Three Quantum-Geometric Contributions to Cubic Orbital Magnetization
Abstract
In noncentrosymmetric metals such as C3v topological-insulator surfaces, moiré heterobilayers, and zincblende crystals, point-group symmetry can forbid the linear and quadratic electric-field-induced orbital magnetization, leaving the cubic response as the leading signal. Using a Ward-complete finite-momentum cubic Kubo kernel with an antisymmetric linear-in-q projection, we show that the dc response separates into three quantum-geometric channels. These are a mixed electric-magnetic positional-shift quadrupole, a quantum-metric drift term, and an orbital-moment octupole. The three contributions share the same point-group symmetry but differ in their lifetime, frequency, and gate fingerprints. For a warped C3v surface the metric channel obeys the cutoff-independent law χG μ-2. We propose third-harmonic magneto-optical Kerr spectroscopy as an experimental route.
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