Abstract:

The discovery and exploration of topological states of matter have profoundly reshaped our understanding of condensed matter physics. The one-dimensional Su-Schrieffer-Heeger (SSH) model, characterized by its mathematical simplicity and physical universality, serves as an ideal platform for investigating topological insulators and their non-Hermitian extensions. This paper reviews the research progress and recent developments regarding one-dimensional extended SSH models. First, we review the theoretical evolution of the SSH model within the Hermitian framework, discussing high winding number topological phases and rich boundary states arising from next-nearest-neighbor long-range interactions and multi-band unit cell structures. Next, we highlight the novel physical phenomena that have emerged as research hotspots following the introduction of non-Hermitian mechanisms: specifically, phase transitions induced by PT-symmetry breaking and the non-Hermitian Skin Effect (NHSE) driven by non-reciprocal coupling. The latter, in particular, leads to the breakdown of the conventional bulk-boundary correspondence, necessitating the development of non-Bloch band theory based on the generalized Brillouin zone. Experimentally, we summarize achievements in simulating these theoretical models using physical platforms such as photonic crystals and RLC topological circuits, discussing key techniques and challenges in experimental observation. Finally, we provide an outlook on future directions, including the extension of non-Hermitian one-dimensional topological physics to higher-dimensional systems, many-body interactions, and novel topological device applications, aiming to provide a reference for researchers in related fields.

Key words: extended SSH model, long-range interactions, non-Hermitian physics, paritytime symmetry, non-Hermitian skin effect