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arXiv 2103.15085cond-mat.mes-hall
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拓扑平坦色散能带结构中的克尔旋转和法拉第旋转

Kerr and Faraday rotations in topological flat and dispersive band structures

Alireza Habibi, Ahmad Z. Musthofa, Elaheh Adibi, Johan Ekström, Thomas L. Schmidt, Eddwi H. Hasdeo

摘要:

双量子霍尔(IQH)态和量子反常霍尔(QAH)态具有相同的静态(dc)响应,但不同的动态(ac)响应。特别地,交流异常霍尔电导率分布$σ_{yx}(ω)$对QAH态的能带形状敏感。例如,色散QAH带示出在带隙处没有符号变化的共振轮廓,而IQH状态示出在回旋加速器能量处的符号变化共振。我们认为,通过平坦化色散QAH带,$σ_{yx}(ω)$应该恢复到IQH中平坦的朗道带,因此有必要知道符号变化的起源。采用带宽可调的拓扑晶格模型,我们发现,符号变化的根源不是带隙而是QAH带的Van Hove奇异能。在小带宽的限制下,平坦QAH频带恢复了IQH朗道频带的$σ_{yx}(ω)$。由于霍尔效应,这些拓扑带在反射波中表现出巨大的偏振旋转和椭圆率(克尔效应),在透射波中表现出精细结构常数量级的旋转(法拉第效应),其轮廓类似于$σ_{yx}(ω)$。我们的结果作为一个简单的指导拓扑平坦带的光学特性。

英文摘要:

Integer quantum Hall (IQH) states and quantum anomalous Hall (QAH) states show the same static (dc) response but distinct dynamical (ac) response. In particular, the ac anomalous Hall conductivity profile $σ_{yx}(ω)$ is sensitive to the band shape of QAH states. For example, dispersive QAH bands shows resonance profile without a sign change at the band gap while the IQH states shows the sign change resonance at the cyclotron energy. We argue by flattening the dispersive QAH bands, $σ_{yx}(ω)$ should recover to that of flat Landau bands in IQH, thus it is necessary to know the origin of the sign change. Taking a topological lattice model with tunable bandwidth, we found that the origin of the sign change is not the band gap but the Van Hove singularity energy of the QAH bands. In the limit of small bandwidth, the flat QAH bands recovers $σ_{yx}(ω)$ of the IQH Landau bands. Because of the Hall response, these topological bands exhibit giant polarization rotation and ellipticity in the reflected waves (Kerr effect) and rotation in the order of fine structure constant in the transmitted waves (Faraday effect) with profile resembles $σ_{yx}(ω)$. Our results serve as a simple guide to optical characterization for topological flat bands.

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