Exploring Anderson localization in metallic zigzag carbon nanotubes: Effects of uncorrelated and correlated disorder

Abstract We perform a detailed numerical study on the impact of uncorrelated and correlated disorder on electron localization in metallic zigzag carbon nanotubes (CNTs). Leveraging the symmetry of the system, we model the Hamiltonian as a set of quasi-one-dimensional modes characterized by distinct wavevectors. Disorder is introduced in two forms: (i) uncorrelated randomness, modeled as uniformly distributed on-site energies with disorder strength W , and (ii) correlated randomness, governed by a correlation parameter α . Through the analysis of key observables, including the Participation Ratio (PR), Entanglement Entropy (EE), Localization Length ( λ ), and the Ratio of Level Spacing ( r n ), we identify a disorder-driven Anderson transition between localized and delocalized electronic states. For uncorrelated disorder, the transition occurs at a critical disorder strength W c ≈ 2, while for correlated disorder, the critical correlation parameter is found to be α c ≈ 2. We observe distinct behavior between delocalized and localized states for W and α in the regimes ≲ 2 and ≳ 2. Our findings highlight the tunability of electronic transport properties in metallic zigzag CNTs via disorder, providing valuable insights for potential applications in nanoelectronics.