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arXiv:1903.09888 · Physical review. B./Physical review. B

Pairing and non-Fermi liquid behavior in partially flat-band systems: Beyond nesting physics

Sharareh Sayyad, Edwin W. Huang, Motoharu Kitatani, Mohammad-Sadegh Vaezi, Zohar Nussinov, Abolhassan Vaezi, Hideo Aoki

Published Jan 6, 2020• 35 citations
arXivHTMLPDF

Abstract

While many-body effects in flat-band systems are receiving renewed hot interest in condensed-matter physics for superconducting and topological properties as well as for magnetism, studies have primarily been restricted to multiband systems (with coexisting flat and dispersive bands). Here we focus on one-band systems where a band is ``partially flat,'' comprising flat and dispersive portions in $k$ space to reveal whether intriguing correlation effects can already arise on the simplest possible one-band level. For that, the two-dimensional repulsive Hubbard model is studied for two models having different flat areas in an intermediate-coupling regime with the dynamical mean-field theory combined with the fluctuation exchange approximation. We have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied and this triggers, for the model with a wider flat portion, a triplet-pair superconductivity favored over an unusually wide filling region, which is taken over by a sharply growing singlet pairing. For the model with a narrower flat portion, ${T}_{C}$ against filling exhibits an unusual double-peaked ${T}_{C}$ dome, associated with different numbers of nodes in the gap function having remarkably extended pairs in real space. We identify these as a manifestation of the physics outside the conventional nesting physics where only the pair scattering across the Fermi surface in designated (hot) spots is relevant. Another correlation effect arising from the flattened band is found in a non-Fermi-liquid behavior as detected in the momentum distribution function, frequency dependence of the self-energy, and spectral function. These indicate that unusual correlation physics can indeed occur in flat-band systems.

DOI
10.1103/physrevb.101.014501

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While many-body effects in flat-band systems are receiving renewed hot interest in condensed-matter physics for superconducting and topological properties as well as for magnetism, studies have primarily been restricted to multiband systems (with coexisting flat and dispersive bands). Here we focus on one-band systems where a band is ``partially flat,'' comprising flat and dispersive portions in kkk space to reveal whether intriguing correlation effects can already arise on the simplest possible one-band level. For that, the two-dimensional repulsive Hubbard model is studied for two models having different flat areas in an intermediate-coupling regime with the dynamical mean-field theory combined with the fluctuation exchange approximation. We have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied and this triggers, for the model with a wider flat portion, a triplet-pair superconductivity favored over an unusually wide filling region, which is taken over by a sharply growing singlet pairing. For the model with a narrower flat portion, TC{T}_{C}TC​ against filling exhibits an unusual double-peaked TC{T}_{C}TC​ dome, associated with different numbers of nodes in the gap function having remarkably extended pairs in real space. We identify these as a manifestation of the physics outside the conventional nesting physics where only the pair scattering across the Fermi surface in designated (hot) spots is relevant. Another correlation effect arising from the flattened band is found in a non-Fermi-liquid behavior as detected in the momentum distribution function, frequency dependence of the self-energy, and spectral function. These indicate that unusual correlation physics can indeed occur in flat-band systems.
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To explore whether a flat-band system can accommodate superconductivity, we consider repulsively interacting fermions on the diamond chain, a simplest possible quasi-one-dimensional system that contains a flat band. Exact diagonalization and the density-matrix renormalization group are used to show that we have a significant binding energy of a Cooper pair with a long-tailed pair-pair correlation in real space when the total band filling is slightly below 1/3, where a filled dispersive band interacts with the flat band that is empty but close to EF{E}_{F}EF​. Pairs selectively formed across the outer sites of the diamond chain are responsible for the pairing correlation. At exactly 1/3-filling an insulating phase emerges, where the entanglement spectrum indicates the particles on the outer sites are highly entangled and topological. These come from a peculiarity of the flat band in which ``Wannier orbits'' are not orthogonalizable.
In a flat band superconductor, bosonic excitations disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all space groups. We analytically compute their many-body excitations and find that the Cooper pair bound states obey an effective single-boson hopping Hamiltonian written in terms of the non-interacting wavefunctions. These bound states possess a unique zero-energy excitation whose quadratic dispersion is determined by the minimal quantum metric. The rest of the bound state spectrum is classified by topological quantum chemistry, which we use to identify Cooper pairs with Weyl nodes, higher angular momentum pairing, and fragile topology. Broadening the band dispersion, we find the strongest pairing occurs at half filling and not at the highest density of states. Our analytical results prove that the elementary fermionic and bosonic excitations, corresponding respectively to pairing and coherence, are governed by distinct properties of the flat band, rigorously establishing its unique phenomenology. Superconductivity in flat bands is a central feature of quantum geometric effects, supported by mean-field theory and numerics. Here, the authors exhibit a large family of flat band Hubbard models whose ground states, Bogoliubov-de-Gennes particles, and Cooper pairs are exactly solvable with analytically calculable dispersions.
The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, Q N , connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from Q N is given by χ − 1 ∝ | Δ q | . Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ − 1 ∝ | Δ q | 2 dependence yields a robust finite- T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the ( t − t ′ ) Hubbard model and found that at large U / t > 5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ − 1 ∝ | Δ q | 2 . Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024