[论文解读] Soliton fractional charges in graphene nanoribbon and polyacetylene: similarities and differences

S.-R. Eric Yang|arXiv (Cornell University)|Jun 19, 2019

Graphene research and applications参考文献 34被引用 16

一句话总结

本文研究了锯齿形石墨烯纳米带（ZGNRs）和聚乙炔中由孤子诱导的分数化边界电荷，发现弱无序可稳定具有 $e/2$ 分数化边缘电荷的能隙中孤子态，而与之相反，在无缺陷的ZGNRs中，反铁磁耦合会强制实现整数电荷。其关键贡献在于识别出无序通过缓解反铁磁耦合，成为实现分数化的稳定因素。

ABSTRACT

An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral soliton. Similarly, in a gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can produce soliton states. In polyacetylene, a soliton is bound to a domain wall connecting two different dimerized phases. In graphene nanoribbons, a domain-wall soliton connects two topological zigzag edges with different chiralities. However, such a soliton does not display spin-charge separation. The existence of a soliton in finite-length polyacetylene can induce formation of fractional charges on the opposite ends. In contrast, for gapful graphene nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges induces integer boundary charges. The presence of disorder in graphene nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the average edge charge of gap states with energies within a small interval is e/2, with significant charge fluctuations. However, midgap states exhibit a well-defined charge fractionalization between the opposite zigzag edges in the weak-disorder regime. Numerous occupied soliton states in a disorder-free and doped zigzag graphene nanoribbon form a solitonic phase.

研究动机与目标

• 比较和对比石墨烯纳米带（GNRs）和聚乙炔中孤子介导的分数化电荷形成机制。
• 理解手征对称性和体-边对应关系在两种体系中实现拓扑边缘态的作用。
• 研究电子-电子相互作用和无序如何影响锯齿形GNRs中的电荷分数化。
• 阐明为何分数化电荷在无序ZGNRs中出现，而在无缺陷、未掺杂的体系中不出现。
• 探索通过扫描隧道显微镜（STM）或输运测量实验检测 $e/2$ 分数化边界电荷的潜力。

提出的方法

• 通过具有扭曲标量质量势的狄拉克方程分析，模拟聚乙炔和GNRs中的孤子态。
• 应用扎克相位以建立体-边对应关系，并保护手征边缘模的拓扑性。
• 使用手征边缘模的成键与反键线性组合，模拟导致分数化的混合手征态。
• 将无序建模为对ZGNRs中相反锯齿形边缘之间反铁磁耦合的抑制性微扰。
• 通过无序系统中能隙态和能隙中态的谱分析，评估电荷局域化与涨落。
• 比较聚乙炔（单位胞选择具有影响）与GNRs（单位胞选择无影响）中的拓扑不变量和单位胞依赖性。

实验结果

研究问题

• RQ1 无序如何影响无缺陷石墨烯纳米带中锯齿形边缘之间的反铁磁耦合？它能否实现分数化边界电荷？
• RQ2 为何聚乙炔中的畴壁孤子表现出异常的自旋-电荷关系，而GNRs中的孤子则不然？
• RQ3 手征对称性和扎克相在稳定聚乙炔和GNRs中拓扑边缘态方面起什么作用？
• RQ4 在无序ZGNRs中，能隙态在何种条件下于每个锯齿形边缘表现出明确的 $e/2$ 分数化电荷？
• RQ5 无序ZGNRs中能隙态的非平凡局域化特性能否通过修正的局域化理论来描述？

主要发现

• 在无缺陷、未掺杂的锯齿形石墨烯纳米带中，相反锯齿形边缘之间的反铁磁耦合强制实现整数边界电荷，从而阻止分数化。
• 弱无序可缓解锯齿形GNRs中反铁磁耦合，稳定具有 $e/2$ 分数化边界电荷的能隙中态。
• 无序ZGNRs中的能隙态表现出明确的 $e/2$ 分数化电荷，且由于能隙较小，量子涨落也较小。
• 在小能量区间 $[E- u, E+ u]$ 内的其他能隙态也表现出每条边缘平均为 $e/2$ 的分数化电荷，尽管涨落更大。
• 在无序存在下，系统转变为莫特-安德森绝缘体，表现为局域化的能隙态和非能隙区的扩展态。
• 无序诱导的分数化在短程势作用下最为有效，这些势对锯齿形边缘态构成奇异微扰。