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 noneqnilibrium Green's functions and the Landauer Biittiker 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 backseattering and is more significant under zigzag boundary condition thail 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 |ini in the presence of a disorder.
Frontiers of Physics in China
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).
Corresponding author:Zhenhua Qiao,E-mail:firstname.lastname@example.org.