Asymmetric hopping (t_R ≠ t_L) causes all bulk eigenstates to localize at one boundary — a hallmark of non-Hermitian topology.
Hatano-Nelson model: H = Σ t_R c†_{i+1}c_i + t_L c†_i c_{i+1}. Under OBC, all N eigenstates pile up at the left boundary when t_R > t_L. Under PBC, spectrum forms a loop in complex plane. Non-Bloch band theory (Yao-Wang 2018) explains OBC spectrum via generalized Brillouin zone.