Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model

Abstract

One of the distinctive features of hole-doped cuprate superconductors is the onset of a “pseudogap” below a temperatureT*. Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is holelike and that, for a broad range of parameters, its opening is concomitant with a Fermi-surface topology change from electronlike to holelike. We identify a common link between these observations: The polelike feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi-surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this polelike feature and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

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Plain Language Summary

Above some critical temperature (Tc), the “normal” state of high-temperature superconductors is nothing like a normal metal. Understanding this state is one of the greatest challenges in condensed-matter physics. We have used numerical simulations to explore some surprises seen in recent experiments that connect the short-range and long-range behaviors of the charge-carrying particles in some high-Tcsuperconductors.

One outstanding characteristic of the normal state is the appearance of a pseudogap, a partial energy gap opening near the Fermi level. Recent experiments have found a surprising connection between the pseudogap and the topology of the Fermi surface, a surface in momentum space that encloses all occupied electron states. However, this topology describes long-distance properties of charge carriers, and there is mounting evidence that the pseudogap is associated with short-range correlations and quantum entanglement similar to that in spin liquids. The connection between these two phenomena is therefore an intriguing and important one to understand.

Our theoretical and computational methods find that the pseudogap never exists when the Fermi surface is electronlike, that is, when the surface surrounds the point of zero momentum. We also show that hole-doped cuprates can be grouped into two families with respect to the interplay between the pseudogap and Fermi-surface topology: Either the pseudogap appears concomitantly with the change of the Fermi-surface topology from electronlike to holelike as hole doping is reduced, or the pseudogap appears when a holelike Fermi surface has already formed. We identify a specific feature of the electronic self-energy that provides a unifying link between the pseudogap and the Fermi-surface topology.

These results explain a large body of experimental observations of high-Tcsuperconductors conducted in parallel and independently from our theoretical work.