Spin Resolved Zero-Line Modes in Minimally Twisted Bilayer Graphene from Exchange Field and Gate Voltage

Abstract The reliance on spin-orbit coupling or strong magnetic fields has always posed significant challenges for the mass production and even laboratory realization of most topological materials. Valley-based topological zero-line modes have attracted widespread attention due to their substantial advantage of being initially realizable with just an external electric field. However, the uncontrollable nature of electrode alignment and precise fabrication has greatly hindered the advancement in this field. By utilizing minimally twisted bilayer graphene and introducing exchange fields from magnetic substrates, we successfully realize a spin-resolved, electrode-free topological zero-line mode. Further integration of electrodes that do not require alignment considerations significantly enhances the tunability of the system’s band structure. Our approach offers a promising new support for the dazzling potential of topological zero-line mode in the realm of low-energy-consumption electronics.