Marginal Metals and Kosterlitz-Thouless Type Phase Transition in Disordered Altermagnets

Altermagnetism, a recently discovered magnetic phase characterized by spin-split bands without net magnetization, has emerged as a promising platform for novel physics and potential applications. However, its stability against disorder—ubiquitous in real materials—remains poorly understood. Here, we study the electron localization properties of two-dimensional d-wave altermagnets subject to disorder. Remarkably, we discover a disorder-driven phase transition from a marginal metallic phase to an insulator, which falls into the Kosterlitz-Thouless class. We demonstrate this by strong numerical evidence and propose an interpretation in terms of vortex-antivortex pairs in the disorder-induced local in-plane spin magnetization. Moreover, we show that the characteristic spin anisotropy of altermagnets persists but gradually fades away across the transition. These changes directly affect the spin-splitting features that are detectable in angle-resolved photoemission spectroscopy and tunneling magnetoconductance. Our findings provide a new perspective on recent experimental observations of altermagnetism in candidate materials.