Identification of the Majorana edge modes in tight-binding systems based on the Krylov method

Low dimensional structures in the non-trivial topological phase can host in-gap Majorana bound states, identified experimentally as zero-bias peaks differential conductance. Theoretical methods for studying modes are mostly based on bulk-boundary correspondence or exact diagonalization of finite systems via, e.g., Bogoliubov-de Gennes formalism. In this paper, we develop an efficient method identifying (edge) states via looking extreme eigenvalues symmetric matrices. The presented approach is Krylov and allows study spatial profile well spectrum system. advantage calculation cost, which shows linear dependence number lattice sites. latter problem may be solved very large clusters arbitrary shape/geometry. order to demonstrate efficiency our approach, two- three-dimensional described by Kitaev Rashba models determine calculate their structures. Additionally, discuss impact system size physical properties magnetic nanoisland deposited superconducting surface. case, have shown that depend length edge.