Interaction-induced sign reversal of the orbital magnetic susceptibility in Chern insulators

It has been well established that the orbital magnetization of interacting electrons can be simply evaluated by applying the single-particle formula to self-consistent HF bands. However, we show that such procedure fails qualitatively for orbital magnetic susceptibility, especially in topological systems: in a Chern-insulating phase of twisted MoTe$_2$, the interaction-induced correction reverses the sign of the susceptibility. This result follows from an algebraic framework that solves the HF problem at finite magnetic field, where noncommuting canonical momenta obstruct a direct calculation: a \emph{reverse Peierls substitution} maps every magnetic-translation-invariant operator to a unique bivariate function, converting the finite-field self-consistency into a function equation that can be expanded systematically in $B$. At first order, this yields a linear equation for the field-induced change $δX$ of the Fock potential, leading to an intrinsically interaction-induced susceptibility in addition to a single-particle-like one. The framework reproduces the Středa formula for insulators, and an auxiliary-Hilbert-space construction carries it to periodic and moiré systems. Finite-field HF calculations in a gapped Dirac model and in the twisted-MoTe$_2$ Chern insulator confirm the theory quantitatively.