Disorder-robust trivial Majorana-like states from smooth confinement in chiral superconducting nanowires

Abstract

Near-zero-energy states in Majorana nanowires can arise from topologically trivial mechanisms such as smooth spatial inhomogeneity and disorder, making zero-energy pinning alone insufficient evidence of bulk topology. Here we identify a real-space mechanism governing their robustness to symmetry-preserving disorder. For a chiral-symmetric Bogoliubov-de Gennes Hamiltonian, we decompose a low-energy state into two normalized components of opposite chirality and show that disorder-induced splitting is bounded by their spatial overlap. We demonstrate this result in a finite Rashba nanowire with smooth chemical potential and pairing profiles. Below the bulk topological transition, smooth confinement produces partially separated chiral components with exponentially small overlap, yielding globally trivial Majorana-like Andreev bound states that remain near zero energy even under strong scalar, nonmagnetic disorder. The chiral overlap therefore provides a direct diagnostic of the protection of low-energy states against local perturbations, independent of the bulk topological invariant.