Boundary induced non-hermiticity and anomalous flat edge states

Non-Hermitian physics expands our understanding of topological phases and open quantum systems. In practice, solving non-self-adjoint boundary problems for differential equations and their physical correspondences is a challenging research topic for both mathematics and physics. Physically, the reciprocal influence of intrinsic boundary conditions on the global properties of otherwise Hermitian bulk systems remains underexplored. Here, we use α -T 3 nanoribbons as a platform to demonstrate that stable anomalous dangling bonds from specific lattice termination provide such non-Hermitian boundary conditions. By rigorously deriving an equivalence boundary-localized complex absorbing potential, we demonstrate that these atomic configurations induce anomalous flat edge states, exceptional points, and imaginary Landau levels. These boundary effects alter bulk transport, leading to a breakdown of the quantized Hall conductance within a specific energy window. Our findings establish boundary engineering as a distinctive mechanism for manipulating quantum transport and topological states in both solid-state materials and synthetic quantum simulators.