We present analytic expressions for the electronic contributions to the linear conductivity $σ^{(1)}_{3d}(ω)$ and the third order optical conductivity $σ^{(3)}_{3d}(ω_1,ω_2,ω_3)$ of three dimensional massless Dirac fermions, the quasi-particles relevant for the low energy excitation of topological Dirac semimetals and Weyl semimetals. Although there is no gap for massless Dirac fermions, a finite chemical potential $μ$ can lead to an effective gap parameter, which plays an important role in the qualitative features of interband optical transitions. For gapless linear dispersion in three dimension, the imaginary part of the linear conductivity diverges as a logarithmic function of the cutoff energy, while the real part is linear with photon frequency $ω$ as $\hbarω>2|μ|$. The third order conductivity exhibits features very similar to those of two dimensional Dirac fermions, i.e., graphene, but with the amplitude for a single Dirac cone generally two orders of magnitude smaller in three dimension than in two dimension. There are many resonances associated with the chemical potential induced gap parameters, and divergences associated with the intraband transitions. The details of the third order conductivity are discussed for third harmonic generation, the Kerr effect and two-photon carrier injection, parametric frequency conversion, and two-color coherent current injection. Although the expressions we derive are limited to the clean limit at zero temperature, the generalization to include phenomenological relaxation processes at finite temperature is straightforward and is presented.
Spin and Valley Splittings in Multilayered Massless Dirac Fermion System
研究了流体静压下多层无质量狄拉克费米子系统$α$ -（BEDT-TTF）$_2$ I $_3$的层间磁电阻效应。在垂直于二维平面的磁场中，我们成功地探测到零模（n=0）朗道能级及其自旋分裂。我们证明了在磁场中的有效库仑相互作用增强了零模朗道载流子的自旋分裂。在低于2K的温度下，几特斯拉以上的磁场打破了双重谷简并。
Quantum Hall effect in multilayered massless Dirac fermion systems with tilted cones
报道了在多层无质量Dirac费米子系统$α$ -（BEDT-TTF）$_2$ I $_3$中首次观测到的Shubnikov-de Haas（SdH）振荡和量子化霍尔电阻.通过接触带电将空穴注入固定在聚萘二甲酸乙二醇酯（PEN）衬底上的薄晶体中。检测到SdH振荡的相位被Berry相位$π$修改，强烈表明在该系统中载流子掺杂是成功的。我们成功地用这种台阶探测到了二维狄拉克费米子系统的本质--量子霍尔效应。在该器件中，有效掺杂层的数量被检查为两个。我们发现，有效层之间的相关性在QHE中起着重要的作用。
Two-dimensional Massless Dirac Fermions in Antiferromagnetic AFe2As2 (A = Ba, Sr)
本文报道了砷化铁超导体的两种代表性母体化合物AFe $_{2}$ As $_{2}$（A = Ba，Sr）在磁场（B）达17.5T下的红外光谱研究。在这两个母体化合物的反铁磁态中观察到朗道能级之间的光学跃迁。我们观察到LL跃迁能量与$\sqrt{B}$的依赖关系，在跃迁能量和能量比的线性外推下，零能量拦截在B = 0 T处（$\sim$ 2.4）之间观察到的LL跃迁，结合二维（2D）动量空间中的线性带色散，通过理论计算获得，证明了反铁磁BaFe $_{2}$ As $_{2}$中存在无质量狄拉克费米子。更重要的是，所观察到的零LL相关的吸收特征的优势和沿动量方向具有极弱色散的计算带$k_{z}$表明，BaFe $_{2}$ As $_{2}$中的无质量狄拉克费米子是2D的。此外，我们还发现锶原子完全取代BaFe $_{2}$ As $_{2}$中的钡原子不仅保持了体系中的二维无质量Dirac费米子，而且提高了它们的费米速度，这支持了铁砷化物母体化合物中Dirac点受到拓扑保护的观点.
