2025/09/10 by Róbert Németh, Németh, Róbert, József Cserti +3
Materials Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Graph theory and applications #Graphene research and applications #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2509.08445
openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's function, we develop a general analytical framework for computing the equivalent resistance between arbitrary nodes. The resulting expression is a one-dimensional integral that is evaluated exactly in special cases. While our analysis is carried out for the square lattice, the method readily extends to other lattice geometries and networks with general impedances. Therefore, this framework is useful for studying the boundary behavior of topolectrical circuits, which serve as classical analogs of topological insulators.