Orbital Magnetization and Streda Formula of Interacting Electrons in the Mean-field Approximation

Abstract

We study the magnetic-field response of interacting electron systems within mean-field theory using perturbation theory. We show that the linear response of the mean-field density-matrix to a weak magnetic field is purely geometric: it depends only on wavefunction derivatives, the Berry connections linking the occupied and unoccupied subspaces, and does not explicitly depend on the interaction potential and the quasiparticle dispersion. This leads to compact, gauge-invariant projector expressions for both the Středa formula and the formula for orbital magnetization. Our calculation explicitly elucidates the role of exchange and self-consistency in defining current vertices for orbital magnetization calculations. Our work establishes a direct connection between mean-field theory, quantum geometry and the non-interacting topological band theory.

6 pages

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