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arXiv 1706.09353cond-mat.str-elcond-mat.dis-nncond-mat.mes-hall
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带隙Dirac相位模型中Weyl半金属的光学响应

Optical response in Weyl semimetal in model with gapped Dirac phase

S. P. Mukherjee, J. P. Carbotte

摘要:

研究了Weyl半金属(WSM)的光学性质,该模型除了描述与费米速度$v_{F}$成正比的孤立狄拉克锥的通常项外,还包含一个能隙项$m$和一个时间反演对称性破缺的塞曼自旋分裂项$b$.运输内久保形式主义和特别注意支付的修改,导致从有限的$m$和$b$。我们考虑如何改变这些修改时,包括一个有限的剩余散射率$Γ$。对于$Γ<m$,A.C.作为光子能量$Ω$的函数的电导率继续显示$Ω$的干净极限的两个准线性能量区域,其低于在($ m+b $)处缺口的第二电子带的开始。对于$m$阶的$Γ$,两个不同的线性能量标度的痕迹很小,并且光学响应已经朝着$m=b=0$的方向发展。虽然存在一些数量上的差异,但没有质量上的差异。零温度下直流电导率$σ^{DC}(T=0)$($T=0$)和化学势($μ=0$)的大小发生变化。虽然它仍然与$Γ$成正比,但它与外尔节点外的有效费米速度成反比,该速度等于$v_{F}^\ast=v_{F}\sqrt{b^2-m^2}/b$,当接近外尔半金属和带隙狄拉克相(GDSM)之间的相边界时,该速度强烈减小到$b=m$。在有限$T/Γ$,$μ/Γ$和$Ω/Γ$的方法中的领先项$σ^{DC}(T=0)$被发现是二次的。这些校正的系数密切跟踪$μ=T=Ω=0$极限的$b/m$依赖性,在WSM-GDSM边界附近差异最大。

英文摘要:

We study the optical properties of Weyl semimetal (WSM) in a model which features, in addition to the usual term describing isolated Dirac cones proportional to the Fermi velocity $v_{F}$, a gap term $m$ and a Zeeman spin-splitting term $b$ with broken time reversal symmetry. Transport is treated within Kubo formalism and particular attention is payed to the modifications that result from a finite $m$ and $b$. We consider how these modifications change when a finite residual scattering rate $Γ$ is included. For $Γ<m$ the A.C. conductivity as a function of photon energy $Ω$ continues to display the two quasilinear energy regions of the clean limit for $Ω$ below the onset of the second electronic band which is gapped at ($ m+b $). For $Γ$ of the order $m$ little trace of two distinct linear energy scales remain and the optical response has evolved towards that for $m=b=0$. Although some quantitative differences remain there are no qualitative differences. The magnitude of the D.C. conductivity $σ^{DC}(T=0)$ at zero temperature ($T=0$) and chemical potential ($μ=0$) is altered. While it remains proportional to $Γ$ it becomes inversely dependent on an effective Fermi velocity out of the Weyl nodes equal to $v_{F}^\ast=v_{F}\sqrt{b^2-m^2}/b$ which decreases strongly as the phase boundary between Weyl semimetal and gapped Dirac phase (GDSM) is approached at $b=m$. The leading term in the approach to $σ^{DC}(T=0)$ for finite $T/Γ$, $μ/Γ$ and $Ω/Γ$ is found to be quadratic. The coefficient of these corrections tracks closely the $b/m$ dependence of the $μ=T=Ω=0$ limit with differences largest near to the WSM-GDSM boundary.

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