Optical spectral weight, phase stiffness, and
 T
 
 c
 
 bounds for trivial and topological flat band superconductors

Verma, Nishchhal; Hazra, Tamaghna; Randeria, Mohit

doi:10.1073/pnas.2106744118

Cited by 39 publications

(11 citation statements)

References 36 publications

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“…The relationship between the superfluid weight and quantum metric has been used to derive various bounds for the superfluid weight [5,6,13,23,54]. The lower bound given in [5] for time-reversal-symmetric systems in terms of the spin Chern number is valid, as it is a lower bound for the quantum metric regardless of the choice of orbital positions.…”

Section: Revisiting the Literaturementioning

confidence: 99%

Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

et al. 2022

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A central result in superconductivity is that flat bands, though dispersionless, can still host a nonzero superfluid weight due to quantum geometry. We show that the derivation of the mean field superfluid weight in previous literature is incomplete, which can lead to severe quantitative and even qualitative errors. We derive the complete equations and demonstrate that the minimal quantum metric, the metric with minimum trace, is related to the superfluid weight in isolated flat bands. We complement this result with an exact calculation of the Cooper pair mass in attractive Hubbard models with the uniform pairing condition. When the orbitals are located at high-symmetry positions, the Cooper pair mass is exactly given by the quantum metric, which is guaranteed to be minimal. Moreover, we study the effect of closing the band gap between the flat and dispersive bands, and develop a mean field theory of pairing for different band-touching points via the S-matrix construction. In mean field theory, we show that a nonisolated flat band can actually be beneficial for superconductivity. This is a promising result in the search for high-temperature superconductivity as the material does not need to have flat bands that are isolated from other bands by the thermal energy. Our work resolves a fundamental caveat in understanding the relation of multiband superconductivity to quantum geometry, and the results on band touchings widen the class of systems advantageous for the search of high-temperature flat band superconductivity.

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Section: Revisiting the Literaturementioning

confidence: 99%

Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

et al. 2022

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“…Our results are not related to topological effects [62,63], since the bandstructure of the bilayer system is nontopological and the wide band features no gap. The findings are also qualitatively different from the previous results related to incipient bands [26][27][28][29][30][31][32], since these works considered the effects of full or empty narrow bands in repulsive models and found that the half-filled situation does not favor superconductivity [29].…”

mentioning

confidence: 52%

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Yue¹,

Aoki²,

Werner³

2022

Preprint

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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. 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 inter-layer 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.

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“…The physics of two-body bound states in the presence of a flat band has been recently explored theoretically in different contexts, including topological matter [17][18][19][20] and the link between the inverse effective mass of the bound state and the quantum metric of the singleparticle states [21][22][23]. This second direction is related to the more general question of understanding how transport and superconductivity can occur in system with quenched kinetic energy [24][25][26][27][28][29][30][31][32]. Transport in many-body bosonic flat-band systems has also been explored, see for instance [33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

Orso,

Singh

2021

Preprint

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We investigate pairing and superconductivity in the attractive Hubbard model on the onedimensional sawtooth lattice. This is a periodic lattice with two sites per unit cell, which exhibits a flat band (FB) by fine-tuning the hopping rates. We first discuss the formation of pairs in vacuum, showing that there is a broad region of hopping rates values around the FB point, for which both the binding energy and the effective mass of the bound state are strongly affected even by weak interactions. Based on the DMRG method, we then address the ground-state properties of a system with equal spin populations as a function of the interaction strength and the hopping rates. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. The chemical potential of a system near the FB point remains always close to its zero-density limit predicted by the two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the binding energy, it is no longer peaked at the FB point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. In particular, we find that three-body bound states (trimers) are allowed in the sawtooth lattice, in sharp contrast with the linear chain geometry.

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Optical spectral weight, phase stiffness, and T _c bounds for trivial and topological flat band superconductors

Cited by 39 publications

References 36 publications

Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

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Optical spectral weight, phase stiffness, and T c bounds for trivial and topological flat band superconductors

Cited by 39 publications

References 36 publications

Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

Contact Info

Product

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Optical spectral weight, phase stiffness, and T _c bounds for trivial and topological flat band superconductors