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Density-operator theory of orbital magnetic susceptibility in periodic insulators

X. Gonze and J. W. Zwanziger
Phys. Rev. B 84, 064445 – Published 30 August 2011

Abstract

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose for insulators a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.

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  • Received 4 August 2011

DOI:https://doi.org/10.1103/PhysRevB.84.064445

©2011 American Physical Society

Authors & Affiliations

X. Gonze1,* and J. W. Zwanziger2,†

  • 1European Theoretical Spectroscopy Facility (ETSF), IMCN/NAPS Université Catholique de Louvain, B-1348, Louvain-la Neuve Belgium
  • 2Departments of Chemistry and of Physics and Atmospheric Sciences, and Institute for Research in Materials, Dalhousie University, Halifax, NS, Canada B3H 4J3

  • *xavier.gonze@uclouvain.be
  • jzwanzig@dal.ca

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Issue

Vol. 84, Iss. 6 — 1 August 2011

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