Notes on Fermi-Dirac Integrals

二维相互作用II型Dirac费米子稳定性的重整化群方法

Renormalization Group Approach to Stability of Two-dimensional Interacting Type-II Dirac Fermions

II型外尔/狄拉克费米子是传统或I型外尔/狄拉克费米子的推广，其圆锥谱倾斜，使得费米面在二维中变成线，在三维中变成面，而不是传统外尔/狄拉克费米子的离散点。与质量无关的重整化群计算表明，倾斜参数随尺度单调减小，导致二维Ⅱ型Weyl/Dirac费米子向Ⅰ型费米子的跃迁.由于费米面的非平凡性，光子通过手征反常部分获得有限质量，导致Weyl/Dirac费米子的强屏蔽效应。因此，各向异性的第二类狄拉克半金属对库仑相互作用变得稳定。这项工作提供了深刻的洞察费米面的几何形状和库仑相互作用之间的相互作用。

Magnetohydrodynamics and electro-electron interaction of massless Dirac fermions

The magnetotransport properties of massless Dirac fermions in a gapless HgTe quantum well are investigated. In samples with narrow channels, a large negative magnetoresistance with a Lorentzian profile is observed, which is interpreted as a manifestation of electron viscosity due to electron-electron interaction. Comparison of experiment with theory yields the shear stress relaxation time of the Dirac fermions caused by electron-electron scattering.

用电场调谐狄拉克材料中的费米速度

Tuning the Fermi velocity in Dirac materials with an electric field

狄拉克物质的特征是能量-动量关系类似于相对论性无质量粒子。通常命名为狄拉克锥，这些色散关系被认为是它们的基本特征。这些材料包括非常不同的实例，例如石墨烯和拓扑绝缘体。能带工程技术的目标应该是完全控制表征狄拉克锥的参数：费米速度。我们提出了一个通用的机制，使微调的费米速度在狄拉克材料在一个容易获得的方式进行实验。通过将样品嵌入均匀电场中，费米速度被显著地修改。我们首先证明了这一结果的解析，为表面态的拓扑绝缘体/半导体界面，并假定其普适性的其他狄拉克材料。然后我们在碳基狄拉克材料，即石墨烯纳米带和纳米管中检验了它的正确性，从而表明我们的假设在连续谱和紧束缚计算以及不同狄拉克系统中的有效性。

狄拉克半金属费米弧表面态的大电导率

Large optical conductivity of Dirac semimetal Fermi arc surfaces states

费米弧表面态是拓扑狄拉克半金属的一个标志，它可以容纳表现出与其母体不同的不寻常动力学的载流子。我们发现本征狄拉克半金属中的费米弧载流子具有强的各向异性轻物质相互作用。其特征在于，当光横向于费米弧偏振时，费米弧光学电导率大;当光沿着费米弧偏振时，费米弧光学电导率显著减弱。大的表面光谱权重被锁定到狄拉克节点之间的宽间隔，并且当系统被掺杂时，作为费米弧载流子的大德鲁德权重而持续存在。因此，大的和各向异性的费米弧电导率提供了一种新的手段，光学查询狄拉克半金属的拓扑表面状态。

Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture

We investigate the non-Fermi-liquid behaviors of the 2D and 3D Dirac/Weyl systems with low-order and higher order dispersion. The self-energy correction, symmetry, free energy, optical conductivity, density of states, and spectral function are studied. We found that, for Dirac/Weyl systems with higher order dispersion, the non-Fermi-liquid features remain even at finite chemical potential, and they are distinct from the ones in Fermi-liquid picture and the conventional non-Fermi-liquid picture. The Landau damping of the longitudinal excitations within random-phase-approximation (RPA) for the n…

$β$-CuI: a Dirac semimetal without surface Fermi arcs

Anomalous surface states with Fermi arcs are commonly considered to be a fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals, however, Fermi arcs of DSMs are not topologically protected. Using first-principles calculations, we predict that $β$-CuI is a peculiar DSM whose surface states form closed Fermi pockets instead of Fermi arcs. In such a fermiological Dirac semimetal, the deformation mechanism from Fermi arcs to Fermi pockets stems from a large cubic term preserving all crystal symmetries, and the small energy difference between the surface and bulk Dirac points. The c…