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

Hui Jiang, Rong Lü and Shu Chen ()
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Hui Jiang: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences
Rong Lü: Tsinghua University
Shu Chen: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences

The European Physical Journal B: Condensed Matter and Complex Systems, 2020, vol. 93, issue 7, 1-13

Abstract: 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. Graphical abstract

Keywords: Mesoscopic; and; Nanoscale; Systems (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1140/epjb/e2020-10036-3

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