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We introduce three new analytical and semi-analytical tools that allow one todetermine the topological character of impurity Shiba chains. The analyticalmethods are based on calculating the effective Green's function of an infiniteembedded chain using the T-matrix formalism and describing the chain as a {\itline impurity}. We thus provide a solution to the longstanding size-effectsproblem affecting the only general alternative method, the numericaltight-binding analysis. As an example we consider a chain of magneticimpurities deposited on an s-wave superconducting substrate with Rashbaspin-orbit and we calculate its topological phase diagram as a function of themagnetic impurity strength and the chemical potential. We find a perfectagreement between all our new techniques and a numerical analysis.

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