Topological Edge States of Honeycomb Lattices with Zero Berry Curvature

Berry curvature, the geometric counterpart of the magnetic field in momentum space, has been applied to various topological materials, such as topological insulators and Weyl semimetals, to give rise to robust edge states that have applications in electron transport and quantum computing. In this work, we show that under zero Berry curvature a honeycomb lattice with a Kekule-like hopping texture possesses topological edge states, which is analogous to the scenario of the Aharonov-Bohm effect. Our results serve for the design of solid-state materials with topological edge states.