Fizika Nizkikh Temperatur: Volume 47, Number 9 (September 2021), p. 819-829 ( to contents , go back )
Electronic spectra, topological states and impurity effects in graphene nanoribbons
Yuriy G. Pogorelov
IFIMUP-IN, Departamento de Física, Universidade do Porto, Porto, Portugal
Institute of Theoretical Physics, University of Regensburg, Regensburg, Germany
Vadim M. Loktev
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, Kyiv 03680, Ukraine
Received April 12, 2021, published online July 26, 2021
We consider the finite ribbons of graphene with two principal orientations, zigzag and armchair, of their edges to study in detail impurity effects on their edge states. An alternative to the known description of quasiparticle states in terms of transversal standing waves is proposed in the recurrence relations for their spectra vs discrete numbers of atomic chains in the ribbon, permitting to simplify the Green function approach to the disorder effects in these systems. The derived analysis shows the microscopic mechanisms of perturbation by different types of impurities on low energy states and clarifies how the stability of topological states in zigzag systems to disorder is related to the discrete amplitudes of these states across the ribbon. An opposite possibility for Mott localization under local impurity perturbations is found for armchair type nanoribbons but at special values of their width.
Key words: graphene nanoribbons, topological states, impurity disorder, Lifshitz model, Anderson model.