Interplay of Altermagnetic Order and Wilson Mass in the Dirac Equation: Helical Edge States without Time-Reversal Symmetry

Abstract: We investigate topological phases in three-dimensional topological insulator (3DTI) thin films interfaced with altermagnetic (AM) orders. Starting from a modified Dirac equation, we elucidate the interplay between the Wilson mass, arising from lattice regularization, and the altermagnetic mass, and show how this interplay fundamentally alters the band topology and boundary modes. In particular, we demonstrate that coupling a 3DTI thin film to AM order induces a topological phase transition: although the total Chern number remains zero across the transition, topological helical edge states emerge after the transition. These helical edge states arise from opposite Chern numbers at different high-symmetry points, and are distinct from both the chiral edge states of the quantum anomalous Hall phase and the helical edge states of the conventional quantum spin Hall states. The quantum transport simulations reveal robust, quantized nonlocal resistance plateaus associated with these helical edge states, which persist even under strong potential and magnetic disorder. Our results establish 3DTI/AM heterostructures as a feasible material platform for engineering and detecting helical topological edge transport without time-reversal symmetry, thus expanding the landscape of topological matter and providing new opportunities for quantum devices.