Recently, the possibility of high-temperature superconductivity (SC) in flat-band (FB) systems has been the focus of a great deal of activity. This study reveals that unlike conventional intra-band SC for which disorder has a dramatic impact, that associated with FBs is surprisingly robust to disorder-induced fluctuations and quasi-particle localization. In particular, for weak off-diagonal disorder, the critical temperature decreases linearly with disorder amplitude for conventional SC, whereas it is only quadratic in the case of SC in FBs. Our findings could have a major impact on the research and development of new compounds whose high purity will no longer be a critical barrier to their synthesis.
Recently, the possibility of high-temperature superconductivity (SC) in flat-band (FB) systems has been the focus of a great deal of activity. This study reveals that unlike conventional intra-band SC for which disorder has a dramatic impact, that associated with FBs is surprisingly robust to disorder-induced fluctuations and quasi-particle localization. In particular, for weak off-diagonal disorder, the critical temperature decreases linearly with disorder amplitude for conventional SC, whereas it is only quadratic in the case of SC in FBs. Our findings could have a major impact on the research and development of new compounds whose high purity will no longer be a critical barrier to their synthesis.
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.
The possibility of an unconventional form of high temperature superconductivity in flat band (FB) material does not cease to challenge our understanding of the physics in correlated systems. Here, we calculate the normal and anomalous one-particle correlation functions in various one and two dimensional FB systems and systematically extract the characteristic lengthscales. When the Fermi energy is located in the FB, it is found that the coherence length ( \xi ξ ) is of the order of the lattice spacing and weakly sensitive to the strength of the electron-electron interaction. Recently, it has been argued that in FB compounds \xi ξ could be decomposed into a conventional part of BCS type ( \xi_{BCS} ξ B C S ) and a geometric contribution which characterises the FB eigenstates, the quantum metric ( \langle g \rangle ⟨ g ⟩ ). However, by calculating the coherence length in two possible ways, our calculations show that \xi ≠ \sqrt{\langle g \rangle.} ξ ≠ ⟨ g ⟩ . This may suggest that the link between QM and coherence length is more complex, and leaves us with the open question: what is the appropriate definition of the coherence length in flat-band systems?
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.
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.
Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, Tc(U)=c∣U∣. However, the value of c and the full nonlinear Tc(U) curve---with a maximum at large ∣U∣---are known beyond mean-field and quantum geometry estimates only for systems with isolated flat bands. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and BEC (preformed Cooper pair) scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of U, leading to a sharp crossover to long-range correlations at a characteristic temperature T∗, which provides a controlled upper bound on Tc. The highest T∗ occurs when all three bands touch at a single momentum point, potentially corresponding to high Tc values.
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.