φ-映射拓扑流理论在Weyl半金属拓扑分类中的应用

用φ-映射拓扑流理论对厄米及非厄米Weyl半金属进行拓扑分类.对一个给定的哈密顿,在动量空间建立一个由自旋组成的■场,再由这个■场给出拓扑荷密度分布.发现只有在■场模的零点,拓扑荷密度的值才不为零,而这些■场模的零点其实就是Weyl点或Weyl奇异点所在位置.通过对拓扑荷密度的积分,得到了可用于对系统进行拓扑分类的整数拓扑数.

一类三阶上三角关系矩阵的Fredholm性和Weyl性

设H_(1),H_(2),H_(3)为无穷维复可分Hilbert空间,对给定关系A∈BR(H_(1)),B∈BR(H_(2)),C∈BR(H_(3)),记M_(D,E,F)={A D E O B F O O C}∈BR(H_(1)■H_(2)■H_(3),给出了存在满足D(0)■A(0),E(0)■A(0),F(0)■B(0)的D∈BR(H_(2),H_(1)),E∈BR(H_(3),H_(1)),F∈BR(H_(3),H_(2))使得M_(D,E,F)为Fredholm关系和Weyl关系的充分必要条件。

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.

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.

Induced magneto-conductivity in a two-nodeWeyl semimetal under Gaussian random disorder

Measuring the magneto-conductivity induced from impurities may help determine the impurity distribution and reveal the structure of a Weyl semimetal sample.To verify this,we utilize the Gaussian random disorder to simulate charged impurities in a two-node Weyl semimetal model and investigate the impact of charged impurities on magneto-conductivity in Weyl semimetals.We first compute the longitudinal magnetic conductivity and find that it is positive and increases proportionally with the parameter governing the Gaussian distribution of charged impurities,suggesting the presence of negative longitudinal magneto-resistivity.Then we consider both the intra-valley and inter-valley scattering processes to calculate the induced transverse magneto-conductivity in the model.Our findings indicate that both inter-valley and intravalley scattering processes play important roles in the transverse magneto-conductivity.The locations of Weyl nodes can also be determined by magneto-conductivity measurements.This is possible if the magnetic field strength and the density of charged impurities are known.Alternatively,the measurement of magnetic conductivity may reveal the distribution of charged impurities in a given sample once the locations of the Weyl nodes have been determined.These findings can aid in detecting the structure of a Weyl semimetal sample,enhancing comprehension of magnetotransport in Weyl semimetals and promoting the development of valley electronics.

一类三阶上三角关系矩阵的左(右)Weyl性

设H_(1),H_(2),H_(3)为无穷维复可分Hilbert空间。对给定关系A∈BR(H1),B∈BR(H_(2)),C∈BR(H_(3)),记MD,E,F=(00C0BFADE)∈BR(H_(1)⊕H_(2)⊕H_(3)),给出存在满足D(0)∈A(0),E(0)∈A(0),F(0)∈B(0)的D∈BR(H_(2),H_(1)),E∈BR(H_(3),H_(1)),F∈BR(H_(3),H_(2)),使得M_(D,E,F)为左(右)Weyl关系的充分必要条件。

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.

Symmetry transformation of nonlinear optical current of tilted Weyl nodes and application to ferromagnetic MnBi_(2)Te_(4)

A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and-independent parts of optical conductivity transform under the reversal of tilt and chirality.Built on this theory, we propose ferromagnetic Mn Bi2Te4as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chiralitydependent and-independent DC photocurrents.These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.

Half-metallic ferromagneticWeyl fermions related to dynamic correlations in the zinc-blende compound VAs

The realization of 100%polarized topologicalWeyl fermions in half-metallic ferromagnets is of particular importance for fundamental research and spintronic applications.Here,we theoretically investigate the electronic and topological properties of the zinc-blende compound VAs,which was deemed as a half-metallic ferromagnet related to dynamic correlations.Based on the combination of density functional theory and dynamical mean field theory,we uncover that the half-metallic ferromagnet VAs exhibits attractive Weyl semimetallic behaviors which are very close to the Fermi level in the DFT+U regime with effect U values ranging from 1.5 eV to 2.5 eV.Meanwhile,we also investigate the magnetization-dependent topological properties;the results show that the change of magnetization directions only slightly affects the positions of Weyl points,which is attributed to the weak spin–orbital coupling effects.The topological surface states of VAs projected on semi-infinite(001)and(111)surfaces are investigated.The Fermi arcs of all Weyl points are clearly visible on the projected Fermi surfaces.Our findings suggest that VAs is a fully spin-polarized Weyl semimetal with many-body correlated effects in the effective U values range from 1.5 eV to 2.5 eV.

Evolution of anomalous Hall effect in ferromagnetic Weyl semimetal Nb_(x)Zr_(1-x)Co_(2)Sn

Magnetic topological semimetal can host various topological non-trivial states leading to exotic novel transport properties.Here we report the systematic magneto-transport studies on the Heusler alloy Nb_(x)Zr_(1-x)Co_(2)Sn considered as a ferromagnetic(FM)Weyl semimetal.The cusp anomaly of temperature-dependent resistivity and large isotropic negative magneto-resistivity(MR)emerge around the FM transition consistent with the theoretical half-metallic predictions.The prominent anomalous Hall effect(AHE)has the same behavior with the applied field along various crystal directions.The Nb doping introduces more disorder resulting in the enhancement of the upturn for the temperature-dependent resistivity in low temperatures.With Nb doping,the AHE exhibits systemic evolution with the Fermi level lifted.At the doping level of x=0.25,the AHE mainly originates from the intrinsic contribution related to non-trivial topological Weyl states.

On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

Matlab程序在计算仿射Weyl群Φ值中的应用

Kazhdan-Lusztig多项式的首项系数在表示理论与李理论中有着非常重要的地位。 Lusztig在研究W -图的非局部有限性时引入的半线性方程组是计算Kazhdan-Lusztig多项式首项系数的重要方法。 本文给出了一个计算任意型的仿射Weyl群中Φ值的程序设计思路,并给出了一个利用Matlab程序计算A~44型仿射Weyl群中所有Φ值的例子,输出结果表明,A~44型仿射Weyl群只有291个非零且各不相同的Φ值。

Weyl定理与(R)性质的判定

利用半Fredholm算子的扰动不变性,研究有界线性算子与上三角算子矩阵的Weyl型定理。首先,给出有界线性算子同时满足Browder定理和(R_(1))性质,或者同时满足Weyl定理和(R)性质的充要条件;然后,讨论上三角算子矩阵同时满足Weyl定理和(R)性质的条件。

两端奇异的左定Sturm-Liouville问题的谱函数与Weyl函数

研究了一类特殊边界条件下两端奇异的左定Sturm-Liouville问题,建立了左定Sturm-Liouville问题的谱矩阵ρ(λ)与Weyl矩阵M(λ),并给出了谱矩阵ρ(λ)的元素与Weyl矩阵M(λ)的元素之间的关系.

弦σ模型中的Ricci流扰动和Weyl反常系数

研究d=2维时空中玻色弦σ模型,采用2种Ricci流扰动方程推导Weyl反常系数.第1种方程是引力子场Gμν\,Dilaton场Φ的双圈流方程;第2种方程是引力子场G_(μν),轴子场B_(μν)和Dilaton场Φ的单圈流方程,通过这些Ricci流方程导出引力场的扰动方程.另外,还导出Weyl反常系数β_(μν)^(G),β_(μν)^(B),β^(Φ)的表达式,分析和讨论这些β函数随动量标度λ变化的物理意义.

有界线性算子和的B-Fredholm谱与B-Weyl谱

研究了对于Banach空间上的两个有界线性算子,当其乘积满足可交换有限秩扰动或可交换幂有限秩扰动时,它们和的B-Fredholm谱及B-Weyl谱与相应谱的并集之间的关系。

上三角算子矩阵的左(右)Weyl谱与Weyl谱

设Mc=A C0B∈B(X Y)为定义在Banach空间X Y上的上三角算子矩阵.讨论Mc的Weyl谱σw与左(右)Weyl谱σlw(σrw)的填洞情况,证明了:σ*(A)∪σ*(B)=σ*(Mc)∪W,其中,W是σ*(Mc)的某些洞的并,σ*∈{σw,σlw,σrw},分别找出了W的具体位置.

关于广义Douglas-Weyl喷射的一个注记

该文研究广义D ouglas-Weyl喷射.证明了一个喷射G是广义D ouglas-Weyl喷射当且仅当它的Weyl张量是二次型的.由此得到一个推论,一个芬斯勒度量是广义Douglas-Weyl度量当且仅当它的Weyl张量是二次型的.进一步,该文研究具有二次型的黎曼曲率张量的喷射,证明了一个喷射具有二次型的黎曼曲率张量当且仅当B_(j)^(i)_(kl)=0.

Enhanced and tunable Imbert–Fedorov shift based on epsilon-near-zero response of Weyl semimetal

We theoretically investigate the reflected spatial Imbert–Fedorov(IF)shift of transverse-electric(TE)-polarized beam illuminating on a bulk Weyl semimetal(WSM).The spatial IF shift is enhanced significantly at two different frequencies close to the epsilon-near-zero(ENZ)frequency,where large values of reflection coefficients|r_(pp)|/|r_(ss)|are obtained due to the ENZ response induced different rapid increasing trends of|r_(pp)|and|r_(ss)|.Particularly,the tunable ENZ effect with tilt degree of Weyl cones and Fermi energy enables the enhanced spatial IF shift at different frequencies.The enhanced spatial IF shift also shows the adjustability of WSM thickness,incident angle and Weyl node separation.Our findings provide easy and available methods to enlarge and adjust the reflected IF shift of TE-polarized light with a WSM.

Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator

One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.