arXiv 1803.062802018-03-16cond-mat.str-el

非中心对称多Weyl半金属中的掺杂和倾斜对光学的影响

Doping and tilting on optics in noncentrosymmetric multi-Weyl semimetals

S. P. Mukherjee, J. P. Carbotte

备注：: 14 pages, minor corrections in the published version
发表信息：: Phys. Rev. B 97, 045150 (2018)
DOI：: 10.1103/PhysRevB.97.045150

摘要：

外尔半金属（WSM）具有倾斜的狄拉克锥，根据倾斜参数（$C$）的大小可以是I型或II型。这两种类型之间的边界是在$C=1$，那里的锥体是倾斜的，有一个Lifshitz过渡。WSM的拓扑荷是1。在多Weyl中，它可以是两个或更多，具体取决于绕组数$J$的值。我们计算了沿倾斜方向（$σ_{zz}$）和垂直于倾斜方向（$σ_{xx}$）的交流光学电导率的吸收部分作为倾斜（$C$）和化学势（$μ$）的函数。对于零倾斜，在光子能量$Ω=2μ$下$σ_{xx}$和$σ_{zz}$都有不连续的上升，随后是$σ_{xx}$在$J=1,2$下和$σ_{zz}$在$J=1$下的通常的线性$Ω$定律。对于$J=2$和$σ_{zz}$，在$Ω$中，带间背景是恒定的，而不是线性的。对于I型，随着倾斜的增加，光谱权重会重新调整。吸收从$2μ/(1+C)$处的零开始，然后以准线性方式上升，直到在$2μ/(1-C)$处与通常的未掺杂的未倾斜带间背景合并。在非倾斜情况下，化学势两倍处的不连续上升消失了。对于II型的未掺杂的非倾斜的情况下，带间背景是永远不会恢复。对于非中心对称的材料，一对相反的手性Weyl节点的能量被$\pm Q_{0}$移动，这导致两个独立的吸收边对应于在$2(μ+χQ_{0})$的两个节点中的每一个的有效化学势，这取决于手性$χ=\pm$。在这种情况下，我们提供的电导率的解析表达式，它只依赖于比例$Q_{0}/μ$和倾斜时，对$Ω/μ$绘制。对于$σ_{zz}$和$J=2$，有限能量位移$Q_{0}$的特征比其他情况更明显。

英文摘要：

Weyl semimetal (WSM) feature tilted Dirac cones and can be type I or II depending on the magnitude of the tilt parameter ($C$). The boundary between the two types is at $C=1$ where the cones are tipped and there is a Lifshitz transition. The topological charge of a WSM is one. In multi-Weyl it can be two or more depending on the value of the winding number $J$. We calculate the absorptive part of the AC optical conductivity both along the tilt direction ($σ_{zz}$) and perpendicular to it ($σ_{xx}$) as a function of the tilt ($C$) and chemical potential ($μ$). For zero tilt there is a discontinuous rise in both $σ_{xx}$ and $σ_{zz}$ at photon energy $Ω=2μ$ followed by the usual linear in $Ω$ law for $σ_{xx}$ at $J=1,2$ and $σ_{zz}$ at $J=1$. For $J=2$ and $σ_{zz}$ the interband background is constant rather than linear in $Ω$. For type I there is a readjustment of optical spectral weight as the tilt is increased. The absorption starts from zero at $2μ/(1+C)$ and then rises in a quasilinear fashion till it merge with the usual undoped untilted interband background at $2μ/(1-C)$. The discontinuous rise at twice the chemical potential of the untilted case is lost. For type II the interband background of the undoped untilted case is never recovered. For noncentrosymmetric materials the energies of a pair of opposite chirality Weyl nodes become shifted by $\pm Q_{0}$ and this leads to two separate absorption edges corresponding to the effective chemical potential of each of the two nodes at $2(μ+χQ_{0})$ depending on chirality $χ=\pm$. We provide analytic expressions for the conductivity in this case which depend only on the ratio $Q_{0}/μ$ and tilt when plotted against $Ω/μ$. The signature of finite energy shift $Q_{0}$ is more pronounced for $σ_{zz}$ and $J=2$ than for the other cases.

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英文摘要：

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