Theory of quantum decoherence and its application to anomalous Hall effect

Abstract

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.

Figures (5)

• Figure 1: A second-order scattering process intrinsically tied to quantum decoherence. Electrons with ($-+$) coherence scatter upward, while those with ($+-$) coherence tend to scatter downward.
• Figure 2: The Feynman diagrams for second-order Born-Markov approximation.
• Figure 3: (a-c) The $\epsilon_L$ dependence of the AHE conductivities derived from (a) ordinary, (b) anomalous, and (c) total off-diagonal density matrix. Panel (d) plots the $n_{\text{i}}$ dependence of $\delta\sigma_{H}$, $\delta \sigma^{\Vert}_{H}$, and $\sigma^{\perp}_{H}$. Other parameters: $v_R/a=12$ meV, and $\epsilon_F=3$ meV, $U/a^2=1$ eV, and $a=0.35$ nm.
• Figure 4: (a-b) $n_{\text{i}}$ dependence of the AHE conductivities derived from side jump (blue), skew scattering (green), and anomalous (magenta) off-diagonal density matrix. The red curves reveal a clear influence of decoherence on the AHE, quantified by $\sigma^{\Vert}_{H}-\sigma^{0}_{H}$. Panels (c) and (d) plot the corresponding $\epsilon_L$ dependence. The inset of panel (a) reveals the $1/n_{\textit{i}}$ scaling of the skew scattering contribution. Other parameters are the same as Fig. \ref{['FIG']}.
• Figure 5: (a,b) $T$ dependence of (a) $\sigma^{\Vert}_{H}$ and (b) $\sigma^{\perp}_{H}$ for different $n_{\text{i}}$, where $\epsilon_F>\epsilon_L$. Panels (c) and (d) plot the situation of $\epsilon_F<\epsilon_L$. Other parameters are the same as Fig. \ref{['FIG']}.