Emerging of Anomalous Higher‐Order Topological Phases in Altermagnet/Topological Insulator Heterostructure by Floquet Engineering

ABSTRACT Altermagnetism, characterized by collinear‐compensated magnetic ordering with vanishing net magnetization, has opened new frontiers in topological matter through its distinctive spin‐momentum locking mechanism. We demonstrate that the altermagnetism in altermagnet/topological insulator (TI) heterostructure breaks time‐reversal symmetry, and in combination with Floquet engineering, gives rise to anomalous higher‐order topological insulator (AHOTI) phases with pure/hybridized ‐corner modes (CMs). Two fundamental breakthroughs by Floquet engineering are revealed. First, three distinct topological phase transitions are established: trivial‐to‐AHOTI with pure ‐CMs (AHOTI‐I), higher‐order TI‐to‐AHOTI with hybridized ‐CMs (AHOTI‐II), and mutual transitions between AHOTI‐I and ‐II. Second, the real‐space locations of topological CMs—not only conventional 0‐ but also anomalous ‐CMs—are synchronously manipulated by Néel vector reorientation, establishing an altermagnetism‐programmable paradigm for topological state localization. The emergent topological phases are systematically characterized through the nested dynamical Wilson loop formalism, deliberately adapted for Floquet‐driven systems, which shows exact correspondence with the observed CMs. This work establishes a universally versatile platform for non‐equilibrium dynamical control of topological phase, thereby providing transformative implications for reconfigurable topological electronics and fault‐tolerant quantum computing architectures.