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arXiv:2408.10465 · Physical review. B./Physical review. B

Theoretical study of spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band

Tetsuaki Aida, Karin Matsumoto, Daisuke Ogura, Masayuki Ochi, Kazuhiko Kuroki

Published Aug 19, 2024• 7 citations
arXivHTMLPDF

Abstract

One promising way to enhance superconductivity is to have coexisting wide and incipient narrow bands, where the Fermi level intersecting the wide band lies just above the narrow band, by which finite-energy spin fluctuations act as glue to mediate pair scattering. As an extreme case of the narrow band dispersion, we investigate spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band. For all of the systems investigated in this study, the Kagome, Lieb, and bilayer square lattices with a flat band, we find that spin-singlet pairing superconductivity is enhanced when the flat band is nearly fully filled, due to the interband pair scattering even when the flat band becomes dispersive by correlation effects. Among these models, enhancement of superconductivity is weak in the Lieb lattice, possibly because the density of states of the wide band goes to zero at the Dirac point where the flat and wide bands intersect. Also, when the electron density is smaller so that the flat band approaches half-filling, ferromagnetic spin fluctuations and spin-triplet pairing arises, which does not develop strongly compared to the case of the spin-singlet pairing for the incipient band situation.

DOI
10.1103/physrevb.110.054516

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•Jan 1, 2019•0 citations
One promising way to enhance superconductivity is to have coexisting wide and incipient narrow bands, where the Fermi level intersecting the wide band lies just above the narrow band, by which finite-energy spin fluctuations act as glue to mediate pair scattering. As an extreme case of the narrow band dispersion, we investigate spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band. For all of the systems investigated in this study, the Kagome, Lieb, and bilayer square lattices with a flat band, we find that spin-singlet pairing superconductivity is enhanced when the flat band is nearly fully filled, due to the interband pair scattering even when the flat band becomes dispersive by correlation effects. Among these models, enhancement of superconductivity is weak in the Lieb lattice, possibly because the density of states of the wide band goes to zero at the Dirac point where the flat and wide bands intersect. Also, when the electron density is smaller so that the flat band approaches half-filling, ferromagnetic spin fluctuations and spin-triplet pairing arises, which does not develop strongly compared to the case of the spin-singlet pairing for the incipient band situation.
Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting Tc{T}_{c}Tc​. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the interlayer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting---and to reach the largest order parameter---in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity.
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.
Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping ${t}_{\ensuremath{\perp}}$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing correlations in the large ${t}_{\ensuremath{\perp}}$ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased Tc{T}_{c}Tc​. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.
Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping t⊥t_\perpt⊥​, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Liftshiz transition and even when it becomes incipient. Here, we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust s±s_\pms±​ pairing correlations in the large t⊥t_\perpt⊥​ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased TcT_cTc​. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.
Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the [Formula: see text]-wave pairing correlation for repulsive on-site Hubbard interaction and [Formula: see text]-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.
In this thesis, superconductivity of fermions in two-dimensional Hubbard lattice models is theoretically studied. Each of the studied lattice structures features intriguing properties that provide valuable insight to understand superconductivity in general. While real condensed matter systems are too complicated to tackle with theoretical tools, the Hubbard model is one of the simplest quantum many-body models to possess a wide spectrum of physically relevant phenomena, from superconductivity to magnetism and topological order. Hubbard models are also interesting as they can be experimentally realized and accurately controlled by utilizing ultracold gases. The first part of the thesis explains the required theoretical background of superconductivity in the level of mean-field and linear response theories. Specifically, we primarily focus on the superfluid weight which implies the existence of the Meissner effect and dissipationless current, defining properties of superconductors. We further discuss how the Berezinskii-Kosterlitz-Thouless (BKT) transition, related to the loss of superconductivity due to the thermal fluctuations of the superconducting order parameter in high enough temperatures, can be accessed via the superfluid weight. In the second part, the main results are discussed. We show how the superconductivity of lattice models featuring dispersionless Bloch bands, so-called flat bands, can be large and originating from the quantum geometric properties of the Bloch states of the flat bands. This is in contrast to conventional dispersive bands where superconductivity is determined by the effective mass of the particles, i.e. by the dispersion relation of the Bloch bands alone and not by the Bloch states. This is well demonstrated in the Lieb lattice geometry, studied in Publication I, which features both a strictly flat and two dispersive Bloch bands, allowing direct comparison of superconductivity in dispersive and flat bands. We show how the superconductivity of the flat band is more robust than that of the dispersive bands and how the superfluid weight behaves non-monotonically as a function of the interaction strength. This non-monotonic behavior should be experimentally accessible. Flat band superconductivity is also the topic of Publication III, where the experimentally realized twisted bilayer graphene (TBG) is studied with local and non-local attractive interactions. We predict qualitative differences between local and non-local interaction schemes which could be distinguished experimentally and reveal the quantum geometric origin of superconductivity in TBG systems in case of both the assumed interaction schemes. Exotic Fulde-Ferrell (FF) superfluid phases, characterized by the non-zero momentum of Cooper pairs, were explored in Publication II. We show how the FF phases can be stabilized against thermal fluctuations in the presence of spin-orbit coupling (SOC) and that topologically non-trivial FF states, created with SOC and Zeeman fields, can be found at finite temperatures.; Tassa…