We systematically studied the influence of magnetic field on zero-line modes (ZLMs) in graphene and demonstrated the physical origin of their enhanced robustness by employing nonequilibrium Green’s functions and the Landauer–Büttiker formula. We found that a perpendicular magnetic field can separate the wavefunctions of the counter-propagating kink states into opposite directions. Specifically, the separation vanishes at the charge neutrality point and increases as the Fermi level deviates from the charge neutrality point and can reach a magnitude comparable to the wavefunction spread at a moderate field strength. Such spatial separation of oppositely propagating ZLMs effectively suppresses backscattering and is more significant under zigzag boundary condition than under armchair boundary condition. Moreover, the presence of magnetic field enlarges the bulk gap and suppresses the bound states, thereby further reducing the scattering. These mechanisms effectively increase the mean free paths of the ZLMs to approximately 1 μm in the presence of a disorder.
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This work was financially supported by the National Key Research and Development Program (Grant No. 2017YFB0405703), the China Government Youth 1000-Plan Talent Program, and the National Natural Science Foundation of China (Grant No. 11474265). We are grateful to the Supercomputing Center of USTC for providing high-performance computing assistance.
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Wang, K., Hou, T., Ren, Y. et al. Enhanced robustness of zero-line modes in graphene via magnetic field. Front. Phys. 14, 23501 (2019). https://doi.org/10.1007/s11467-018-0869-9
- topological state
- zero-line state
- electronic transport