The interband optical response of a three-dimensional Dirac cone is linear inphoton energy ($\Omega$). Here, we study the evolution of the interbandresponse within a model Hamiltonian which contains Dirac, Weyl and gappedsemimetal phases. In the pure Dirac case, a single linear dependence isobserved, while in the Weyl phase, we find two quasilinear regions withdifferent slopes. These regions are also distinct from the large-$\Omega$dependence. As the boundary between the Weyl (WSM) and gapped phases isapproached, the slope of the low-$\Omega$ response increases, while thephoton-energy range over which it applies decreases. At the phase boundary, asquare root behaviour is obtained which is followed by a gapped response in thegapped semimetal phase. The density of states parallels these behaviours withthe linear law replaced by quadratic behaviour in the WSM phase and the squareroot dependence at the phase boundary changed to $|\omega|^{3/2}$. The opticalspectral weight under the intraband (Drude) response at low temperature ($T$)and/or small chemical potential ($\mu$) is found to change from $T^2$ ($\mu^2$)in the WSM phase to $T^{3/2}$ ($|\mu|^{3/2}$) at the phase boundary.
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机译：三维狄拉克锥的带间光响应是线性光子能量（$ \ Omega $）。在这里，我们研究了包含Dirac，Weyl和gappedsemimetal相的哈密顿模型中带间响应的演化。在纯狄拉克情况下，观察到一个线性相关性，而在韦尔相中，我们发现两个具有不同斜率的准线性区域。这些区域也与大$ \ Omega $依赖性不同。随着接近Weyl（WSM）和带隙相之间的边界，低$ \ Omega $响应的斜率增加，而其应用的光子能量范围减小。在相边界处，获得方根行为，随后在有间隙的半金属相中产生有间隙的响应。状态密度使这些行为与WSM阶段中被二次行为所取代的线性定律平行，并且在相边界处的平方根依赖性变为$ | \ omega | ^ {3/2} $。发现在低温（$ T $）和/或小化学势（$ \ mu $）的带内（Drude）响应下的光谱权重在变化时从$ T ^ 2 $（$ \ mu ^ 2 $）变化WSM相位在相位边界处变为$ T ^ {3/2} $（$ | \ mu | ^ {3/2} $）。
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