Coherent electronic transport in periodic crystals. (English) Zbl 1472.82034
Summary: 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 quantization 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.
MSC:
| 82C70 | Transport processes in time-dependent statistical mechanics |
| 82D25 | Statistical mechanics of crystals |
| 81V70 | Many-body theory; quantum Hall effect |
| 82C35 | Irreversible thermodynamics, including Onsager-Machlup theory |
| 82D35 | Statistical mechanics of metals |
| 82D80 | Statistical mechanics of nanostructures and nanoparticles |
Keywords:
electronic transport; periodic crystals; Hall conductivity of insulators; electrons in metals; graphenReferences:
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