Higher-order topological phases emerging from Su-Schrieffer-Heeger stacking

In this work, we develop a systematic 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 an analytical solution of the CZESs in a series of 2D systems stacking the 1D extended Su-Schrieffer-Heeger (SSH) model, two copies of the two-band SSH model, along with 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 name it 2D crossed SSH model.