Higher-order topological insulator phase in a modified Haldane model
Baokai Wang, Xiaoting Zhou, Hsin Lin, Arun Bansil
Abstract
We explore the topological properties of a modified Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor hopping terms is made unequal and the threefold rotational symmetry ${\mathcal{C}}_{3}$ is broken by introducing a dimerization term ($|{t}_{1w(2w)}|<{t}_{1s(2s)}$) in the Hamiltonian. Using the parameter $\ensuremath{\eta}={t}_{1w}/{t}_{1s}={t}_{2w}/{t}_{2s}$, we show that this MHM supports a transition from the quantum anomalous Hall insulator to a higher-order topological insulator (HOTI) phase at $\ensuremath{\eta}=\ifmmode\pm\else\textpm\fi{}0.5$. It also hosts a zero-energy corner mode on a nanodisk that can transition to a trivial insulator without gap closing when the inversion symmetry is broken. The gap-closing critical states are found to be magnetic semimetals with a single Dirac node which, unlike the classic Haldane model, can move along the high-symmetry lines in the Brillouin zone. Our MHM offers a rich tapestry of HOTIs and other topological and nontopological phases.