Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion

Lau, Alexander; Peotta, Sebastiano; Pikulin, Dmitry I.; Rossi, Enrico; Hyart, Timo

doi:10.48550/arxiv.2203.01058

Cited by 4 publications

(6 citation statements)

References 44 publications

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“…The superfluid weight has been computed from mean field theory in a variety of multiband systems [6,7,13,14,28,34,43,[50][51][52][53] including magic-angle twisted bilayer graphene [23][24][25]. The impact of the terms arising from the derivatives of the order parameters in Eq.…”

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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“…This equation is the same as (52) but with the effective fields replaced by the one-particle density matrix. The third equality in (54) is a consequence of the fact that in (41) and (42) the only term that gives a direct dependence on A is Tr[K(A)P 11 ] = Ĥ free (A) , while the last equality comes from (9). The result in (54) is valid for arbitrary A, therefore, for the second full derivative of the grand potential we have d 2 Ω m.f.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 97%

“…Nevertheless, disorder has a significant effect on many of the observable properties of superconductors and when increased above a certain threshold it drives a transition to the normal state, which can be metallic or even insulating [1][2][3][4][5][6]. The interplay between superconductivity and disorder is a vast research subject and many questions remain open [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Superconductivity, generalized random phase approximation and linear scaling methods

Peotta

2022

New J. Phys.

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The superfluid weight is an important observable of superconducting materials since it is related to the London penetration depth of the Meissner effect. It can be computed from the change in the grand potential (or free energy) in response to twisted boundary conditions in a torus geometry. Here we review the Bardeen-Cooper-Schrieffer mean-field theory emphasizing its origin as a variational approximation for the grand potential. The variational parameters are the effective fields that enter in the mean-field Hamiltonian, namely the Hartree-Fock potential and the pairing potential. The superfluid weight is usually computed by ignoring the dependence of the effective fields on the twisted boundary conditions. However, it has been pointed out in recent works that this can lead to unphysical results, particularly in the case of lattice models with flat bands. As a first result, we show that taking into account the dependence of the effective fields on the twisted boundary conditions leads in fact to the generalized random phase approximation. Our second result is providing the mean-field grand potential as an explicit function of the one-particle density matrix. This allows us to derive the expression for the superfluid weight within the generalized random phase approximation in a transparent manner. Moreover, reformulating mean-field theory as a well-posed minimization problem in terms of the one-particle density matrix is a first step towards the application to superconducting systems of the linear scaling methods developed in the context of electronic structure theory.

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“…The superfluid weight has been computed from meanfield theory in a variety of multiband systems [6,7,12,13,27,40,41,[50][51][52] including magic-angle twisted bilayer graphene [22][23][24] and flat band systems with disorder [53]. The impact of the terms arising from the derivatives of the order parameters should be examined on a case-by-case basis.…”

Section: Revisiting the Literaturementioning

confidence: 99%

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

Huhtinen,

Herzog-Arbeitman,

Chew

et al. 2022

Preprint

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Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion

Cited by 4 publications

References 44 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, generalized random phase approximation and linear scaling methods

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

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