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Journal Articles Annales Henri Poincaré Year : 2021

Coherent electronic transport in periodic crystals

Abstract

We consider independent electrons in a periodic crystal in their ground state, and turn on a uniform electric field at some prescribed time. We rigorously define the current per unit volume and study its properties using both linear response and adiabatic theory. Our results provide a unified framework for various phenomena such as the quantification of Hall conductivity of insulators with broken time-reversibility, the ballistic regime of electrons in metals, Bloch oscillations in the long-time response of metals, and the static conductivity of graphene. We identify explicitly the regime in which each holds.
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Dates and versions

hal-02468564 , version 1 (05-02-2020)
hal-02468564 , version 2 (09-11-2020)

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Eric Cancès, Clotilde Fermanian Kammerer, Antoine Levitt, Sami Siraj-Dine. Coherent electronic transport in periodic crystals. Annales Henri Poincaré, 2021, 22, pp.2643-2690. ⟨10.1007/s00023-021-01026-3⟩. ⟨hal-02468564v2⟩
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