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arXiv:2301.04556 · Modern Physics Letters B

Non-Fermi liquid behavior in a simple model of Fermi arcs and pseudogap

Ruojun Wang, Kun Yang

Published Jun 28, 2023• 5 citations
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Abstract

In this paper, we consider a perturbed version of a very simple and exactly solvable model that supports Fermi arcs and pseudogap in its ground state and excitation spectrum, which includes Hubbard-like interactions in both momentum and real spaces. We find that the combined effects give rise to non-Fermi liquid behavior in the electron self-energy. This points to a novel mechanism that leads to non-Fermi liquid behavior, which is of strong current interest in the context of strongly correlated metals, that often become superconductors. Comparison will be made with phenomenology of high- temperature cuprate superconductors.

DOI
10.1142/s0217984923501191

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In this paper, we consider a perturbed version of a very simple and exactly solvable model that supports Fermi arcs and pseudogap in its ground state and excitation spectrum, which includes Hubbard-like interactions in both momentum and real spaces. We find that the combined effects give rise to non-Fermi liquid behavior in the electron self-energy. This points to a novel mechanism that leads to non-Fermi liquid behavior, which is of strong current interest in the context of strongly correlated metals, that often become superconductors. Comparison will be made with phenomenology of high- temperature cuprate superconductors.
An exactly soluble one-dimensional model of electrons interacting with order-parameter fluctuations associated with short-range order is considered. The energy and momentum dependence of the electronic self-energy and spectral function are calculated and found to exhibit non-Fermi-liquid features similar to that seen for the two-dimensional Hubbard model: a pseudogap, shadow bands, anomalies in the self-energy, and breakdown of the quasiparticle picture. Deviations from Fermi-liquid behavior are largest close to the Fermi surface and as the correlation length increases.
Since the discovery of the pseudogap and Fermi arc states in underdoped cuprates, the understanding of such non-Fermi-liquid states and the associated violation of Luttinger's theorem have been the central theme in correlated electron systems. However, still lacking is a well-accepted theoretical framework to unambiguously explain these metallic states that are clearly beyond Landau's Fermi liquid and Luttinger's theorem of a Fermi surface and electron filling. Here, we design a lattice model of orthogonal metals with fermion and Ising matter fields coupled to topological order and, by solving the model via unbiased quantum Monte Carlo simulation at generic electron fillings, find that the system gives birth to phenomena of the Fermi arc and pseudogap in the single-particle spectrum that go beyond the Luttinger sum rule with broken Fermi surface but no symmetry breaking. The pseudogap and Fermi arcs coexist with a background of a deconfined Z2{Z}_{2}Z2​ gauge field, and we further find that the confinement transition of the gauge field triggers a superconductivity instability and that the hopping of the gauge-neutral fermions brings the ``large'' Fermi surface back from the Fermi arc state. Our unbiased numerical results provide a concrete model realization and theoretical framework for the coupling between gauge field and fermions and, in the process, generate the rich phenomena of the pseudogap, the Fermi arc, and superconductivity in generic correlated electron systems.
Fermi gases and liquids display an excitation spectrum that is simply connected, ensuring closed Fermi surfaces. In strongly correlated systems such as the cuprate superconductors, the existence of open sheets of Fermi surface known as Fermi arcs indicate a distinctly different topology of the spectrum with no equivalent in Fermi-liquid theory. Here, we demonstrate a generic mechanism by which correlation effects in fermionic systems can change the topology of the spectrum. Using diagrammatic Monte Carlo simulations, we demonstrate the existence of disconnected and multiply connected excitation spectra in the attractive Hubbard model in the BCS-BEC crossover regime. These topologically nontrivial spectra are a prerequisite for Fermi arcs.
Abstract Non-Fermi liquid behavior and pseudogap formation are among the most well-known examples of exotic spectral features observed in several strongly correlated materials such as the hole-doped cuprates, nickelates, iridates, ruthenates, ferropnictides, doped Mott organics, transition metal dichalcogenides, heavy fermions, d- and f-electron metals, etc. We demonstrate that these features are inevitable consequences when fermions couple to an unconventional Bose metal (Hegg et al 2021 Proc. Natl. Acad. Sci. 118) mean field consisting of lower-dimensional coherence. Not only do we find both exotic phenomena, but also a host of other features that have been observed e.g. in the cuprates including nodal anti-nodal dichotomy and pseudogap asymmetry (symmetry) in momentum (real) space. Obtaining these exotic and heretofore mysterious phenomena via a mean field offers a simple, universal, and therefore widely applicable explanation for their ubiquitous empirical appearance.