Geometric orbital magnetization in adiabatic processes

Abstract

We consider periodic adiabatic processes of gapped many-body spinless electrons. We find an additional contribution to the orbital magnetization due to the adiabatic time evolution, dubbed \textit{geometric} orbital magnetization, which can be expressed as derivative of the many-body Berry phase with respect to an external magnetic field. For two-dimensional band insulators, we show that the geometric orbital magnetization generally consists of two pieces, the topological piece that is expressed as third Chern-Simons form in $(t,k_x,k_y)$ space, and the non-topological piece that depends on Bloch states and energies of both occupied and unoccupied bands.

Published version with few typos corrected. 15 pages, 5 figures

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• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Corner charge and bulk multipole moment in periodic systems
• Conversion between electron spin and microscopic atomic rotation
• Current-induced orbital magnetization in systems without inversion symmetry
• Gate-tunable phonon magnetic moment in bilayer graphene
• $N$-band Hopf insulator
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• Quadrupole moments, edge polarizations, and corner charges in the Wannier representation
• Thermodynamic approach to electric quadrupole moments
• Chiral-phonon-induced current in helical crystals
• Rotational $g$ factors and Lorentz forces of molecules and solids from density-functional perturbation theory
• Conversion of chiral phonons into magnons in ferromagnets and antiferromagnets
• Theory of spin magnetization driven by chiral phonons
• Unconventional Metallic Magnetism: Non-analyticity and Sign-changing Behavior of Orbital Magnetization in ABC Trilayer Graphene
• Gauge theory of giant phonon magnetic moment in doped Dirac semimetals
• Many-Body Quadrupolar Sum Rule for Higher-Order Topological Insulator
• Dynamical Orbital Angular Momentum Induced by Circularly Polarized Phonons
• Rototranslational sum rules for nuclear dynamics via traveling pseudopotentials
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries