Electronic properties of zero-line modes in bilayer graphene: An ab initio study

Abstract

The inversion symmetry breaking in a Bernal-stacked graphene bilayer, e.g., by applying a perpendicular electric field, can open a band gap harboring the quantum valley Hall effect. The different valley Hall topologies induced by a spatially varying electric field lead to the formation of a one-dimensional topological conducting channel, also called the zero-line mode (ZLM), existing at the zero-field region. The ZLMs were theoretically predicted by an atomic model and experimentally realized in bilayer graphene. Although the atomic model has been extensively utilized to investigate the electronic properties of ZLMs, a comprehensive ab initio study that precisely characterizes the critical condition of ZLMs is still lacking. In this paper, by employing first-principles method, we systematically investigate the electronic properties in two realistic systems, i.e., bilayer graphene with different types of line defects and with dual-split gates. The characteristics of ZLMs in different systems are demonstrated. Interestingly, we find that bilayer graphene with a pentagon-heptagon type of line defect is the optimal geometry to realize ZLMs due to its minimum critical device width as well as a lower formation energy. Our first-principles study implements the research gap between the atomic model and the experimental realization of ZLMs, and provides a practical scheme for realizing ZLMs in bilayer graphene systems.