  In this work, we develop a systematical approach of constructing and
classifying the model Hamiltonians for two-dimensional (2D) higher-order
topological phase with corner zero energy states (CZESs). Our approach is based
on the direct construction of analytical solution of the CZESs in a series of
2D systems that stack the 1D extended Su-Schrieffer-Heeger (SSH) model, two
copies of the original SSH model, along two orthogonal directions.
Fascinatingly, our approach not only gives the celebrated
Benalcazar-Bernevig-Hughes and 2D SSH models but also reveals a novel model and
we refer it to crossed 2D SSH model. Although these three models exhibit
completely different bulk topology, we find that the CZESs can be universally
characterized by edge winding number for 1D edge states, attributing to their
unified Hamiltonian construction form and edge topology. Remarkably, our
principle of obtaining CZESs can be readily generalized to arbitrary dimension
and superconducting systems. Thus, our work sheds new light on the theoretical
understanding of the higher-order topological phase and paves the way to
looking for higher-order topological insulators and superconductors.
