[论文解读] Frequency-dependent Faraday and Kerr rotation in anisotropic nonsymmorphic Dirac semimetals

A. Chakraborty, Guang Bian+1 more|arXiv (Cornell University)|Feb 10, 2023

Topological Materials and Phenomena被引用 5

一句话总结

本文从理论上研究了在自旋轨道耦合导致的垂直方向Zeeman项打开能隙的各向异性、非对称性二维狄拉克半金属中，频率依赖的法拉第旋转和克尔旋转。通过引入本征各向异性和无序的模型，研究发现法拉第旋转和克尔旋转角在Zeeman能隙边缘附近出现对数增强，克尔旋转达到高达π/2的巨大峰值，法拉第旋转则实现数量级增强，即使在中等无序条件下依然显著，凸显其在磁光器件中的应用潜力。

ABSTRACT

We calculate the frequency-dependent longitudinal and Hall conductivities and the Faraday and Kerr rotation angles for a single sheet of anisotropic Dirac semimetal protected by nonsymmorphic symmetry in the presence of a Zeeman term coupling to the out-of-plane component of the spin. While the Zeeman term causes a rotation of the plane of polarization of the light, the anisotropy causes the appearance of an elliptically polarized component in an initially linearly polarized beam. The two effects can be combined in a single complex Faraday rotation angle. At the zero-frequency limit, we find a finite value of the Faraday rotation angle, which is given by $2α_F$, where $α_F$ is the effective fine structure constant associated with the velocity of the linearly dispersing Dirac fermions. We also find a logarithmic enhancement of the Faraday (and Kerr) rotation angles as the frequency of the light approaches the absorption edge associated with the Zeeman-induced gap. While the enhancement is reduced by impurity scattering, it remains significant for an attainable level of material purity. These results indicate that two-dimensional Dirac materials protected by nonsymmorphic symmetry are responsive to Zeeman couplings and can be used as platforms for magneto-optic applications, such as the realization of polarization-rotating devices.

研究动机与目标

• 理解受非对称性保护的二维狄拉克半金属在Zeeman耦合作用下的磁光响应。
• 分析本征各向异性在Zeeman诱导能隙存在下对法拉第和克尔旋转的影响。
• 评估无序对磁光响应的影响，特别是吸收边附近的峰结构。
• 建立一个将光学电导率与各向异性2D狄拉克材料中偏振旋转相联系的理论框架。
• 提出这些材料作为偏振旋转和非互易光学器件的鲁棒平台。

提出的方法

• 利用各向异性非对称性狄拉克半金属的低能有效哈密顿量，推导出频率依赖的纵向和霍尔电导率。
• 通过求解二维层与真空界面处的麦克斯韦方程组，将电导率张量与透射和反射矩阵关联。
• 利用边界匹配条件，从电导率张量计算法拉第和克尔旋转角。
• 通过无量纲参数ρ < 1引入各向异性，以模拟系统中的双折射。
• 通过将自能中的无穷小虚部η替换为有限值δ = 1/τ来模拟动量弛豫，从而建模无序效应。
• 使用复对数函数计算有限能隙和无序存在下的电导率与旋转角。

Figure 1 : (a) Schematic band diagram of a nonsymmorphic two-dimensional Dirac semimetal in the presence of a magnetic exchange potential. The exchange potential (in the form of a Zeeman term) creates the gap in otherwise linearly dispersing bands when it couples to out-of-plane spin. For an in-plan

实验结果

研究问题

• RQ1 非对称性狄拉克半金属中的本征各向异性如何影响频率依赖的法拉第和克尔旋转角？
• RQ2 Zeeman项在诱导能隙和增强磁光效应方面起到什么作用？
• RQ3 系统在与Zeeman能隙相关的吸收边附近如何响应？
• RQ4 法拉第和克尔旋转的对数增强在多大程度上对杂质散射和无序具有鲁棒性？
• RQ5 由各向异性诱导的椭圆偏振分量能否作为磁光响应的可测量特征？

主要发现

• 法拉第旋转角在吸收边处出现对数发散，与零频值相比实现数量级增强。
• 克尔旋转角在低频极限下达到约π/2的巨大值，且在吸收边之上发生符号反转。
• 各向异性（ρ < 1）使吸收边处的法拉第旋转峰变尖锐，同时降低克尔旋转的幅值。
• 无序使法拉第旋转峰展宽并抑制，但在中等纯度水平下仍可观测到显著增强。
• 由于各向异性，透射或反射光中发展出椭圆偏振分量，该分量与偏振旋转内在关联。
• 通过近邻效应实现的有效Zeeman耦合避免了轨道耦合，保持了响应的外尔特性，从而实现清晰的磁光效应。

Figure 2 : (a) The band dispersion of $\alpha$ -Bi near the $X_{1}$ Dirac point. (b) This figure shows that only intra-valley transitions are possible as the two valleys hold opposite eigenvalues for $\tilde{M}_{z}$ when there is a gap present in the system.