Conductivity in flat bands from the Kubo-Greenwood formula

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorHuhtinen, Kukka-Emiliaen_US
dc.contributor.authorTörmä, Päivien_US
dc.contributor.departmentDepartment of Applied Physicsen
dc.contributor.groupauthorQuantum Dynamicsen
dc.date.accessioned2023-10-25T07:37:19Z
dc.date.available2023-10-25T07:37:19Z
dc.date.issued2023-10-05en_US
dc.description.abstractConductivity in a multiband system can be divided into intra- and interband contributions, and the latter further into symmetric and antisymmetric parts. In a flat band, intraband conductivity vanishes and the antisymmetric interband contribution, proportional to the Berry curvature, corresponds to the anomalous Hall effect. We investigate whether the symmetric interband conductivity, related to the quantum metric, can be finite in the zero frequency and flat band limit. Starting from the Kubo-Greenwood formula with a finite scattering rate η, we show that the DC conductivity is zero in a flat band when taking the clean limit (η→0). If commonly used approximations involving derivatives of the Fermi distribution are used, finite conductivity appears at zero temperature T=0; we show however that this is an artifact due to the lack of Fermi surfaces in a (partially) flat band. We then analyze the DC conductivity using the Kubo-Streda formula, and note similar problems at T=0. The predictions of the Kubo-Greenwood formula (without the approximation) and the Kubo-Streda formula differ significantly at low temperatures. We illustrate the results within the Su-Schrieffer-Heger model where one expects vanishing DC conductivity in the dimerized limit as the unit cells are disconnected. We discuss the implications of our results to previous work which has proposed the possibility of finite flat band DC conductivity proportional to the quantum metric. Our results also highlight that care should be taken when applying established transport and linear response approaches in the flat band context, since many of them utilize the existence of a Fermi surface and assume scattering to be weak compared to kinetic energy.en
dc.description.versionPeer revieweden
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationHuhtinen, K-E & Törmä, P 2023, ' Conductivity in flat bands from the Kubo-Greenwood formula ', Physical Review B, vol. 108, no. 15, 155108 . https://doi.org/10.1103/PhysRevB.108.155108en
dc.identifier.doi10.1103/PhysRevB.108.155108en_US
dc.identifier.issn2469-9950
dc.identifier.issn2469-9969
dc.identifier.otherPURE UUID: f91dd851-4d10-449e-add3-a098805e58e9en_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/f91dd851-4d10-449e-add3-a098805e58e9en_US
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dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/125205296/SCI_Huhtinen_etal_PhysRevB_2023.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/124291
dc.identifier.urnURN:NBN:fi:aalto-202310256664
dc.language.isoenen
dc.publisherAmerican Physical Society
dc.relation.ispartofseriesPhysical Review Ben
dc.relation.ispartofseriesVolume 108, issue 15en
dc.rightsopenAccessen
dc.titleConductivity in flat bands from the Kubo-Greenwood formulaen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion

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