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arXiv:2011.01680 · Physical review. B./Physical review. B

Exactly solvable model of Fermi arcs and pseudogap

Kun Yang

Published Jan 29, 2021• 23 citations
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Abstract

We introduce a very simple and exactly solvable model that supports Fermi arcs in its ground state and excitation spectrum. These arcs come in pairs, and merge into what we call a pseudo-Fermi surface along which fermions are gapped; this fermion gap is naturally identified as a pseudogap. A comparison will be made with the phenomenology of high-temperature cuprate superconductors.

DOI
10.1103/physrevb.103.024529

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We introduce a very simple and exactly solvable model that supports Fermi arcs in its ground state and excitation spectrum. These arcs come in pairs, and merge into what we call a pseudo-Fermi surface along which fermions are gapped; this fermion gap is naturally identified as a pseudogap. A comparison will be made with the phenomenology of high-temperature cuprate superconductors.
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Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gap-like behavior on parts of the Fermi surface, leaving a non-gapped segment known as Fermi arc around the diagonal of the Brillouin zone. Starting from the ttt-JJJ model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase in the framework of a novel renormalization scheme called PRM. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at a renormalized 'free' Hamiltonian for correlated electrons. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: We find well-defined excitation peaks around ω=0ω=0ω=0 near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small ωωω-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.
We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015).PNASA60027-842410.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-T_{c} cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.
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.
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.
Pseudogap phenomena and the formation of Fermi arcs in underdoped cuprates are numerically studied in the presence of phase fluctuations that are simulated by an XYXYXY model. Most importantly the spectral function for each Monte Carlo sample is calculated directly and efficiently by the Chebyshev polynomials without having to diagonalize the fermion Hamiltonian, which enables us to handle a system large enough to achieve sufficient momentum/energy resolution. We find that the momentum dependence of the energy gap is identical to that of a pure ddd-wave superconductor well below the Kosterlitz-Thouless (KT) transition temperature (TKT)({T}_{\text{KT}})(TKT​) while displays an upturn deviation from $\text{cos}\text{ }{k}_{x}\ensuremath{-}\text{cos}\text{ }{k}_{y}$ with increasing temperature. An abrupt onset of the Fermi arcs is observed above TKT{T}_{\text{KT}}TKT​ and the arc length exhibits a similar temperature dependence to the thermally activated vortex excitations.