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arXiv:2312.17700 · Physical Review Letters

Fermi and Luttinger Arcs: Two Concepts, Realized on One Surface

Paul Worm, M. Reitner, Karsten Held, A. Toschi

Published Oct 16, 2024• 15 citations
arXivHTMLPDF

Abstract

We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory provides a transparent description of a precise mechanism, capable of driving the formation of disconnected segments along the Fermi surface (the highly debated "Fermi arcs"), as well as the opening of a pseudogap in hole and electron doping. This occurs through a specific mechanism: The electronic states on the Fermi arcs remain intact, while the Fermi surface part where the gap opens transforms into a Luttinger arc.

DOI
10.1103/physrevlett.133.166501

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We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory provides a transparent description of a precise mechanism, capable of driving the formation of disconnected segments along the Fermi surface (the highly debated "Fermi arcs"), as well as the opening of a pseudogap in hole and electron doping. This occurs through a specific mechanism: The electronic states on the Fermi arcs remain intact, while the Fermi surface part where the gap opens transforms into a Luttinger arc.
We analyze the pseudogap phenomenon of hole-doped cuprates via a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures the pivotal interplay between Mott localization and Fermi surface topology beyond weak-coupling spin fluctuations, which open a spectral gap near hot spots. We show that strong coupling and particle-hole asymmetry give rise to another mechanism: the spin-fermion vertex develops a large imaginary part. While its real part always suppresses the electronic lifetime, the imaginary part has a twofold effect. For antinodal fermions a gap opening is boosted; conversely, around the node Fermi arcs are protected.
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.
Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada [Phys. Rev. X 10, 041023 (2020)]. Here we generalize the approach to systems with open boundary conditions in the absence of translational invariance. Removing these constraints permits the application of embedding techniques like cluster perturbation theory (CPT). Using this approach we provide robust evidence of the existence of Fermi arcs in the one-band Hubbard model, an enduring problem in the physics of the pseudogap in cuprate high-temperature superconductors. We study the behavior of the Fermi surface and of the density of states as a function of hole doping for clusters of up to 64 sites, well beyond the reach of modern exact diagonalization solvers. We observe that the technique reliably captures the transition from a Mott insulator at half filling to a pseudogap, evidenced by the formation of Fermi arcs, and finally to a metallic state at large doping. The ability to treat large clusters with quantum cluster methods helps to minimize potential finite-size effects and enables the study of systems with long-range orders, which will help extend the reach of these already powerful methods and provide important insights on the nature of various strongly correlated many-electron systems, including the high-Tc{\mathrm{T}}_{c}Tc​ cuprate superconductors.
Abstract The pseudogap in high-temperature superconducting cuprates is an exotic state of matter, displaying emerging Fermi arcs and a momentum-selective suppression of spectral weight upon cooling. We show how these phenomena are captured in the three-band Emery model by performing dynamical vertex approximation calculations for its normal state. For the hole-doped parent compound, our results demonstrate the formation of a pseudogap due to short-ranged commensurate antiferromagnetic fluctuations. At larger doping values, progressively, incommensurate correlations and a metallic regime appear. Our results are in qualitative agreement with this doping trend in the normal state of cuprates, and hence, represent a step towards the uniform description of their phase diagrams within a single theoretical framework.
One of the primary reasons that superconductivity in underdoped cuprates is enigmatic is that it emerges from an incoherent Fermi-arc state, so the applicability of the Bardeen-Cooper-Schrieffer (BCS) theory is questionable. Here we approach this problem by investigating unconventional ddd-wave superconductivity in a recently proposed solvable model for strongly correlated Fermi arcs. We show analytically that the exact incorporation of Fermi arcs fundamentally modifies the BCS equations, which enables us to isolate a many-body effect that suppresses the superconducting transition temperature TcT_cTc​ beyond the simple reduction expected from a shrinking Fermi surface. The theory unambiguously produces: (i) a TcT_cTc​ tracing out a dome as a function of hole doping, (ii) a new low-energy mode upon entering superconductivity, (iii) a suppressed superfluid stiffness in the underdoped regime, and (iv) a gap-to-TcT_cTc​ ratio far exceeding the BCS limit, all consistent with experimental observations in cuprate superconductors. These findings provide an analytic benchmark for understanding how superconductivity emerges from a correlated Fermi-arc state in high-TcT_cTc​ superconductors.