Half-Quantized Hall Metal and Marginal Metal in Disordered Magnetic Topological Insulators

A semimagnetic topological insulator -- a heterostructure combining a topological insulator with a ferromagnet -- exhibits a half-quantized Hall effect, characterized by a quantized Hall conductance of $\frac{1}{2}\frac{e^{2}}{h}$ (where $e$ is the elementary charge and $h$ is the Planck constant), which reinforces the established understanding of topological phenomena in condensed matter physics. However, its stability in realistic, disordered systems remains poorly understood. Here, we demonstrate the robustness of the half-quantized Hall effect in weakly disordered systems, stemming from a single gapless Dirac cone of fermions and coexisting with weak antilocalization due to the $\pi$ Berry phase that suppresses backscattering. Furthermore, we uncover a marginal metallic phase emerging between weak antilocalization and Anderson insulation -- a transition that defies conventional metal-insulator transitions by lacking an isolated critical point -- where both conductance and normalized localization length exhibit scale invariance, independent of system size. The half-quantized Hall metal and the marginal metallic phase challenge existing localization theories and provide insights into disorder-driven topological phase transitions in magnetic topological insulators, opening avenues for exploring quantum materials and next-generation electronic devices.