Projectively topological exceptional points in non-Hermitian Rice-Mele model

• URL: http://arxiv.org/abs/2011.03743v1
• Date: Sat, 7 Nov 2020 10:20:06 GMT
• Title: Projectively topological exceptional points in non-Hermitian Rice-Mele model
• Authors: C. Li and Z. Song
• Abstract summary: We study coupled non-Hermitian Rice-Mele chains, which consist of Su-Schrieffer-Heeger (SSH) chain system with staggered on-site imaginary potentials. In two dimensional (2D) thermodynamic limit, the exceptional points (EPs) are shown to exhibit topological feature. EPs correspond to topological defects of a real auxiliary 2D vector field in k space, which is obtained from the Bloch states of the non-Hermitian Hamiltonian.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study coupled non-Hermitian Rice-Mele chains, which consist of Su-Schrieffer-Heeger (SSH) chain system with staggered on-site imaginary potentials. In two dimensional (2D) thermodynamic limit, the exceptional points (EPs) are shown to exhibit topological feature: EPs correspond to topological defects of a real auxiliary 2D vector field in k space, which is obtained from the Bloch states of the non-Hermitian Hamiltonian. As a topological invariant, the topological charges of EPs can be $\pm$1/2, obtained by the winding number calculation. Remarkably, we find that such a topological characterization remains for a finite number of coupled chains, even a single chain, in which the momentum in one direction is discrete. It shows that the EPs in the quasi-1D system still exhibit topological characteristics and can be an abridged version for a 2D system with symmetry protected EPs that are robust in perturbations, which proves that topological invariants for a quasi-1D system can be extracted from the projection of the corresponding 2D limit system on it.

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