In this paper, we make a comprehensive study of the properties of a gapped Dirac semimetal model, which was originally proposed in the magnetoinfrared spectroscopy measurement of $\mathrm{Ze}{\mathrm{Te}}_5$, and includes both the linear and parabolic dispersions in all three directions. We find that, depending on the band inversion parameters, ${\zeta }^{\prime }$ and ${\zeta }_z^{\prime }$, the model can support three different phases: the single Dirac point (DP) phase, the double DPs phase, and the Dirac ring phase. The three different phases can be distinguished by their low-energy features in the density of states (DOS) and optical conductivity. At high energy, both the DOS and optical conductivity exhibit power-law-like behaviors, with the asymptotic exponents depending heavily on the signs of ${\zeta }^{\prime }$ and ${\zeta }_z^{\prime }$. Moreover, the thumb-of-rule formula between the DOS and optical conductivity is satisfied only when $({\zeta }^{\prime },{\zeta }_z^{\prime })>0$. The implications of our results for experiments are discussed.

中文翻译：

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带混合线性和抛物线色散的带间隙Dirac半金属

在本文中，我们对带间隙的狄拉克半金属模型的性质进行了全面的研究，该模型最初是在磁红外光谱测量中提出的。 $泽{特}_5$，并且包括所有三个方向上的线性和抛物线色散。我们发现，根据频带反转参数，${\zeta }^{\prime }$ 和 ${\zeta }_{ž}^{\prime }$，该模型可以支持三个不同的阶段：单狄拉克点（DP）阶段，双DPs阶段和狄拉克环阶段。这三个不同的相位可以通过其低能量特性（态密度（DOS）和光导率）来区分。在高能量下，DOS和光导率都表现出类似幂律的行为，而渐近指数在很大程度上取决于${\zeta }^{\prime }$ 和 ${\zeta }_{ž}^{\prime }$。此外，仅当满足以下条件时，才可以满足DOS和光导率之间的经验公式：$（{\zeta }^{\prime }，{\zeta }_{ž}^{\prime }）>0$。讨论了我们的结果对实验的意义。