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Topological edge states on time-periodically strained armchair graphene nanoribbons

机译：周期应变扶手椅石墨烯纳米带的拓扑边缘态

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We report the emergence of electronic edge states in time-periodically driven strained armchair terminated graphene nanoribbons. This is done by considering a short-pulse spatial-periodic strain field. Then, the tight-binding Hamiltonian of the system is mapped into a one-dimensional ladder. The time periodicity is considered within the Floquet formalism. Thus the quasienergy spectrum is found numerically by diagonalizing the evolution operator. For some particular cases, the quasienergy spectrum is found analytically. We found that the system is able to support gapless and gapped phases. Very different edge states emerge for both the gapless and the gapful phases. In the case of the gapped phase, edge states emerge at the gap centered at zero quasienergy, although the Chern number is zero due to the chiral symmetry of the system. For the gapless phase, besides edge states at zero quasienergy, cosinelike edge states which merge and coexist with the bulk band are observed. To confirm the topological nature of these edge states, we analytically obtained the effective Hamiltonian and its spectrum for a particular case, finding that the edge states are topologically weak. Finally, we found analytically the evolution of band edges and their crossings as a function of the driven period. Topological modes arise at such crossings.
机译：我们报告了时间周期驱动应变扶手椅终止的石墨烯纳米带中电子边缘态的出现。这是通过考虑短脉冲空间周期应变场来完成的。然后，将系统的紧束缚哈密顿量映射到一维阶梯。在Floquet形式主义中考虑了时间周期。因此，通过对角化演化算子可以在数值上找到准能谱。对于某些特定情况，可以通过分析找到准能谱。我们发现该系统能够支持无间隙和间隙阶段。无间隙阶段和无间隙阶段都出现了非常不同的边缘状态。在带隙相的情况下，尽管由于系统的手性对称，Chern数为零，但边缘状态出现在以零准能为中心的间隙处。对于无间隙相位，除了零准能量处的边缘状态外，还观察到了与体能带合并并共存的余弦状边缘状态。为了确认这些边缘态的拓扑性质，我们通过分析获得了特定情况下的有效哈密顿量及其谱，发现边缘态在拓扑上是弱的。最后，我们从分析上发现带边缘及其交叉的演变是驱动周期的函数。在这种交叉口出现拓扑模式。

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  • 来源
    《Physical review》 |2017年第15期|155435.1-155435.10|共10页
  • 作者

    Pedro Roman-Taboada; Gerardo G. Naumis;

  • 作者单位

    Departamento de Sistemas Complejos, Instituto de Fisica, Universidad National Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico, Ciudad de Mexico, Mexico;

    Departamento de Sistemas Complejos, Instituto de Fisica, Universidad National Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico, Ciudad de Mexico, Mexico;

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