Theory of quantum decoherence and its application to anomalous Hall effect

Coherent quantum phenomena can only emerge when decoherence is minimized, and mastery over decoherence is technologically crucial for designing and operating functional quantum devices. However, its microscopic mechanisms in spin-orbit-coupled ferromagnets remain elusive, and quantitative treatments have long been challenging. To solve this fundamentally significant and technologically crucial problem, we develop a quantum master-equation framework with a general ansatz for the off-diagonal density matrix that simultaneously captures electric-field-driven coherence and impurity-scattering-induced decoherence. This unified approach enables quantitative analysis of how decoherence reshapes the intrinsic anomalous Hall effect, revealing a clear crossover between intrinsic and extrinsic regimes. Remarkably, we identify a previously unrecognized extrinsic contribution: a second-order scattering process tightly relative to quantum decoherence-that is fundamentally distinct from both skew scattering and side jump mechanisms, yet substantially more significant than the skew scattering mechanism. Our work establishes decoherence as a key element in quantum transport and provides a systematic extension of the Boltzmann transport equation to incorporate decoherence, with broad implications for robust spintronic functionality.