论文标题
石墨烯的粘性大厅液体的光学$ n $ invariant
Optical $N$-invariant of graphene's viscous Hall fluid
论文作者
论文摘要
在过去的三十年中，石墨烯已成为发现拓扑问题独特阶段的典型平台。 Chern绝缘子$ c \ in \ Mathbb {z} $和量子旋转厅绝缘子$ν\ in \ mathbb {z} _2 $首先在石墨烯中预测，这导致了对拓扑材料的研究爆炸。在这里，我们介绍了二维物质的新拓扑分类 - 光学$ n $ - plase $ n \ in \ mathbb {z} $。 $ c $和$ν$阶段分别与充电和旋转运输有关，而$ n $ theades与极化运输相关。在所有三种情况下，电荷/自旋/极化量子的运输均禁止在大体中，但允许在边缘。一个基本差异是，在所有Matsubara频率和波形上，$ n $ invariant定义用于动态电磁波。我们显示，仅通过易感性张量$χ（ω，\ Mathbf {q}）$的时空分散捕获此拓扑量子数。我们还证明$ n \ neq 0 $在石墨烯的粘性大厅液中并不普遍，而基本的物理机制是霍尔粘度$η_h$。在非平凡阶段，我们发现了一个深层的次波长现象，让人联想到Meissner效应：在特别大的光子动量$ q = d_h^{ - 1} $下，由Hall扩散长度$ d_H $定义，磁场完全从粘性大厅的流体中排出。我们提出了一个新的探针，探测拓扑物质，evaneScent Mage-Optic Kerr效应（E-MOKE）光谱，以揭示这种新型的光学$ N $ invariant并验证磁场驱动。我们的工作表明，带有霍尔粘度的石墨烯是物质拓扑磁相的第一个候选材料。
Over the past three decades, graphene has become the prototypical platform for discovering unique phases of topological matter. Both the Chern insulator $C\in\mathbb{Z}$ and the quantum spin Hall insulator $ν\in\mathbb{Z}_2$ were first predicted in graphene, which led to a veritable explosion of research in topological materials. Here, we introduce a new topological classification of two-dimensional matter -- the optical $N$-phases $N\in\mathbb{Z}$. The $C$ and $ν$ phases are related to charge and spin transport respectively, whereas the $N$-phases are connected to polarization transport. In all three cases, transportation of charge/spin/polarization quanta is forbidden in the bulk but permitted on the edge. One fundamental difference is that the $N$-invariant is defined for dynamical electromagnetic waves over all Matsubara frequencies and wavevectors. We show this topological quantum number is captured solely by the spatiotemporal dispersion of the susceptibility tensor $χ(ω,\mathbf{q})$. We also prove $N\neq 0$ is nontrivial in graphene's viscous Hall fluid with the underlying physical mechanism being Hall viscosity $η_H$. In the nontrivial phase, we discover a deep sub-wavelength phenomenon reminiscent of the Meissner effect: at a particularly large photon momentum $q=D_H^{-1}$ defined by the Hall diffusion length $D_H$, the magnetic field is completely expelled from the viscous Hall fluid. We propose a new probe of topological matter, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, to unravel this novel optical $N$-invariant and verify the magnetic field expulsion. Our work indicates that graphene with Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.
