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The aim of this paper is fourfold: (i) to obtain explicit formulas for theeigenpairs of perturbed tridiagonal block Toeplitz matrices; (ii) to make useof such formulas in order to provide a mathematical justification of thenon-Hermitian skin effect in dimer systems by proving the condensation of thesystem's bulk eigenmodes at one of the edges of the system; (iii) to show thetopological origin of the non-Hermitian skin effect for dimer systems and (iv)to prove localisation of the interface modes between two dimer structures withnon-Hermitian gauge potentials of opposite signs based on new estimates of thedecay of the entries of the eigenvectors of block matrices with mirroredblocks.

Perturbed Block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators