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arXiv:2104.07583 · New Journal of Physics

Probing a Bose metal via electrons: inescapable non-Fermi liquid scattering and pseudogap physics

Xinlei Yue, Anthony Hegg, Xiang Li, Wei Ku

Published Apr 19, 2023• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/acce5b

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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.
We establish that a doping-driven first-order metal-to-metal transition, from a pseudogap metal to Fermi Liquid, can occur in correlated quantum materials. Our result is based on the exact Dynamical Mean Field Theory solution of the Dimer Hubbard Model. This transition elucidates the origin of many exotic features in doped Mott materials, like the pseudogap in cuprates, incoherent bad metals, enhanced compressibility and orbital selective Mott transition. This phenomenon is suggestive to be at the roots of the many exotic phases appearing in the phase diagram of correlated materials.
We compute high-resolution angle-resolved photoemission spectroscopy of the Hubbard model using the unbiased determinant quantum Monte Carlo algorithm, revealing an asymmetry between electron and hole doping. Electron doping exhibits more coherent quasiparticles and stronger antiferromagnetic correlations compared to hole doping. At low doping, a nodal-antinodal dichotomy on the Fermi surface is observed, similar to cuprate experiments. The dichotomy reflects the momentum dependence of the Mott gap, as manifested in both the spectral function and the self-energy. For hole doping, we observe a transition towards the pseudogap, without signature of pocket formation. The simulated nuclear magnetic resonance pseudogap temperatures do not necessarily agree with the temperature determined by spectroscopy. These findings collectively suggest the pseudogap is a smooth crossover driven by strong correlations.
Strongly correlated solids exhibit phenomena -- from Mott localization to high-temperature superconductivity -- that escape conventional band theory. Efforts to address this unconventional physics have been typically cast in the language of Green's function theories, with the associated self-energies capturing strong correlations beyond the reach of mean-field theories. Here, we underscore that frequency- and momentum-dependent self-energies emerge also from mean-field solutions that break translational symmetry, and that these self-energies can display the characteristic fingerprints of strong correlations for certain, physically meaningful, spatial patterns. In the paradigmatic case of the 2D Hubbard model, we find that already at the mean-field level the doped antiferromagnet develops, in addition to long-range ordered stripes, many quasi-degenerate self-consistent solutions with antiferromagnetic textures organized into antiphase domains separated by hole-rich interfaces of convoluted shape, reminiscent of the phase-separation scenario. Remarkably, these solutions map into spectral functions that display very distinctively the phenomenology of the pseudogap, including the nodal-antinodal dichotomy, Fermi arcs, and a complementary Luttinger surface. The result is a conceptually simple description of such a complex phenomenon, where a pseudogap emerges as the momentum-space spectral portrait of the real-space interplay between antiferromagnetic domains and their metallic interfaces.
Understanding non-Fermi liquids in dimensions higher than one has been a subject of great interest. Such phases may serve as parent states for other unconventional phases of quantum matter, in a similar manner that conventional broken symmetry states can be understood as instabilities of the Fermi liquid. In this work, we investigate the emergence of an exotic non-Fermi liquid in two dimensions, where the fermions with quadratic band-touching dispersion interact with Bose metal. The bosonic excitations in Bose metal possess an extended nodal-line spectrum in momentum space, which arises due to the subsystem symmetry or the restricted motion of bosons. Using renormalization group analysis and direct computations, we show that the extended infrared singularity of Bose metal leads to a line of interacting fixed points of an exotic non-Fermi liquids, where the anomalous dimension of the fermions varies continuously, akin to the Luttinger liquid in one dimension. Further, the generalization of the model with multiple low-energy excitations is used to explore other unusual features of the resulting ground state.
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.
To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of the Hubbard model on the square lattice has been conducted by means of the ladder dual-fermion approximation with an electron self-energy correction. It is found that the appearance of these two states requires that the characteristic hole concentration below which the Mott-Heisenberg and Slater mechanisms of electron localization occurs pMSp_{\rm MS}pMS​ nearly coincides with the hole concentration where the Van Hove singularity (VHS) point is placed at the vicinity of the Fermi level. When this condition is met the VHS point is pinned at which the nesting condition of the antiferromagnetic (AFM) fluctuation is fulfilled almost everywhere on the Fermi surface in wide range of the hole concentration in a metallic state, i.e., the strange metal state. The spin fluctuation of the strange metal state is nearly quantum critical and the dynamical spin susceptivity is well described by overdamped spin wave having the ω/Tω/Tω/T scaling with the relaxation rate at the Planckian limit. Because of these distinctive features of the strange metal state, the kkk dependence of scattering rate of electrons is small and electrons behave as the marginal Fermi liquid, resulting in TTT-linear resistivity. In contrast, the pseudogap state is magnetically in the renormalized classical regime and the pseudogap is formed near the X point where the nesting condition of the short-range AFM order is fulfilled.