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Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model

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Abstract

Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological properties, we investigate the topological phase diagrams and the zero-mode edge states of a generalized non-reciprocal Su-Schrieffer-Heeger model with a general form fulfilling the chiral symmetry, based on some analytical results. Meanwhile, we provide a concise geometrical interpretation of the bulk topological invariants in terms of two independent winding numbers and also give an alternative interpretation related to the linking properties of curves in three-dimensional space. For the system under the open boundary condition, we construct analytically the wavefunctions of zero-mode edge states by properly considering a hidden symmetry of the system and the normalization condition with the use of biorthogonal eigenvectors. Our analytical results directly give the phase boundary for the existence of zero-mode edge states and unveil clearly the evolution behavior of edge states. In comparison with results via exact diagonalization of finite-size systems, we find our analytical results agree with the numerical results very well.

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Authors and Affiliations

  1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Hui Jiang & Shu Chen

  2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, P.R. China

    Hui Jiang & Shu Chen

  3. Department of Physics, Tsinghua University, Beijing, 100084, P.R. China

    Rong Lü

  4. Collaborative Innovation Center of Quantum Matter, Beijing, P.R. China

    Rong Lü

  5. Yangtze River Delta Physics Research Center, Liyang, Jiangsu, 213300, P.R. China

    Shu Chen

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  1. Hui Jiang
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Correspondence to Shu Chen.

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Jiang, H., Lü, R. & Chen, S. Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model. Eur. Phys. J. B 93, 125 (2020). https://doi.org/10.1140/epjb/e2020-10036-3

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