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arXiv 1302.3483cond-mat.mes-hall
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无序石墨烯临界点零能朗道能级的分裂和普适耗散电导

Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene

Frank Ortmann, Stephan Roche

摘要:

我们报告的强大功能的纵向电导率($σ_{xx}$)的石墨烯零能朗道水平存在的障碍和变化的磁场。通过混合一个安德森无序势与低密度的亚晶格杂质,从金属到绝缘状态的转变理论上探讨了作为朗道能级分裂的函数,使用高效的实空间方法来计算久保电导率($σ_{xx}$和霍尔$σ_{xy}$)。只要保持谷简并性,所获得的临界电导率$σ_{xx}\simeq 1.4 e^{2}/h$在无序增加(几乎一个数量级)和磁场范围从约2到200特斯拉时是稳健的。当亚晶格对称性被破坏时,$σ_{xx}$由于局域化效应最终在狄拉克点处消失,而赝自旋分裂态的临界电导率(决定$σ_{xy}=0$平台的宽度)变为$σ_{xx}\simeq e^{2}/h$,而不管分裂强度、叠加无序或磁场强度如何。这些发现指向在朗道能级分裂存在下无序石墨烯中的量子霍尔效应的非耗散性质。

英文摘要:

We report on robust features of the longitudinal conductivity ($σ_{xx}$) of the graphene zero-energy Landau level in presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both $σ_{xx}$ and Hall $σ_{xy}$). As long as valley-degeneracy is maintained, the obtained critical conductivity $σ_{xx}\simeq 1.4 e^{2}/h$ is robust upon disorder increase (by almost one order of magnitude) and magnetic fields ranging from about 2 to 200 Tesla. When the sublattice symmetry is broken, $σ_{xx}$ eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a $σ_{xy}=0$ plateau) change to $σ_{xx}\simeq e^{2}/h$, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the non dissipative nature of the quantum Hall effect in disordered graphene in presence of Landau level splitting.

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