Analytical and semianalytical tools to determine the topological character of Shiba chains

We introduce three new analytical and semi-analytical tools that allow one to determine the topological character of impurity Shiba chains. The methods are based on calculating effective Green's function an infinite embedded chain using T-matrix formalism describing as a {\it line impurity}. thus provide solution longstanding size-effects problem affecting only general alternative method, numerical tight-binding analysis. As example we consider magnetic impurities deposited s-wave superconducting substrate with Rashba spin-orbit calculate its phase diagram strength chemical potential. find perfect agreement between all our techniques