论文标题
无序石墨烯丝带作为拓扑多政治系统
Disordered Graphene Ribbons as Topological Multicritical Systems
论文作者
论文摘要
曲折石墨烯色带的低能光谱包含两个具有高度非线性分散体的无间隙带，$ε（k）= \ pm |π-k |^w $，其中$ w $是色带的宽度。相应的状态位于两个相反的曲折边缘。它们的存在反映了一个事实，即干净的色带是一个自然调整到拓扑{\ em多政治}点的准单维系统。这个量子关键点将拓扑琐碎的阶段与指数$ w $的拓扑阶段分开。在这里，我们研究了（手性）赋予对称性障碍对这种多政治点的影响。我们表明，该系统具有与$ W = 1 $关键点一致的方式的定位长度以零能量差异的定位状态。对于表现出通用dyson奇异性的状态密度（DOS）的密度也是如此，尽管干净的DO基本上取决于$ w $。另一方面，与晶格的零能量定位长度临界指数不普遍，并且取决于拓扑指数$ w $。
The low energy spectrum of a zigzag graphene ribbon contains two gapless bands with highly non-linear dispersion, $ε(k)=\pm |π-k|^W$, where $W$ is the width of the ribbon. The corresponding states are located at the two opposite zigzag edges. Their presence reflects the fact that the clean ribbon is a quasi one dimensional system naturally fine-tuned to the topological {\em multicritical} point. This quantum critical point separates a topologically trivial phase from the topological one with the index $W$. Here we investigate the influence of the (chiral) symmetry-preserving disorder on such a multicritical point. We show that the system harbors delocalized states with the localization length diverging at zero energy in a manner consistent with the $W=1$ critical point. The same is true regarding the density of states (DOS), which exhibits the universal Dyson singularity, despite the clean DOS being substantially dependent on $W$. On the other hand, the zero-energy localization length critical exponent, associated with the lattice staggering, is not universal and depends on the topological index $W$.
