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arXiv · 2002.01990

Coherent electronic transport in periodic crystals

Eric Cancès·Clotilde Fermanian Kammerer·Antoine Levitt·Sami Siraj-Dine
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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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Eric Cancès, Clotilde Fermanian Kammerer, Antoine Levitt, Sami Siraj-Dine. 2020-02-05. Coherent electronic transport in periodic crystals. https://doi.org/10.1007/s00023-021-01026-3

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