Orbital polarization and magnetization for independent particles in disordered media

Abstract

Formulas for the contribution of the conduction electrons to the polarization and magnetization are derived for disordered systems and within a one-particle framework. These results generalize known formulas for Bloch electrons and the presented proofs considerably simplify and strengthen prior justifications. The new formulas show that orbital polarization and magnetization are of geometric nature. This leads to quantization for a periodically driven Piezo effect as well as the derivative of the magnetization w.r.t. the chemical potential. It is also shown how the latter is connected to boundary currents in Chern insulators. The main technical tools in the proofs are an adaption of Nenciu's super-adiabatic theory to C${}^{\ast }$-dynamical systems and Bellissard's Ito derivatives w.r.t. the magnetic field.

Errors and misprints corrected; introduction expanded; to appear in CMP

References in corpus (4)

• Berry phase effect in anomalous thermoelectric transport
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Theory of Orbital Magnetization in Solids
• Equality of the bulk and edge Hall conductances in a mobility gap

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