Dirac states from px,y orbitals in the buckled honeycomb structures: A tight-binding model and first-principles combined study**Project supported by the National Key Research and Development Projects of China (Grant No. 2016YFA0202300), the National Natural Science Foundation of China (Grant No. 61390501), the Science Fund from the Chinese Academy of Sciences (Grant No. XDPB0601), and the US Army Research Office.

Abstract

Dirac states composed of px,y orbitals have been reported in many two-dimensional (2D) systems with honeycomb lattices recently. Their potential importance has aroused strong interest in a comprehensive understanding of such states. Here, we construct a four-band tight-binding model for the px,y-orbital Dirac states considering both the nearest neighbor hopping interactions and the lattice-buckling effect. We find that px,y-orbital Dirac states are accompanied with two additional narrow bands that are flat in the limit of vanishing π bonding, which is in agreement with previous studies. Most importantly, we analytically obtain the linear dispersion relationship between energy and momentum vector near the Dirac cone. We find that the Fermi velocity is determined not only by the hopping through π bonding but also by the hopping through σ bonding of px,y orbitals, which is in contrast to the case of pz-orbital Dirac states. Consequently, px,y-orbital Dirac states offer more flexible engineering, with the Fermi velocity being more sensitive to the changes of lattice constants and buckling angles, if strain is exerted. We further validate our tight-binding scheme by direct first-principles calculations of model-materials including hydrogenated monolayer Bi and Sb honeycomb lattices. Our work provides a more in-depth understanding of px,y-orbital Dirac states in honeycomb lattices, which is useful for the applications of this family of materials in nanoelectronics.