Quantum spin Hall effect on the porphyrin lattice

We study the physics of quantum spin Hall (QSH) effect and topological quantum phase transition on the porphyrin lattice. We show that in a special limit the pristine model on this lattice reduces to the usual topological insulator (TI) thin film model. By incorporating explicit time reversal symmetry (TRS) breaking interactions, we explore the topological properties of this model and show that it exhibits an ordinary insulator phase, a quantum anomalous Hall (QAH) phase, and a quantum spin Hall (QSH) phase.