Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
By D. Ceresoli, T. Thonhauser, D. Vanderbilt, Raffaele Resta. 2005
244 citations recorded by the source corpus.
We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in two dimensions (2D) the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [Thonhauser, Ceresoli, Vanderbilt, and Resta, Phys. Rev. Lett. 95, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge invariant, in the multi-band formulation only the sum of both terms is gauge invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2D model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2D model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/d23ee89bd6ff6562ae24dd958a3d3ade68cd5dc8
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Berry phase effects on electronic properties (2009, methodology): “Similar formula for insulators with zero Chern number has been obtained by Ceresoli et al. (2006); Thonhauser et al. (2005) using the Wannier function approach, and has been numerically confirmed for a tightbinding model.”
- Maximally-localized Wannier Functions: Theory and Applications (2011, methodology): “Derivations of this formula via a semiclassical (Xiao et al., 2005) or long-wave quantum (Shi et al., 2007) approach are possible, but here we emphasize the derivation carried out in the Wannier representation (Ceresoli et al., 2006; Souza and Vanderbilt, 2008; Thonhauser et al., 2005).”