Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Single pair of charge-2 Dirac and charge-2Weyl phonons in GeO_(2)

The presence of a pair of Weyl and Dirac points(WP-DP)in topological semimetal states is intriguing and sought after due to the effects associated with chiral topological charges.However,identifying these states in real materials poses a significant challenge.In this study,by means of first-principles calculations we predict the coexistence of charge-2 Dirac and charge-2 Weyl phonons at high-symmetry points within a noncentrosymmetric P4_(1)2_(1)2 space group.Furthermore,we propose GeO_(2)as an ideal candidate for realizing these states.Notably,we observe two distinct surface arcs that connect the Dirac and Weyl points across the entire Brillouin zone,which could facilitate their detection in future experimental investigations.This study not only presents a tangible material for experimentalists to explore the topological properties of WP-DP states but also opens up new avenues in the quest for ideal platforms to study chiral particles.

Coexistence of Dirac and Weyl points in non-centrosymmetric semimetal NbIrTe_(4)

Using angle-resolved photoemission spectroscopy and density functional theory calculations methods,we investigate the electronic structures and topological properties of ternary tellurides NbIrTe_(4),a candidate for type-II Weyl semimetal.We demonstrate the presence of several Fermi arcs connecting their corresponding Weyl points on both termination surfaces of the topological material.Our analysis reveals the existence of Dirac points,in addition to Weyl points,giving both theoretical and experimental evidences of the coexistence of Dirac and Weyl points in a single material.These findings not only confirm NbIrTe_(4) as a unique topological semimetal but also open avenues for exploring novel electronic devices based on its coexisting Dirac and Weyl fermions.

一类具有复权函数和两个不连续点的Dirac算子的逆问题

本文考虑了一类具有转移条件和复值权函数的Dirac算子的逆问题,采用了谱映射的方法得到了具有两个不连续点的Dirac算子的势函数在整个区间能被两组谱或Weyl函数唯一确定。

Dirac-Weyl半金属结中电磁控制的克莱因隧穿和电荷电导

从理论上研究了Dirac-Weyl半金属结中电磁控制的克莱因隧穿和电荷电导.研究发现:完美电子隧穿显著依赖于电势垒的大小、磁场幅度及其方向.当电势垒接近费米能时,该结构显示了明显的波矢过滤特性.通过调节磁场幅度和方向,可以获得任意入射角度的完美隧穿电子波矢.基于电子的透射概率,进一步计算了电势垒和磁场幅度对电荷电导的影响,通过选择合适的电势垒或磁场幅度,可以实现电子开关的功能.这些理论结果为设计基于Dirac-Weyl半金属结中纳米电子器件提供了基础.

Electron transport in Dirac and Weyl semimetals

Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport phenomena in Dirac andWeyl semimetals. Section 1 is a brief introduction to the topological semimetals（TSMs）. In Section 2 and Section 3, the intriguing transport phenomena in Dirac semimetals（DSMs） andWeyl semimetals（WSMs） are reviewed, respectively. The most widely studied Cd_3A_（s2） and the TaAs family are selected as representatives to show the typical properties of DSMs and WSMs, respectively. Beyond these systems, the advances in other TSM materials,such as ZrTe_5 and the MoTe_2 family, are also introduced. In Section 4, we provide perspectives on the study of TSMs especially on the magnetotransport investigations.

Thermodynamic properties of massless Dirac–Weyl fermions under the generalized uncertainty principle

The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.

部分势函数确定的逆Dirac问题

本文讨论了在一定的条件下,势函数的部分信息和有限的特征值可以唯一确定势函数。

weyl规则的三维表述

众所周知,仅根据对应原理和厄米性要求,尚不能唯一确定与经典力学量相对应的量子学算符。力为了唯一确定这种厄米对应关系,文[1]提出,可以借助於Wey1规则。

拓扑量子材料的研究进展

拓扑量子材料近年来已经成为凝聚态物理领域研究的国际前沿课题。在过去的几十年中凝聚态物理学者对量子霍尔效应进行了广泛研究,提出了一种基于拓扑序的研究范式,并且将拓扑这一数学概念与能带理论相结合,成功将其引入到固体电子材料的理论、计算与实验研究之中。拓扑材料具有奇特的表面态和低能耗的电子输运等性质,这些效应是由于拓扑量子态受到严格的对称性保护,对于普通的材料杂质、缺陷或无序具有很高的鲁棒性,并可以通过量子调控或相变改变其拓扑性质。这一新兴研究领域为未来的电子材料和器件,乃至基于量子拓扑体系与计算的信息技术创新探索提供了多种可能。对整个材料学的发展而言,拓扑概念的引入使人们对物质的研究更加深入,并且开始使用更加先进的数学工具描述新材料的属性。文章从拓扑绝缘体和拓扑半金属等材料计算科学的角度探讨拓扑量子材料的一些基本概念以及近年来国内外的研究进展。

拓扑半金属的红外光谱研究

拓扑半金属是一类全新的拓扑电子态,展现出丰富而有趣的物理性质.这类材料不仅在未来电子器件方面具有潜在的应用价值,同时也是目前量子材料领域研究的热点和前沿.根据在三维动量空间中能带结构特点的不同,拓扑半金属可以分为Dirac半金属、Weyl金属和Nodal-line半金属等.人们已经利用各种实验技术手段对这些材料的物理性质进行了系统的研究.例如:角分辨光电子能谱可以直接观测到Weyl半金属表面态上连接两个具有相反手性的Weyl费米子的费米弧;软X射线的角分辨光电子能谱还可以直接观测到这些拓扑半金属体态中的Dirac点,Weyl点以及Nodal-line;电输运测量验证了拓扑半金属中由手性反常导致的负磁阻现象;圆偏振光产生光电流的实验证明了Weyl半金属TaAs中存在相反手性的Weyl费米子;此外,人们还发现Weyl半金属具有非常强的非线性效应,主要表现为很强的二次谐波产生和THz发射效应等.红外光谱是一种体敏感的实验手段.该手段不仅覆盖很宽的能量范围(meV到几个eV),而且具有很高的能量分辨率(最高可达几十个μeV量级),因此适合研究拓扑半金属体态的电子结构以及晶格振动行为.研究拓扑半金属材料的红外光谱学性质不仅可以帮助人们更深入理解这类材料的物理性质以及发现新的物理现象,还可以为拓扑半金属在光学领域的研究和应用奠定基础.本文介绍了近年来上面提到的几类拓扑半金属材料的红外光谱研究的进展情况.

Weyl points and Dirac lines protected by multiple screw rotations

In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ） and No. 198 （P213）, which have three orthogonal screw rotation axes. In the case of space groups No. 61 （Pbca） and No. 205 （Pa-3） that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the F point and R point, respectively.

拓扑声子晶体

拓扑物态是当前凝聚态及材料物理领域的关注焦点.声子晶体是具有周期性结构的人工材料,其中的声子态或声波态也可具有拓扑性质.从声子晶体的背景知识出发,介绍了2类拓扑声子晶体的研究进展,即能谷声子晶体和外尔声子晶体,它们具有良好鲁棒性及超导传输特性的拓扑界/表面波,这种无障碍的传输特性具有广阔的应用前景.

New family of Dirac and Weyl semimetals in XAuTe(X=Na, K,Rb) ternary honeycomb compounds

We propose a new family of 3D Dirac semimetals based on XAuTe(X = K, Na, Rb) ternary honeycomb compounds, determined based on first-principles calculations, which are shown to be topological Dirac semimetals in which the Dirac points are induced by band inversion. Dirac points with four-fold degeneracy that are protected by C3 rotation symmetry and located on the Γ-A high-symmetry path are found. Through spatial-inversion symmetry breaking, a K(Au0.5 Hg0.5)(Te0.5As0.5) superlattice structure composed of KHgAs and KAuTe compounds is proven to be a Weyl semimetal with type-II Weyl points, which connect electronand hole-like bands. In this superlattice structure, the six pairs of Weyl nodes are distributed along the K-Γ high-symmetry path on the kz = 0 plane. Our research expands the family of topological Dirac and type-II Weyl semimetals.

On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic four-potentials

In this work we study in detail the connection between the solutions to the Dirac and Weyl equations and the associated electromagnetic four-potentials.First,it is proven that all solutions to the Weyl equation are degenerate,in the sense that they correspond to an infinite number of electromagnetic four-potentials.As far as the solutions to the Dirac equation are concerned,it is shown that they can be classified into two classes.The elements of the first class correspond to one and only one four-potential,and are called non-degenerate Dirac solutions.On the other hand,the elements of the second class correspond to an infinite number of four-potentials,and are called degenerate Dirac solutions.Further,it is proven that at least two of these fourpotentials are gauge-inequivalent,corresponding to different electromagnetic fields.In order to illustrate this particularly important result we have studied the degenerate solutions to the forcefree Dirac equation and shown that they correspond to massless particles.We have also provided explicit examples regarding solutions to the force-free Weyl equation and the Weyl equation for a constant magnetic field.In all cases we have calculated the infinite number of different electromagnetic fields corresponding to these solutions.Finally,we have discussed potential applications of our results in cosmology,materials science and nanoelectronics.

Chiral Current in a Graphene Battery

We review the formulation of graphene’s massless Dirac equation, under the chiral electromagnetism approach, hopefully demystifying the material’s unusual chiral, relativistic, effective theory. In Dirac’s theory, many authors replace the speed of light by the Fermi velocity, in this paper we deduce that in graphene the Fermi velocity is obtained from the connection between the electromagnetic chirality and the fine structure constant when the electric wave E is quasi parallel to the magnetic wave H. With this approach we can consider the properties of electric circuits involving graphene or Weyl semimetals. The existence of the induced chiral magnetic current in a graphene subjected to magnetic field causes an interesting and unusual behavior of such circuits. We discuss an explicit example of a circuit involving the current generation in a “chiral battery”. The special properties of this circuit may be utilized for creating “chiral electronic” devices.

狄拉克算子的谱与从属解

本文利用解的L^(2)范数,定义了狄拉克方程组■的从属解,并给出了Weyl-Titchmarsh函数与从属解的关系,然后利用此关系和谱测度的最小支集得到了从属解的同谱分解。

Inverse Problems for the Dirac Operator on a Star Graph

Following the previous work,we shall study some inverse problems for the Dirac operator on an equilateral star graph.It is proven that the so-called Weyl function uniquely determines the potentials.Furthermore,we pay attention to the inverse problem of recovering the potentials from the spectral data,which consists of the eigenvalues and weight matrices,and present a constructive algorithm.The basic tool in this paper is the method of spectral mappings developed by Yurko.

High-pressure phases of Weyl semimetals NbP, NbAs, TaP,and TaAs

In this study, we used the crystal structure search method and first-principles calculations to systematically explore the highpressure phase diagrams of the TaAs family （NbP, NbAs, TaP, and TaAs）. Our calculation results show that NbAs and TaAs have similar phase diagrams, the same structural phase transition sequence I41md→Pδm2→}P21/c→Pm3m, and slightly different transition pressures. The phase transition sequence of NbP and TaP differs somewhat from that of NbAs and TaAs, in which new structures emerge, such as the Cmcm structure in NbP and the Pmmn structure in TaP. Interestingly, we found that in the electronic structure of the high-pressure phase Pδm2-NbAs, there are coexisting Weyl points and triple degenerate points, similar to those found in high-pressure Pδm2-TaAs.

A semiclassical approach to surface Fermi arcs in Weyl semimetals

We present a semiclassical explanation for the morphology of the surface Fermi arcs of Weyl semimetals.Viewing the surface states as a two-dimensional Fermi gas subject to band bending and Berry curvatures,we show that it is the non-parallelism between the velocity and the momentum that gives rise to the spiral structure of Fermi arcs.We map out the Fermi arcs from the velocity field for a single Weyl point and a lattice with two Weyl points.We also investigate the surface magnetoplasma of Dirac semimetals in a magnetic field,and find that the drift motion,the chiral magnetic effect and the Imbert-Fedorov shift are all involved in the formation of surface Fermi arcs.Our work not only provides an insightful perspective on the surface Fermi arcs and a practical way to find the surface dispersion,but also paves the way for the study of other physical properties of the surface states of topological semimetals,such as transport properties and orbital magnetization,using semiclassical methods.