We investigate the spectral and transport properties of a diatomic square lattice with hopping to the next-nearest-neighbors and broken time-reversal symmetry, which behaves as a Chern insulator. In a finite-size approach, the attention is paid to the formation of chiral edge states in the topological insulating phase, but also in the semimetallic one. The edge states are revealed in the ribbon and plaquette geometries by analytical and numerical methods, significant differences being produced by the specific atomic connectivity at the boundary. The Hall resistance $R_H$ is calculated in the plaquette geometry using the Landauer-Büttiker approach. The chiral edge states located in the unique gap of the energy spectrum manifest themselves by quantized values $R_H=\pm h/e^2$ specific to the Chern insulator. The semimetallic system containing chiral edge states embedded in the quasicontinuum of bulk states shows a disorder-driven AQHE as a consequence of the Anderson localization process.

• Received 23 April 2018
• Revised 27 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.125403