Topological phases in the non-Hermitian Su-Schrieffer-Heeger model

By S. Lieu. 2017

412 citations recorded by the source corpus.

We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally symmetric SSH model will possess a ``conjugated-pseudo-Hermiticity'' which we show is responsible for a quantized ``complex'' Berry phase. Consequently, we provide an example where the complex Berry phase of a band is used as a quantized invariant to predict the existence of gapless edge modes in a non-Hermitian model. The chirally broken, $PT$-symmetric model is studied; we suggest an explanation for why the topological invariant is a global property of the Hamiltonian. A geometrical picture is provided by examining eigenvector evolution on the Bloch sphere. We justify our analysis numerically and discuss relevant applications.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d035df9e3c88c0f636affbfe09715020fd65e2ee

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Citations in the corpus

Symmetry-protected nodal phases in non-Hermitian systems (2018, background): “Very recently, intense theoretical [7–37] and experimental [38–45] efforts have been made to extend the concept of topological band structures to non-Hermitian (NH) systems which play an important role in the effective description of dissipation effects in various physi-”
Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “Both systems are essentially described by the Su-Schrieffer-Heeger model [158] with balanced gain and loss [102, 105, 114]:”
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems. (2018, background): “, rR = rL = −t1/t2 and, thus, |ψR〉 = |ψL〉, where the non-Hermiticity is included as a staggering potential instead of a hopping term [20], was experimentally realized in Ref.”
Non-Hermitian systems and topology: A transfer-matrix perspective (2018, neutral): “[18, 86].”
Edge States and Topological Invariants of Non-Hermitian Systems. (2018, neutral): “[52] Simon Lieu, “Topological phases in the non-hermitian suschrieffer-heeger model,” Phys.”
Exceptional topology of non-Hermitian systems (2019, neutral): “The influence of symmetries on BBC in NH has been widely studied (Esaki et al. , 2011; Lieu, 2018a; Brzezicki and Hyart, 2019; Kawabata, Shiozaki et al. , 2019; Kunst and Dwivedi, 2019) (see also Sect.”