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arXiv:1811.08848 · Physical review. B./Physical review. B

Enhanced correlations and superconductivity in weakly interacting partially flat-band systems: A determinantal quantum Monte Carlo study

Edwin W. Huang, Mohammad-Sadegh Vaezi, Zohar Nussinov, Abolhassan Vaezi

Published Jun 13, 2019• 18 citations
arXivHTMLPDF

Abstract

Motivated by recent experiments realizing correlated phenomena and superconductivity in two-dimensional (2D) van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model and a partially flat-band structure containing a nondispersing region, with identical total noninteracting bandwidth ${W}_{\mathrm{tot}}$. For both repulsive and attractive weak interactions ($|U|\ensuremath{\ll}{W}_{\mathrm{tot}}$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with $U$ being an order of magnitude smaller than ${W}_{\mathrm{tot}}$, we find the presence of a Mott insulating state near half filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.

DOI
10.1103/physrevb.99.235128

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Motivated by recent experiments realizing correlated phenomena and superconductivity in two-dimensional (2D) van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model and a partially flat-band structure containing a nondispersing region, with identical total noninteracting bandwidth Wtot{W}_{\mathrm{tot}}Wtot​. For both repulsive and attractive weak interactions (∣U∣\ensuremath≪Wtot|U|\ensuremath{\ll}{W}_{\mathrm{tot}}∣U∣\ensuremath≪Wtot​), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with UUU being an order of magnitude smaller than Wtot{W}_{\mathrm{tot}}Wtot​, we find the presence of a Mott insulating state near half filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.
The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with an unequal number of sites in each sublattice must have nonzero spin SSS at half filling. Recently, there has been interest in Lieb geometries due to the possibility of topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using determinant quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems. Specifically, our results show unusual charge and charge transfer signatures within the flat band, and a reduction in pairing order at $\ensuremath{\rho}=2/3$ and $\ensuremath{\rho}=4/3$, the points at which the flat band is first occupied and then completely filled. We compare our results to the case of flat bands in the Kagome lattice and demonstrate that the behavior observed in the two cases is rather different.
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.
Studies of systems with two fermionic bands with repulsive interaction strength U have a long history, with the Periodic Anderson Model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use Quantum Monte Carlo to study analogous issues for attractive interactions. As in the Periodic Anderson Model, we focus on a case where one band is uncorrelated (U=0), and focus on the effect of hybridization V between the bands on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are able to explore the physics of doped multi-band attractive systems at low temperatures whereas ground state properties of repulsive models can be determined only at half-filling. For small V, pairing in the U<0 layer induces pairing in the U=0 layer. At larger V the ground state of the coupled system loses its superconducting character. The Quantum Monte Carlo data are complemented by results obtained with the Bogoliubov-de Gennes approximation.
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.
Studies of systems with two fermionic bands (or equivalently, layers) with repulsive interaction strength U have a long history, with the periodic Anderson model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use quantum Monte Carlo to study analogous issues for attractive interactions. As in the PAM, we focus on a case where one band (layer) is uncorrelated ( U = 0), and the effect of hybridization V between the bands (layers) on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are better able to explore the physics of doped bilayer attractive systems at low temperatures (except in the case of exponentially small transition temperatures) whereas ground state properties of repulsive models can be determined only at half-filling. For small V , pairing in the U < 0 layer induces pairing in the U = 0 layer. At larger V superfluidity is suppressed at the low but finite T at which the quantum Monte Carlo was performed. The quantum Monte Carlo data are complemented by results obtained with the Bogoliubov–de Gennes approximation.
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.