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

Huhtinen, Kukka-Emilia; Herzog-Arbeitman, Jonah; Chew, Aaron; Bernevig, Bogdan Andrei; Törmä, Päivi

doi:10.48550/arxiv.2203.11133

Cited by 1 publication

(8 citation statements)

References 59 publications

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“…In Section IV, we express the mean-field grand potential as an explicit function of the one-particle density matrix: the main result is given by Eqs. ( 41)- (42). We conclude the Section by arguing that, based on our results, the application of linear scaling method to superconducting systems should be rather straightforward.…”

Section: Introductionmentioning

confidence: 70%

“…For simplicity, we choose to use the grand potential here and refer to Ref. 42 for an in depth discussion regarding this issue.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

“…43, is the same as using the response functions ( 46)-(47) computed with the mean-field Hamiltonian (see Appendix A). In two recent works [29,42] it has been pointed out that it is important to take into account the dependence of the effective fields on the vector potential A when using Eq. ( 51), otherwise one may obtain unphysical results in the case of multiband/multiorbital lattices, in particular when flat bands are present.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

“…We mention in passing that in Ref. 42 an alternative approach based on a modified form of linear response theory and equivalent to Eq. ( 51) has been proposed.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

“…In Ref. 42 it has been shown that it is possible evaluate Eq. ( 51) by solving the mean-field problem for A = 0 only.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

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Superconductivity, generalized random phase approximation and linear scaling methods

Peotta¹

2022

Preprint

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We review the Bardeen-Cooper-Schrieffer mean-field theory emphasizing its origin as a variational approximation for the grand potential. This is done by using the Bogoliubov inequality as the starting point. Then we write the mean-field grand potential as an explicit function of the one-particle density matrix, which turns out to be a natural generalization of the Mermin functional. This result opens the way for the application to superconducting systems of the linear scaling methods developed in the context of electronic structure theory. Finally, we show that computing the superfluid weight from the derivatives of the mean-field grand potential naturally leads to the generalized random phase approximation. Our results showcase the advantage of a density matrix-based approach and are potentially interesting for the study of disordered superconductors and superconductors with large unit cell, such as twisted bilayer graphene and other moiré materials.

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Section: Introductionmentioning

confidence: 70%

“…For simplicity, we choose to use the grand potential here and refer to Ref. 42 for an in depth discussion regarding this issue.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

“…We mention in passing that in Ref. 42 an alternative approach based on a modified form of linear response theory and equivalent to Eq. ( 51) has been proposed.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

“…In Ref. 42 it has been shown that it is possible evaluate Eq. ( 51) by solving the mean-field problem for A = 0 only.…”

Section: Superfluid Weight and Generalized Random Phase Approximationmentioning

confidence: 99%

See 3 more Smart Citations

Superconductivity, generalized random phase approximation and linear scaling methods

Peotta¹

2022

Preprint

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show abstract

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

Cited by 1 publication

References 59 publications

Superconductivity, generalized random phase approximation and linear scaling methods

Superconductivity, generalized random phase approximation and linear scaling methods

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