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Topological States Due to Third‐Neighbor Coupling in Diatomic Linear Elastic Chains
Author(s) -
Grundmann Marius
Publication year - 2020
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.202000176
Subject(s) - k nearest neighbors algorithm , diatomic molecule , coupling (piping) , coupling constant , physics , topology (electrical circuits) , spring (device) , condensed matter physics , quantum mechanics , materials science , mathematics , combinatorics , thermodynamics , computer science , molecule , artificial intelligence , metallurgy
The vibrations of a diatomic linear chain exhibit two bands, the acoustic and the optical one. In the case of equal masses and nearest‐neighbor spring constants, no gap exists. The effects of nearest, next‐nearest, and third‐nearest neighbor coupling with different spring constants are analyzed. Nearest neighbor coupling leads to two topologically different bulk states with winding numbers ν = 0 and −1. Next‐nearest neighbor coupling does not change the topological properties and introduces only a trivial “Semenov” gap. Third‐nearest neighbor coupling leads to four distinct topological bulk phases with winding numbers ν = 0 , ± 1 , and − 2 .