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.

References in corpus (14)

• Electronic transport in two dimensional graphene
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• Semiclassical approximations for Hamiltonians with operator-valued symbols
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Cited by in corpus (1)

• A new approach to transport coefficients in the quantum spin Hall effect