Three-Band Anderson Lattice Model Reveals Co-Evolution of Topological and Magnetic Phases Driven by Electron Correlation

Abstract

Understanding the interplay of band topology, strong electron correlation, and magnetic order is the fundamental core bottleneck for realizing robust high-temperature quantum anomalous Hall effect (QAHE). Conventional two-band Anderson models are limited to paramagnetic Kondo topological insulators, failing to capture coupled topological-magnetic phase evolution relevant to the QAHE benchmark MnBi2Te4 family. We develop a minimal three-band Anderson lattice model incorporating Hubbard interaction, s-d exchange coupling, and a BHZ-like topological mechanism. Using the Kotliar-Ruckenstein slave-boson approach, we map correlation-driven phase transitions at filling v=2: increasing U drives a trivial-to-Kondo topological insulator transition, then activates the third band to mediate a paramagnetic topological insulator-to-ferromagnetic metal transition. The accompanying band reconstruction--fully spin-polarized d-orbitals sinking below the Fermi level, leaving itinerant p-orbitals to dominate low-energy physics--qualitatively matches published first-principles results for MnBi2Te4. In the strong-correlation regime, exchange coupling J stabilizes a Chern-Kondo insulator (C=1) and Weyl nodal-line semimetal. Critically, we reveal full d-orbital spin polarization renders the topological gap immune to correlation-induced narrowing, resolving the long-standing strong correlation-large gap incompatibility. Our results show excellent qualitative alignment with recent state-of-the-art QAHE experiments, providing a unified framework for correlated magnetic topological materials and new pathways to high-temperature QAHE.