical point (QCP), where interaction, mediated by a soft critical boson, provides a mechanism for pairing and at the same time gives rise to non-Fermi liquid normal state behavior. The issues the PI will address include understanding: the competition between fermionic incoherence and Cooper pairing, a fundamentally non-BCS pairing mechanism, how dynamical vortices emerge, a topological transition that occurs when the number of vortices becomes infinite, the bound pair state without phase coherence, and the collective modes of a quantum-critical superconductor. The PI will also analyze theoretically superconductivity emerging from a pseudogap state, with special emphasis on the behavior of superfluid stiffness and on the range where bound pairs of fermions form, but remain incoherent and do not give rise to supercurrent. In related studies, the PI will analyze superconductivity in a two-dimensional metal near a van Hove singularity and near the end point of s-wave superconductivity in systems with electron-phonon attraction and Hubbard repulsion. The PI will contribute to the development of the scientific workforce by training two graduate students in modern theoretical condensed matter physics and will continue running conferences and workshops and lecturing at schools for graduate students and junior faculty. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.