2024/04/01 by Wen-Chuang Shang, Yi-Ning Han, Shang, Wen-Chuang +5
Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Enhanced Data Rates for GSM Evolution #FOS: Physical sciences #Mathematics #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Physics #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Telecommunications #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2404.01097
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the topological properties of a two-chain quantum ladder with uneven legs, i.e. the two chains differ in their periods by a factor of two. Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps. It also provides opportunities to explore fundamental concepts concerning band topology and edge modes, including the difference of intracellular and intercellular Zak phases, and the role of the inversion symmetry (IS). We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation, respectively. We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap, while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgap but also within the band continuum. Furthermore, by projecting to the two sublattices, we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su-Schrieffer-Heeger model or Rice-Mele model whose hopping amplitudes depend on the quasimomentum. In this way, the topological phases can be efficiently extracted through winding numbers. We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.