We investigate the disordered flat-band superconductivity within the attractive Hubbard model on the kagome lattice by contrasting the flat-band-preserving disorder [Phys. Rev. B 98, 235109 (2018)] with the random hopping disorder that breaks the flat-band degeneracy. Through Bogoliubov-de Gennes mean-field calculations, we find that the superfluid weight is much more robust under the flat-band-preserving disorder, while the system eventually undergoes a transition to an insulator as disorder becomes strong enough. The almost linear interaction-dependence of the superfluid weight in the weak coupling limit found with the flat-band-preserving disorder confirms the persistent flat-band signature, whereas the exponential behavior of a dispersive-band character arises with the random hopping counterpart. In addition, in the exact diagonalization of the one-particle density matrix, we identify an occupation spectrum structure attributed to the flat-band states, demonstrating the connection between the resilient flat band and the enhanced robustness of superconductivity.
We investigate the disordered flat-band superconductivity within the attractive Hubbard model on the kagome lattice by contrasting the flat-band-preserving disorder [Phys. Rev. B 98, 235109 (2018)] with the random hopping disorder that breaks the flat-band degeneracy. Through Bogoliubov-de Gennes mean-field calculations, we find that the superfluid weight is much more robust under the flat-band-preserving disorder, while the system eventually undergoes a transition to an insulator as disorder becomes strong enough. The almost linear interaction-dependence of the superfluid weight in the weak coupling limit found with the flat-band-preserving disorder confirms the persistent flat-band signature, whereas the exponential behavior of a dispersive-band character arises with the random hopping counterpart. In addition, in the exact diagonalization of the one-particle density matrix, we identify an occupation spectrum structure attributed to the flat-band states, demonstrating the connection between the resilient flat band and the enhanced robustness of superconductivity.
We study the interplay between on-site disorder and fermion pairing on the quasi-one-dimensional flat-band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat-band superconductivity is robust against disorder: The critical disorder strength Wc required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength U and is proportional to the superconducting weight Ds of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that Wc can be accurately determined by using an appropriate scaling function.
We use the density-matrix renormalization group method to investigate the superconductor-insulator transition (SIT) in disordered quasi-one-dimensional systems. Focusing on the case of an interacting spinful Hamiltonian at quarter filling, we contrast the differences arising in the SIT when the parent noninteracting model features flat or dispersive bands. Furthermore, we unveil the critical disorder amplitude that triggers insulating behavior by comparing disorder distributions that preserve or not SU(2) symmetry. While scaling analysis suggests the transition be of a Berezinskii-Kosterlitz-Thouless type for all models (two lattices and two disorder types), only in the flat-band model with Zeeman-like disorder is the critical disorder nonvanishing. In this sense, the flat-band structure does strengthen superconductivity in the presence of attractive interactions. For both flat- and dispersive-band models, (i) in the presence of SU(2)-symmetric random chemical potentials, the disorder-induced transition is from superconductor to insulator of singlet pairs; (ii) for the Zeeman-type disorder, the transition is from superconductor to insulator of unpaired fermions. In all cases, our numerical results suggest no intermediate disorder-driven metallic phase.
Kagome metals exhibit a rich interplay of topology, electronic correlations, and lattice dynamics. Recent discoveries of Kagome materials with a flat band near the Fermi level have revealed a variety of correlated electronic phases. However, elucidating their microscopic origin remains challenging, as realistic descriptions require accounting for multiple orbitals and competing interactions on an equal footing. To disentangle correlation effects from material-specific details and identify the essential physics of the flat-band regime, we study the single-orbital Kagome-Hubbard model at flat-band fillings using dynamical mean-field theory. We find strong signatures of flat-band ferromagnetism, consistent with exact and mean-field ground-state results. Moreover, we uncover an unconventional quasi-ordered phase in which a partially filled spin-polarized flat band pinned at the Fermi level gives rise to persistent local spin fluctuations down to zero temperature, in striking contrast to the classical behavior expected for a conventional ferromagnet. Our results demonstrate that these anomalous fluctuations are an intrinsic consequence of the flat-band degeneracy and establish a minimal framework for understanding correlation effects in flat-band Kagome systems.
Flat-band systems provide a promising platform for exploring exotic correlated phases owing to quenched kinetic energy and enhanced interaction effects. In this work, we investigate the flat-band superfluid transition in the attractive kagome Hubbard model using large-scale determinant quantum Monte Carlo simulations accelerated by fast Fourier transforms and delay updates. Through systematic calculations of the transition temperature, spin susceptibility, and density compressibility, we establish the finite-temperature phase diagram at the flat-band filling ρ=5/3 and find a clear linear scaling of the superfluid transition temperature with the interaction strength, Tc=0.0314∣U∣. Our results reveal a wide separation of temperature scales between local pair formation and global phase coherence, which stabilizes a broad intermediate supercompressible bosonic fluid region of preformed pairs that bridges the normal Fermi gas and the flat-band superfluid. We further demonstrate that both the transition temperature and density compressibility are significantly enhanced in the flat band compared to van Hove fillings. Our findings highlight the essential role of flat-band-enhanced pair-density fluctuations in separating the pairing and phase-coherence scales, offering clear experimental signatures for probing flat-band superfluidity and superconductivity in cold-atom and kagome-material platforms.
We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap and winding number of the flat band. Using full multiband mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We obtain excellent agreement between MF and DMRG calculations. The SC weight Ds on the gapped topological, $W\ensuremath{\ne}0$, flat band increases linearly with interaction strength U for low values and with a slope that depends on the details of the compact localized state at U=0. As $U\ensuremath{\rightarrow}0$ for the gapped nontopological flat band (W=0), Ds decays with a power law faster than quadratically but slower than exponentially. In the gapless case (flat band touching the band above it), we find at low U (for both W=0 and $W\ensuremath{\ne}0$) that ${D}_{s}\ensuremath{\propto}{U}^{\ensuremath{\varphi}}$, with $\ensuremath{\varphi}<1$. In other words, Ds increases faster than linearly for low U, thus favoring SC at weak interaction more than the gapped case. Our results reestablish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.
Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T c for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T c (in the weak-coupling region) or significantly increase T c (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band.