Transport and Superconductivity in Strongly Correlated Quantum Matter

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NONTECHNICAL SUMMARYThis award supports theoretical research aimed at understanding electronic and transport properties of systems in which strong interactions between electrons lead to emergent behavior such as high temperature superconductivity. In a superconductor, electrons conduct electricity without any loss, but this typically happens only at low temperatures. As electrical loss represents a significant portion of all electrical bills, a room temperature superconductor would represent a major advance in power transmission. The PI's work is focused on understanding a class of high-temperature superconductors discovered in 1987 that have defied understanding within the so-called BCS theory proposed in 1957 by Bardeen, Cooper, and Schrieffer. The primary difficulty is that while the BCS theory works fine for metals such aluminum where the interaction between the electrons can be ignored, this is not the case for the high-temperature superconductors where superconductivity occurs by doping materials which are insulators due to strong repulsion between electrons. The PI has advanced an exactly solvable model for such systems and shown how superconductivity emerges. Since the model is exactly solvable, a clear picture emerges as to how the BCS theory must be modified. The PI will work to quantify the differences and construct the universal features of superconductivity in these materials that have defied description in terms of the standard BCS theory.This award also supports training of graduate students seeking their PhD degrees in theoretical physics. The PI will be involved with other educational and outreach activities, such as continuing to revise his graduate textbook in theoretical solid state physics, serving on the Editorial Boards of prominent scientific journals, advancing initiatives within the American Physical Society at the intersection of physics and race, and working to increase diversity in the scientific workforce.TECHNICAL SUMMARYThis award supports theoretical research focused on new methods for the transport and superconducting properties of strongly correlated electron systems by using exactly solvable models, numerical calculations, and renormalization techniques to establish the existence of strongly coupled fixed points. The exactly solvable models allow new insight into the 35-year old problem of superconductivity in doped Mott insulators such as the high-temperature superconductors. The goal is to ascertain what new features emerge from Mott physics in the superconducting state. Another goal of the exactly solvable models is to determine if the physics they embody is governed by a new strongly coupled fixed point in much the same way Fermi liquid theory dictates the physics of simple metals. Success here could provide an organizing principle in the physics of strongly correlated electron matter. Finally, the focus on numerical calculations to determine the phase diagram of the dilute electron gas in the presence of a periodic potential is aimed at informing new experiments that have revealed novel insulating states that break translational symmetry in Moire bilayer systems.This award also supports training of graduate students seeking their PhD degrees in theoretical physics. The PI will be involved with other educational and outreach activities, such as continuing to revise his graduate textbook in theoretical solid state physics, serving on the Editorial Boards of prominent scientific journals, advancing initiatives within the American Physical Society at the intersection of physics and race, and working to increase diversity in the scientific workforce.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.