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

TL;DR

This paper investigates how third-nearest-neighbor interactions in 1D chains induce twofold topological phase transitions, revealing new topological phases with unique pseudospin structures and modified Dirac dynamics, and proposes an experimental realization.

Contribution

It introduces a novel topological phase transition mechanism driven by third-nearest-neighbor interactions in 1D chains, expanding understanding beyond the SSH model.

Findings

Identification of a twofold nontrivial topological phase transition

Analysis of low-energy excitations following a modified Dirac equation

Proposal of an experimental setup in elastic chains

Abstract

Strong long-range hoppings up to third nearest neighbors may induce a topological phase transition in one-dimensional chains. Unlike the Su-Schrieffer-Heeger model, this transition from trivial to topological phase occurs with the emergence of a pseudospin valley structure and a twofold nontrivial topological phase. Within a tight-binding approach, these topological phases are analyzed in detail and it is shown that the low-energy excitations follow a modified Dirac equation, in which the dynamics of particles with positive and negative mass occur differently. An experimental realization in a one-dimensional elastic chain, where it is feasible to tune directly the third-nearest-neighbor hoppings, is proposed.