Abstract
We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.
Highlights
The Su–Schrieffer–Heeger (SSH) model is an important and basic model in describing band topology in condensed matter physics
The photonic systems provide a flexible platform for the SSH model, as the hopping of adjacent lattices can be controlled as desired by tuning distance via nanofabrication
Imaginary coupling is employed through adiabatic elimination and appropriately fixing the onsite gain and loss in different waveguides
Summary
The Su–Schrieffer–Heeger (SSH) model is an important and basic model in describing band topology in condensed matter physics. The two-dimensional SSH model is able to retain nontrivial topological phase in the absence of Berry curvature and further can support second-order topological bound modes at its corners [18,19]. Another important extension is to examine the SSH model in non-Hermitian systems [20,21,22,23]. We present full wave simulation by using planar optical waveguides to carry out the extended SSH model and numerically investigate the topological bound modes. The topological aspects with and without chiral symmetry are discussed in detail
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