Pairing of Incoherent Fermions in Quantum-Critical Metals

NONTECHNICAL SUMMARY

This award supports theoretical research and education on fundamental properties of electrons in quantum materials. Electrons, carrying negative charge, repel one another via the usual Coulomb interaction. However, there are certain circumstances within materials where this repulsive interaction is screened and becomes attractive at certain distances, which can lead to the formation of electron pairs and superconductivity. Yet, the same screened Coulomb interaction also tends to scatter electrons and thereby destroy their coherent motion, which in turn is destructive for superconductivity.

The key goal of this project is to understand the delicate interplay between these two competing tendencies. The PI will analyze specific models relevant to current experiments with the aim to understand when a superconducting state is most stable, and how to increase the temperature at which superconductivity is destroyed, thereby extending the temperature range that is useful for applications. Such understanding could lead to general conclusions about the complex behavior of electrons in materials and is also relevant for practical uses of superconductivity in, for example, energy storage, magnetically levitated trains, superconducting power lines, MRI imaging, and particle accelerators.

The problems the PI proposes to study are quite general and are of interest to a broad community of physicists. The project could have an impact on several other areas of science, such as mathematics and high-energy physics. A major component of this project is the mentoring and training of graduate students who will be involved in all aspects of the research.

TECHNICAL SUMMARY

This award supports theoretical research and education on strongly correlated electron systems, which are at the center of experimental and theoretical activities in condensed-matter physics. The PI will address several fundamental problems related to physics near a quantum critical point (QCP), where interaction with a critical boson gives rise to strong correlations and non-Fermi-liquid behavior.

The problems considered include the competition between fermionic incoherence and a strong tendency towards Cooper pairing, the interplay between pairing of incoherent fermions and superconductivity, the comparison of analytical theory with Quantum Monte Carlo data, and the special role of backscattering near a critical point. Near a QCP towards spin or charge order, the interaction with soft fluctuations of the order parameter destroys fermionic coherence either on the whole Fermi surface or in some (hot) portions of it. The same interaction also tends to bind fermions into Cooper pairs. The PI's plan is to analyze the competition between these two tendencies. In particular, he will address the issue whether one can get a non-Fermi-liquid behavior down to T=0, uninterrupted by the pairing. He will next study whether the pairing of incoherent fermions leads to true superconductivity or to pseudogap behavior of preformed pairs due to strong fluctuations of a superconducting order parameter. His specific goal is to understand the role of fluctuations of the shape of the frequency dependent gap, as these 'longitudinal' fluctuations likely become soft at least in some quantum-critical systems. To do this, the PI will derive the full Luttinger-Ward functional, whose minimization yields Eliashberg equations. He will analyze the profile of this functional away from the minimum and verify whether the stiffness of longitudinal fluctuations has extra smallness at a QCP. If this is the case, there should exist an intermediate temperature range where the pairing gap is already developed, but fermions remain incoherent and do not superconduct. This should answer the most fundamental questions about the behavior of a metal near a QCP.

The problems the PI proposes to study are quite general and are of interest to a broad community of physicists. The project could have an impact on several other areas of science, such as mathematics and high-energy physics. A major component of this project is the mentoring and training of graduate students who will be involved in all aspects of the research.

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.