  In recent years, the study of topologically non-trivial structures in
one-dimensional models has been dominated by the Su--Schrieffer--Heeger model
due to its simplicity in design and its ability to support edge states with
robustness to disorder in couplings, protected by chiral and inversion
symmetry. Here, we present a novel study on a zigzag quasi-one-dimensional
model, which supports topologically protected edge states without relying on
conventional symmetries. Our model utilises next-neighbour couplings to mediate
edge states and is simultaneously resilient to dissipation, couplings and
on-site energy disorders. In order to understand the topological properties of
this model, we introduce a novel way to demonstrate the bulk-boundary
correspondence of the edge states and construct a topological invariant that
returns quantized values. Our study sheds light on the possibility of
constructing topological phases in new ways, even in the absence of
conventional symmetries, and opens up new avenues for research in this field.
In addition, we demonstrate a possible photonic realization of these models
with the help of an orbital-induced synthetic flux.
