Deviation from perfect conical dispersion in Dirac materials, such as the presence of mass or tilting, enhances control and directionality of electronic transport. To identify these signatures, we analyze the thermal derivative spectra of optical reflectivity in doped massive tilted Dirac systems. The density of states and chemical potential are determined as preliminary steps to calculate the optical conductivity tensor at finite temperature using thermal convolution. Changes in reflection caused by temperature variations enable clear identification of critical frequencies in the optical response. By measuring these spectral features in the thermoderivative spectrum, energy gaps and band structure tilting can be determined. A comparison is presented between the spectra of various low-energy Dirac Hamiltonians. Our findings suggest that thermal difference spectroscopy holds promise as a valuable technique for probing interband transitions of 2D Dirac fermions
1T$^\prime$-MoS$_2$ exhibits valley-spin-polarized tilted Dirac bands in the presence of external vertical electric field and undergoes a topological phase transition between the topological insulator and band insulator around the critical value of the electric field. Within the linear response theory, we theoretically investigate the anisotropic longitudinal optical conductivities of tilted Dirac bands in both undoped and doped 1T$^\prime$-MoS$_2$, including the effects of the vertical electric field. The influence of the spin-orbit coupling gap, band tilting, and vertical electric field on t…
The interband optical absorption of linearly polarised light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the bandstructure is analysed theoretically. Super-critically tilted (type-II) Dirac cones are characterised by an absorption that is highly dependent on the incident photon polarisation and frequency, and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence,…
Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones
众所周知，手征性是狄拉克-费米子系统的一个重要对称性，它导致了石墨烯中的零模朗道能级，在这里，我们探讨这个概念是否可以扩展到有机金属中遇到的倾斜狄拉克锥。我们发现存在一种“广义手征对称性“，它包含倾斜狄拉克锥，其中广义手征算符$γ$，满足$γ^{\dagger} H + Hγ=0$的哈密顿量$H$，保护零模。我们可以利用这一点来证明$n=0$朗道能级是类似δ函数的（没有加宽），这是通过扩展阿哈罗诺夫-卡舍的论证来实现的。数值计算证实了具有广义手征的晶格模型具有非常尖锐的空间关联随机朗道能级。
Magneto-optics of quasi-relativistic electrons in tilted Dirac cones in graphene and $α$-(BEDT-TTF)$_2$I$_3$
无质量狄拉克费米子以低能模式出现在几个准二维凝聚态系统中，如石墨烯、块状拓扑绝缘体的表面和层状有机半导体中。当这种系统的旋转对称性被面内电场或狄拉克锥的固有倾斜所降低时，所允许的偶极光学跃迁从几个选定的跃迁演变成宽扇的带间跃迁。我们表明，低能量载流子的洛伦兹协方差允许一个简洁的分析新兴的磁光特性。我们预测，红外吸收光谱产生的倾斜狄拉克锥结构的有机化合物，如$α$ -（BEDT-TTF）$_2$ I $_3$的定量信息。
We explore topological transitions in the type of propagation of surface electromagnetic modes in massive anisotropic tilted Dirac systems. The presence of tilting and mass gives rise to an indirect band gap that strongly modifies the joint density of states compared to the gapless system. New van Hove singularities appear, and the interplay between intra and interband transitions leads to an anisotropic optical conductivity with imaginary parts acquiring opposite signs in orthogonal directions, opening the possibility of having hyperbolic propagation of plasmons. Isofrequency contours and low…
Interband optical conductivities in two-dimensional tilted Dirac bands revisited within the tight-binding model
Sichuan Normal University（四川师范大学）；Renmin University of China（中国人民大学）；The Hong Kong University of Science and Technology（香港科技大学）；Yangzhou University（扬州大学）
Magnetoplasmons of the tilted-anisotropic Dirac cone material $α-$(BEDT-TTF)$_2$I$_3$
研究了有机化合物$α-$（BEDT-TTF）$_2$ I $_3$在垂直磁场中准二维电子液体的低能连续模型的集体模.零磁场输运实验和\textit{ab initio}理论证明，该材料同时具有无质量和有质量的低能载流子，前者可用倾斜的各向异性狄拉克锥描述。这些锥的极化率是各向异性的，并且在任何两个回旋共振之间发生两组磁等离子体激元模式。我们表明，锥的倾斜导致一个独特的谷间阻尼效应：上混合模式的一个锥是阻尼的粒子孔连续的其他锥在通用方向。我们分析了大量载流子的存在如何影响系统的响应，并演示了掺杂如何可以调整$α-$（BEDT-TTF）$_2$ I $_3$之间的各向同性和各向异性的筛选制度。
Surface plasmons, which allow extreme confinement of light, suffer from high intrinsic electronic losses. It has been shown that stimulated emission of electrons can transfer energy to plasmons and compensate for the high intrinsic losses. To-date, these realizations have relied on introducing an external gain media coupled to the surface plasmon. Here, we propose that plasmons in two-dimensional materials with closely located electron and hole Fermi pockets can experience gain, when an electrical current bias is applied along the displaced electron-hole pockets, without the need for an extern…
Lifshitz transition is a kind of topological phase transition in which the Fermi surface is reconstructed. It can occur in the two-dimensional (2D) tilted Dirac materials when the energy bands change between the type-I phase ($0<t<1$) and the type-II phase ($t>1$) through the type-III phase ($t=1$), where different tilts are parametrized by the values of $t$. In order to characterize the Lifshitz transition therein, we theoretically investigate the longitudinal optical conductivities (LOCs) in type-I, type-II, and type-III Dirac materials within linear response theory. In the undoped case, the…
Anomalous acoustic plasmons in two-dimensional over-tilted Dirac bands
Sichuan Normal University（四川师范大学）；Beijing Forestry University（北京林业大学）；High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院高磁场科学中心）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）
Longitudinal conductivity of massless fermions with tilted Dirac cone in magnetic field
研究了在磁场中具有倾斜狄拉克锥的二维相对论电子气的纵向电导率。结果表明，电导率在平行于和垂直于圆锥倾斜方向上表现不同。在高磁场的电导率在非零朗道水平在垂直于倾斜的方向修改非平凡的，在平行的情况下。本文用数值方法研究了零温下狄拉克点处电导率从高到低磁场的交叉。研究发现，倾斜产生的各向异性的电导率随磁场，这是不同的各向异性来自费米速度。我们还讨论了在有限温度和有限磁场下的电导率，这些电导率可以直接与$α$ -（BEDT-TTF）$_2$ I $_3$有机导体的实验进行比较。我们发现，倾斜并没有影响这么多的磁场依赖性的电导率除了前因子。我们讨论了最近的实验数据的解释，并提出了一些建议，以检测在未来的实验倾斜的效果。
In the presence of an external vertical electric field and strain, it is evident that 1T${^\prime}$-MoS$_2$ exhibits tilted Dirac bands which are valley-spin-polarized. Additionally, this material experiences a topological phase change between a topological insulator and band insulator for a critical value of the electric field. Using linear response theory, we calculated the polarization function which is in turn employed to obtain the dielectric function. This latter quantity is subsequently utilized in calculations to determine the plasmons dispersion relation, their decay rate and impurity…
Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmn borophene: The role of different frequency, temperature and scattering limits
The effect of the Dirac cone tilt of anisotropic two-dimensional materials on the time evolution of coherent electron states in the presence of electric and magnetic fields is studied. We propose a canonical transformation that maps the anisotropic Dirac-Weyl Hamiltonian with tilted Dirac cones to an effective and isotropic Dirac Hamiltonian under these fields. In this way, the well-known Landau-level spectra and wave functions allow calculating the Wigner matrix representation of Landau and coherent states. We found a valley dependency in the behavior of the Wigner function for both Landau an…
Nodal line in single-component molecular conductor [Pd(dddt)_2] has been examined to understand the tilted Dirac cone on the non-coplanar loop. In the previous work [J. Phys. Soc. Jpn. 87, 113701 (2018)], the velocity of the cone was calculated at respective Dirac points on the nodal loop based on our first-principles band structure calculations, which was a new method to derive an effective Hamiltonian with a 2 x 2 matrix. However, the Dirac cones on the nodal line are fully reproduced only at symmetric points. In the present paper, we show that our improved method well reproduces reasonable …
A new type of angular oscillations of the high-frequency conductivity for conductors with a band-contact line has been predicted. The effect is caused by groups of charge carriers near the self-intersection points of the Fermi surface, where the electron energy spectrum is near-linear and can be described by anisotropic Dirac cone model. The amplitude of the resonance peaks satisfies the simple sum rule. The ease in changing the degree of anisotropy of the Dirac cone due to the angle of inclination of the magnetic field makes the considered type of oscillations attractive for experimental obse…
We explore the effect of valley-contrasting gaps in the optical response of two-dimensional anisotropic tilted Dirac systems. We study the spectrum of intraband and interband transitions through the joint density of states (JDOS), the optical conductivity tensor, and the Drude spectral weight. The energy bands present an indirect gap in each valley. Thus a new possibility opens for the position of the Fermi level (an ``indirect zone''), and for the momentum space for allowed transitions. The JDOS near each gap displays a set of three van Hove singularities which are in contrast to the case of …
The group delay time of Dirac fermions subjected to a tilting barrier potential along the $ x $-axis is investigated in graphene. We start by finding the eigenspinor solution of the Dirac equation and then relating it to incident, reflected, and transmitted beam waves. This relationship allows us to compute the group delay time in transmission and reflection by obtaining the corresponding phase shifts. We discovered that the barrier width, incident energy, and incident angle can all be used to modify the group delay time, and that the particles travel through the barrier at the Fermi velocity …
