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Strong long-range interactions up to third nearest neighbors may induce atopological phase transition in one-dimensional chains. Unlike theSu-Schrieffer-Heeger model, this transition from trivial to topological phaseoccurs with the emergence of a pseudospin valley structure and a twofoldnontrivial topological phase. Within a tight-binding approach, thesetopological phases are analyzed in detail and it is shown that the low-energyexcitations follow a modified Dirac equation. An experimental realization in aone-dimensional elastic chain, where it is feasible to tune directly thethird-nearest-neighbor interaction strength, is proposed.

Twofold topological phase transitions induced by third-nearest-neighbor interactions in 1D chains