Topologically protected helical states at a mass-inverted quantum dot in graphene are studied by analyzing both tight-binding and kernel polynomial method calculations. The mass-inverted quantum dot is introduced by considering a heterojunction between two different mass domains, which is similar to the domain wall in bilayer graphene. The numerical results show emergent metallic channels across the mass gap when the signs of the mass terms are opposite. The eigenstates of the metallic channels are revealed to be doubly degenerate—each state propagates along opposite directions, maintaining the time-reversal symmetry of graphene. The robustness of the metallic channels is further examined, concluding with the fact that helical states are secured unless atomic vacancies form near the domain wall. Such helical states circulating along the topological defects may pave a novel route to engineering topological states based on graphene.

通过分析紧束缚和核多项式方法的计算，研究了石墨烯中质量反转量子点处的拓扑受保护的螺旋态。通过考虑两个不同质量域之间的异质结来引入质量反转的量子点，该异质结类似于双层石墨烯中的域壁。数值结果显示，当质量项的符号相反时，会出现穿过质量间隙的金属通道。金属通道的本征态显示出是双重简并的-每个态都沿相反的方向传播，从而保持了石墨烯的时间反转对称性。进一步检查了金属通道的坚固性，并得出结论，除非在畴壁附近形成原子空位，否则将确保螺旋状态。