Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure

Wickles, Christian; Belzig, Wolfgang

Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure

Dateien

Wickles_224769.pdfGröße: 757.54 KBDownloads: 109

Datum

2012

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Physik

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows us to systematically construct the unitary transformation that brings the Hamiltonian into band-diagonal form. We address the issue of gauge invariance and discuss the necessity of using kinetic variables in order to obtain a low energy effective description that is consistent with the original theory. Essentially, our analysis is a semiclassical one and quantum corrections appear as Berry curvatures in addition to quantities that are related to the appearance of persistent currents. We develop a transport framework which is manifestly gauge invariant and it is based on a quantum Boltzman formulation along with suitable definitions of current density operators such that Liouville's theorem is satisfied. Finally, we incorporate the effects of an external electromagnetic field into our theory.

Fachgebiet (DDC)

530 Physik

Zitieren

ISO 690

WICKLES, Christian, Wolfgang BELZIG, 2012. Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure

BibTex

@unpublished{Wickles2012Effec-22476,
  year={2012},
  title={Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure},
  author={Wickles, Christian and Belzig, Wolfgang}
}

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