We study theoretically the construction of topological conducting domain walls with a finite width between AB/BA stacking regions via finite element method in bilayer graphene systems with tunable commensurate twisting angles. We find that the smaller is the twisting angle, the more significant the lattice reconstruction would be, so that sharper domain boundaries declare their existence. We subsequently study the quantum transport properties of topological zero-line modes which can exist because of the said domain boundaries via Green’s function method and Landauer—Büttiker formalism, and find that in scattering regions with tri-intersectional conducting channels, topological zero-line modes both exhibit robust behavior exemplified as the saturated total transmission G_tot ≈ 2e²/h and obey a specific pseudospin-conserving current partition law among the branch transport channels. The former property is unaffected by Aharonov—Bohm effect due to a weak perpendicular magnetic field, but the latter is not. Results from our genuine bilayer hexagonal system suggest a twisting angle around θ ≈ 0.1° for those properties to be expected, consistent with the existing experimental reports.

我们通过有限元方法从理论上研究了在具有可调相称扭转角的双层石墨烯系统中，在 AB/BA 堆叠区域之间构建具有有限宽度的拓扑导电畴壁。我们发现扭转角越小，晶格重建的意义就越大，因此更清晰的域边界表明它们的存在。随后，我们通过格林函数方法和Landauer-Büttiker形式研究了由于所述域边界而可能存在的拓扑零线模式的量子输运性质，发现在具有三交叉导电通道的散射区域中，拓扑零线模式两者都表现出稳健的行为，例如饱和总传输G _tot ≈ 2 e² / h并遵守分支传输通道之间特定的伪自旋守恒电流分配定律。由于弱垂直磁场，前者不受 Aharonov-Bohm 效应的影响，而后者则不受。我们真正的双层六边形系统的结果表明，对于那些预期的特性，扭转角约为θ ≈ 0.1°，与现有的实验报告一致。