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Efficient computation of Kubo conductivity for incommensurate 2D heterostructures

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  • Daniel Massatt

    (University of Chicago)

  • Stephen Carr

    (Harvard University)

  • Mitchell Luskin

    (School of Mathematics, University of Minnesota)

Abstract

We introduce a numerical method for computing conductivity via the Kubo formula for incommensurate 2D bilayer heterostructures using a tight-binding framework. We begin by deriving the momentum space formulation and Kubo formula from the real space tight-binding model using the appropriate Bloch transformation operator. We further discuss the resulting algorithm along with its convergence rate and computational cost in terms of model parameters such as relaxation time and temperature. In particular, we show that for low frequencies, low temperature, and long relaxation times conductivity can be computed very efficiently using the momentum space algorithm for a wide class of materials. We then showcase our method by computing conductivity for twisted bilayer graphene (tBLG) for small twist angles. Graphical abstract

Suggested Citation

  • Daniel Massatt & Stephen Carr & Mitchell Luskin, 2020. "Efficient computation of Kubo conductivity for incommensurate 2D heterostructures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(4), pages 1-9, April.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:4:d:10.1140_epjb_e2020-100518-7
    DOI: 10.1140/epjb/e2020-100518-7
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