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Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures

Eric Cancès 1, 2 Paul Cazeaux 3 Mitchell Luskin 3 
Abstract : We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C*-algebra framework introduced by Bellissard and collaborators to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.
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https://hal.inria.fr/hal-01403588
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Submitted on : Saturday, November 18, 2017 - 9:44:29 PM
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Eric Cancès, Paul Cazeaux, Mitchell Luskin. Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures. Journal of Mathematical Physics, American Institute of Physics (AIP), 2017, 58 (6), pp.1-29. ⟨10.1063/1.4984041⟩. ⟨hal-01403588v2⟩

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