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Efficient computation of Kubo conductivity for incommensurate 2D heterostructures

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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.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Chicago, Chicago, IL, 60615, USA

    Daniel Massatt

  2. Department of Physics, Harvard University, Cambridge, MA, 02138, USA

    Stephen Carr

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Mitchell Luskin

Authors
  1. Daniel Massatt
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  2. Stephen Carr
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  3. Mitchell Luskin
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Correspondence to Mitchell Luskin.

Additional information

Contribution to the Topical Issue “Advances in Quasi-Periodic and Non-Commensurate Systems”, edited by Tobias Stauber and Sigmund Kohler.

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Massatt, D., Carr, S. & Luskin, M. Efficient computation of Kubo conductivity for incommensurate 2D heterostructures. Eur. Phys. J. B 93, 60 (2020). https://doi.org/10.1140/epjb/e2020-100518-7

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  • DOI: https://doi.org/10.1140/epjb/e2020-100518-7

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