Orbital Magnetization as a Local Property

Abstract

The modern expressions for polarization $\P$ and orbital magnetization $\M$ are $\k$-space integrals. But a genuine bulk property should also be expressible in $\r$-space, as unambiguous function of the ground-state density matrix, "nearsighted" in insulators, independently of the boundary conditions---either periodic or open. While $\P$---owing to its "quantum" indeterminacy---is {\it not} a bulk property in this sense, $\M$ is. We provide its $\r$-space expression for any insulator, even with nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory.

Phys. Rev. Lett, in press

References in corpus (8)

• Orbital magnetization in periodic insulators
• Mapping topological order in coordinate space
• The insulator/Chern-insulator transition in the Haldane model
• Dichroic f-sum rule and the orbital magnetization of crystals
• Electric polarization in a Chern insulator
• Topological edge states and quantum Hall effect in the Haldane model
• Orbital magnetization and Chern number in a supercell framework: Single k-point formula
• When does Magnetization Depend on the Boundary?

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