On the theory of two-dimensional materials with tilted Dirac cones

开发具有电子、光子、磁振子和声子“设计者”谱的新型材料和超材料是当代凝聚态物理学的发展趋势。研究的潮流正在转向理论预测，然后是对固态系统中的奇异准粒子（如Weyl和Majorana费米子）的实验观察。自20世纪80年代以来，二维（2D）系统为发现新的准粒子提供了一个特别丰富的平台，包括量子霍尔系统中的分数带电任意子和石墨烯和拓扑绝缘体中的无质量狄拉克费米子作为最壮观的例子。与此同时，纳米技术的最新进展包括货车德瓦尔斯异质结构（由货车德瓦尔斯力保持的人工少层材料）的发展，以及找到一种生产具有选定手性的碳纳米管的方法。拟议的理论博士研究将集中在一个新的设计师2D货车范德华材料的电子性能形成的平面规则阵列的单壁碳纳米管。单壁碳纳米管是长圆柱形分子，其电子性质完全由它们从石墨烯片上滚下来的方式来定义。也就是说，它们可以是半导体的，带隙高达几个电子伏特，金属没有任何带隙或准金属的曲率效应引起的几个meV的微小带隙。在一个规则的平面阵列中组合的管应该会导致出现的2D准粒子的强各向异性分散。最有趣的结果是预期的金属和准金属纳米管阵列的运动垂直于纳米管轴将导致在电子性质的最戏剧性的变化。特别地，带隙可以在金属管阵列中打开或对于准金属纳米管塌陷。垂直于管轴的运动也会导致高度对称的锯齿形纳米管中的谷简并度提升，从而导致倾斜的狄拉克锥，支持具有双曲色散的新型2D Weyl费米子。该系统中特有的低能电子色散（能量对2D动量的依赖性）的分析描述将是拟议研究的核心。我们将研究这种色散产生的大量独特的物理效应，包括不寻常的磁输运现象和带间偶极跃迁，预计这些效应将在备受追捧的太赫兹频率范围内。

Developing novel materials and metamaterials with "designer" spectra for electrons, photons, magnons and phonons is the growing trend in contemporary condensed matter physics. The tide of research is turning towards theoretical predictions followed by experimental observations of exotic quasiparticles in solid state systems such as Weyl and Majorana fermions. Since the 1980's, two-dimensional (2D) systems provided a particularly rich playground for the discovery of new quasiparticles, including fractionally charged anyons in quantum Hall systems and massless Dirac fermions in graphene and topological insulators as the most spectacular examples. Simultaneously, the most recent advances in nanotechnology include the development of van der Waals heterostructures (artificial few-layer materials held by van der Waals forces) and finding a way of producing carbon nanotubes of selected chirality. The proposed theoretical PhD research will focus on the electronic properties of a novel designer 2D van der Waals material formed by a planar regular array of single-walled carbon nanotubes. Single-walled carbon nanotubes are long cylindrical molecules with electronic properties defined entirely by the way they are rolled from a graphene sheet. Namely, they can be semiconducting with a bandgap up to several electron-volts, metallic without any bandgap or quasi-metallic with a tiny bandgap of a few meV induced by curvature effects. Combining the tubes in a regular planar array should result in a strongly anisotropic dispersion of the emerging 2D quasiparticles. The most interesting results are expected for arrays of metallic and quasi-metallic nanotubes for which the motion normal to the nanotube axis will result in the most dramatic changes in the electronic properties. In particular, a bandgap may be opened in an array of metallic tubes or collapse for quasi-metallic nanotubes. The motion normal to the tube axis will also result in lifting the valley degeneracy in highly-symmetric zigzag nanotubes leading to tilted Dirac cones supporting a new type of 2D Weyl fermions with hyperbolic dispersion. An analytic description of the peculiar low-energy electronic dispersion (dependence of energy on the 2D momentum) in this system will be at the core of the proposed research. We will study a plethora of unique physical effects stemming from this dispersion including unusual magneto-transport phenomena and interband dipole transitions, which are expected to be in the highly sought-after terahertz frequency range.