Nonlinear effects in topological materials

Materials,where charge carriers have a linear energy dispersion,usually exhibit a strong nonlinear optical response in the absence of disorder scattering.This nonlinear response is particularly interesting in the terahertz frequency region.We present a theoretical and numerical investigation of charge transport and nonlinear effects,such as the high harmonic generation in topological materials including Weyl semimetals(WSMs)and α-T_(3)systems.The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix.We show that the nonlinear response is strongly dependent on temperature and topological parameters,such as the Weyl point(WP)separation b and Berry phase ФB.A finite spectral gap opening can further modify the nonlinear effects.Under certain parameters,universal behaviors of both the linear and nonlinear response can be observed.Coupled with experimentally accessible critical field values of 10^(4)-10^(5) V=m,our results provide useful information on developing nonlinear optoelectronic devices based on topological materials.

Structural phase transition and transport properties in topological material candidate NaZn_(4)As_(3)

We report a comprehensive study on a layered-structure compound of NaZn_(4)As_(3),which has been predicted to be an ideal topological semimetal(TSM) candidate.It is found that NaZn_(4)As_(3) undergoes a structural transformation from high temperature rhombohedral to a low temperature monoclinic phase.The electric resistivity exhibits a metal-to-insulatorlike transition at around 100 K,and then develops a plateau at low temperature,which might be related to the protected topologically conducting surface states.Our first-principles calculation confirms further that NaZn_(4)As_(3) is a topological insulator(TI) for both different phases rather than a previously proposed TSM.The Hall resistivity reveals that the hole carriers dominate the transport properties for the whole temperature range investigated.Furthermore,an obvious kink possibly associated to the structure transition has been detected in thermopower around ~ 170 K.The large thermopower and moderate κ indicate that NaZn_(4)As_(3) and/or its derivatives can provide a good platform for optimizing and studying the thermoelectric performance.

Doping tuned anomalous Hall effect in the van der Waals magnetic topological phases Mn(Sb_(1-x)Bi_(x))_(4)Te_(7)

The van der Waals(vdW)MnSb4Te7is a newly synthesized antiferromagnetic(AFM)topological insulator hosting a robust axion insulator state irrelative to the specific spin structure.However,the intrinsic hole doped character of MnSb_4Te_7makes the Fermi level far away from the Dirac point of about 180 meV,which is unfavorable for the exploration of exotic topological properties such as the quantum anomalous Hall effect(QAHE).To shift up the Fermi level close to the Dirac point,the strategy of partially replacing Sb with Bi as Mn(Sb_(1-x)Bi_(x))_(4)Te_(7)was tried and the magnetotransport properties,in particular,the anomalous Hall effect,were measured and analyzed.Through the electron doping,the anomalous Hall conductanceσAH changes from negative to positive between x=0.3 and 0.5,indicative of a possible topological transition.Besides,a charge neutrality point(CNP)also appears between x=0.6 and 0.7.The results would be instructive for further understanding the interplay between nontrivial topological states and the magnetism,as well as for the exploration of exotic topological properties.

Configurable topological beam splitting via antichiral gyromagnetic photonic crystal

Antichiral gyromagnetic photonic crystal(GPC)in a honeycomb lattice with the two interpenetrating triangular sublattices A and B magnetically biased in opposite directions can realize antichiral one-way edge states propagating along the same direction at its two parallel edges.Here,we report the construction and observation of topological beam splitting with the easily adjustable right-to-left ratio in an antichiral GPC.The splitter is compact and configurable,has high trans-mission efficiency,and allows for multi-channel utilization,crosstalk-proof,and robust against defects and obstacles.This magnificent performance is attributed to the peculiar property that antichiral one-way edge states exist only at zigzag edge but not at armchair edge of antichiral GPC.When we combine two rectangular antichiral GPCs holding left-and right-propagating antichiral one-way edge states respectively,bidirectionally radiating one-way edge states at two paral-lel zigzag edges can be achieved.Our observations can enrich the understanding of fundamental physics and expand to-pological photonic applications.

A Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Lattice

Here the notion of geometric phase acquired by an electron in a one-dimensional periodic lattice as it traverses the Bloch band is carefully studied. Such a geometric phase is useful in characterizing the topological properties and the electric polarization of the periodic system. An expression for this geometric phase was first provided by Zak, in a celebrated work three decades ago. Unfortunately, Zak’s expression suffers from two shortcomings: its value depends upon the choice of origin of the unit cell, and is gauge dependent. Upon careful investigation of the time evolution of the system, here we find that the system displays cyclicity in a generalized sense wherein the physical observables return in the course of evolution, rather than the density matrix. Recognition of this generalized cyclicity paves the way for a correct and consistent expression for the geometric phase in this system, christened as Pancharatnam-Zak phase. Pancharatnam-Zak geometric phase does not suffer from the shortcomings of Zak’s expression, and correctly classifies the Bloch bands of the lattice. A naturally filled band extension of the Pancharatnam-Zak phase is also constructed and studied.

Multiple surface states,nontrivial band topology,and antiferromagnetism in GdAuAl_(4)Ge_(2)

Magnetic topological states of matter provide a fertile playground for emerging topological physics and phenomena.The current main focus is on materials whose magnetism stems from 3d magnetic transition elements,e.g.,MnBi_(2)Te_(4),Fe_(3)Sn_(2),and Co_(3)Sn_(2)S_(2).In contrast,topological materials with the magnetism from rare earth elements remain largely unexplored.Here we report rare earth antiferromagnet GdAuAl_(4)Ge_(2)as a candidate magnetic topological metal.Angle resolved photoemission spectroscopy(ARPES)and first-principles calculations have revealed multiple bulk bands crossing the Fermi level and pairs of low energy surface states.According to the parity and Wannier charge center analyses,these bulk bands possess nontrivial Z2 topology,establishing a strong topological insulator state in the nonmagnetic phase.Furthermore,the surface band pairs exhibit strong termination dependence which provides insight into their origin.Our results suggest GdAuAl_(4)Ge_(2)as a rare earth platform to explore the interplay between band topology,magnetism and f electron correlation,calling for further study targeting on its magnetic structure,magnetic topology state,transport behavior,and microscopic properties.

Families of magnetic semiconductors——an overview

The interplay of magnetic and semiconducting properties has been in the focus for more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magnetic semiconductor families, including europium chalcogenides, chromium spinels, dilute magnetic semiconductors, dilute ferromagnetic semiconductors and insulators, mentioning also sources of non-uniformities in the magnetization distribution, accounting for an apparent high Curie temperature ferromagnetism in many systems. Our survey is carried out from today's perspective of ferromagnetic and antiferromagnetic spintronics as well as of the emerging fields of magnetic topological materials and atomically thin 2D layers.

Design considerations for re-functionalizing electrocatalytic materials

Electrocatalytic materials are a critical bottleneck for the development of new energy economics.This review summarizes the unique physicochemical properties of topological,magnetic,and rare earth materials and their applications in the functionalization of electrocatalysts.Topological materials have unique band structures and geometric structures,and the interface difference in charge transport structures can give rise to topological insulators,topological superconductors,and Dirac metals.Magnetic materials possess distinctive electron spin-splitting configurations,and varying spin strengths induce disparate impacts on the intermediate equilibrium adsorption capability.Rare earth materials have unique f-electron roaming properties,broad atomic radius,and f-orbital configurations,which typically confer notable advantages in oxygen reduction reactions.Furthermore,the catalytic performance exhibits significant differences under an external alternating electric,thermal,and magnetic field.These new materials show great potential in the re-functionalization of electrocatalytic materials and are expected to lead the development of the next generation of emerging energy materials.

Helicity‐dependent THz emission induced by ultrafast spin photocurrent in nodal‐line semimetal candidate Mg3Bi2

Helicity-dependent ultrafast spin current generated by circularly polarized photons in topological materials holds the crux to many technological improvements,such as quantum communications,on-chip communication processing and storage.Here,we present the manipulation of helicity-dependent terahertz emission generated in a nodal line semimetal candidate Mg3Bi2 by using photon polarization states.The terahertz emission is mainly ascribed to the helicity-dependent photocurrent that is originated from circular photogalvanic effects,and the helicity-independent photocurrent that is attributed to linear photogalvanic effect.Our work will inspire more explorations into novel nodal line semimetals and open up new opportunities for developing ultrafast optoelectronics in the topological system.

Large linear magnetoresistance in a new Dirac material BaMnBi_2

Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles.Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials.In this paper,we report the synthesis of high quality single crystals of BaMnBi;and investigate the transport properties of the samples.BaMnBi;is a metal with an antiferromagnetic transition at T;= 288 K.The temperature dependence of magnetization displays different behavior from CaMnBi;and SrMnBi;,which suggests the possible different magnetic structure of BaMnBi;.The Hall data reveals electron-type carriers and a mobility μ（5K）= 1500 cm;/V·s.Angle-dependent magnetoresistance reveals the quasi-two-dimensional（2D） Fermi surface in BaMnBi;- A crossover from semiclassical MR;dependence in low field to MR;dependence in high field,which is attributed to the quantum limit of Dirac fermions,has been observed in magnetoresistance.Our results indicate the existence of Dirac fermions in BaMnBi;.

Exotic electronic states in the world of flat bands:From theory to material

It has long been noticed that special lattices contain single-electron flat bands （FB） without any dispersion. Since the kinetic energy of electrons is quenched in the FB, this highly degenerate energy level becomes an ideal platform to achieve strongly correlated electronic states, such as magnetism, superconductivity, and Wigner crystal. Recently, the FB has attracted increasing interest because of the possibility to go beyond the conventional symmetry-breaking phases towards topologically ordered phases, such as lattice versions of fractional quantum Hall states. This article reviews different aspects of FBs in a nutshell. Starting from the standard band theory, we aim to bridge the frontier of FBs with the textbook solid- state physics. Then, based on concrete examples, we show the common origin of FBs in terms of destructive interference, and discuss various many-body phases associated with such a singular band structure. In the end, we demonstrate real FBs in quantum frustrated materials and organometallic frameworks.

Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization

Converting ambient vibration energy into electrical energy by using piezoelectric energy harvester has attracted a lot of interest in the past few years.In this paper,a topology optimization based method is applied to simultaneously determine the optimal layout of the piezoelectric energy harvesting devices and the optimal position of the mass loading.The objective function is to maximize the energy harvesting performance over a range of vibration frequencies.Pseudo excitation method （PEM） is adopted to analyze structural stationary random responses,and sensitivity analysis is then performed by using the adjoint method.Numerical examples are presented to demonstrate the validity of the proposed approach.

Unusual electronic structure of Dirac material BaMnSb_(2) revealed by angle-resolved photoemission spectroscopy

High resolution angle resolved photoemission measurements and band structure calculations are carried out to study the electronic structure of BaMnSb_(2). All the observed bands are nearly linear that extend to a wide energy range. The measured Fermi surface mainly consists of one hole pocket around Γ and a strong spot at Y which are formed from the crossing points of the linear bands. The measured electronic structure of BaMnSb_(2) is unusual and deviates strongly from the band structure calculations. These results will stimulate further efforts to theoretically understand the electronic structure of BaMnSb_(2) and search for novel properties in this Dirac material.

Advances in bismuth-based topological quantum materials by scanning tunneling microscopy

In recent years,topological quantum materials(TQMs)have attracted intensive attention in the area of condensed matter physics due to their novel topologies and their promising applications in quantum computing,spin electronics and next-generation integrated circuits.Scanning tunneling microscopy/spectroscopy(STM/STS)is regarded as a powerful technique to characterize the local density of states with atomic resolution,which is ideally suited to the measurement of the bulk-boundary correspondence of TQMs.In this review,using STM/STS,we focus on recent research on bismuth-based TQMs,including quantum-spin Hall insulators,3D weak topological insulators(TIs),high-order TIs,topological Dirac semi-metals and dual TIs.Efficient methods for the modulation of the topological properties of the TQMs are introduced,such as interlayer interaction,thickness variation and local electric field perturbation.Finally,the challenges and prospects for this field of study are discussed.

Anisotropic interfacial superconductivity induced at point contacts on topological semimetal grey arsenic

The origin of superconductivity observed at the point contact between the normal metal tip and the topological material remains uncertain due to the potential presence of superconducting elements or allotropes impurities.It is imperative to seek out a topological material entirely free of superconducting impurities and induce superconductivity between it and normal tips to verify the source of the induced superconductivity.Here,we report the observation of superconductivity up to 9 K induced at point contacts between normal metal tips and the topological material grey arsenic,which is free of superconductivity.The determined temperature dependencies of superconducting gapsΔ(T)deviate from the Bardeen-Cooper-Schriefer(BCS)superconductivity law,exhibiting abnormal behavior.Furthermore,the highly anisotropic upper critical field H_(c2)(T)suggests the anisotropy of the projected interfacial Fermi surface.By tuning the junction resistance,we obtained a negative correlation between the superconducting gapΔand the efective barrier height Z,which validates the interfacial coupling strength as a key factor in the observed tip-induced superconductivity.These experimental results provide guidance for the relevant theory about tip-induced superconductivity on topological materials.

Topology optimization of compliant adaptive wing leading edge with composite materials

An approach for designing the compliant adaptive wing leading edge with composite material is proposed based on the topology optimization. Firstly, an equivalent constitutive relationship of laminated glass fiber reinforced epoxy composite plates has been built based on the symmetric laminated plate theory. Then, an optimization objective function of compliant adaptive wing leading edge was used to minimize the least square error（LSE） between deformed curve and desired aerodynamics shape. After that, the topology structures of wing leading edge of different glass fiber ply-orientations were obtained by using the solid isotropic material with penalization（SIMP） model and sensitivity filtering technique. The desired aerodynamics shape of compliant adaptive wing leading edge was obtained based on the proposed approach. The topology structures of wing leading edge depend on the glass fiber ply-orientation. Finally, the corresponding morphing experiment of compliant wing leading edge with composite materials was implemented, which verified the morphing capability of topology structure and illustrated the feasibility for designing compliant wing leading edge. The present paper lays the basis of ply-orientation optimization for compliant adaptive wing leading edge in unmanned aerial vehicle（UAV） field.

拓扑异质结(PbSe)_(5)(Bi_(2)Se_(3))_(6)高压诱导超导电性研究

最近,天然异质结(PbSe)_(5)(Bi_(2)Se_(3))_(6)在理论上预测并实验证实为拓扑绝缘体.本文通过高压原位量子调控在(PbSe)_(5)(Bi_(2)Se_(3))_(6)中成功引入超导电性.当压力增加到10 GPa时,超导电性突然出现,T_(c)约为4.6 K,随后T_(c)急剧下降.值得注意的是,当进一步施加压力到30 GPa以上时,出现了一种新的超导态,且T_(c)直到本实验最高压力仍未饱和.结合XRD和拉曼光谱,我们认为(PbSe)_(5)(Bi_(2)Se_(3))_(6)中两个超导态的出现与压力诱导的结构相变有关.拓扑异质结压力下出现新的量子态,为进一步研究拓扑和超导的关系提供了一个良好的平台.

Anisotropic magnetoelastic response in the magnetic Weyl semimetal Co_(3)Sn_(2)S_(2)

Co_(3)Sn_(2)S_(2) is a recently identified magnetic Weyl semimetal in Shandite compounds. Upon cooling, Co_(3)Sn_(2)S_(2) undergoes a ferromagnetic transition with c-axis polarized moments(0.3 μ_(B)/Co) around T_(C)= 175 K, followed by another magnetic anomaly around T_(A)≈ 140 K. A large intrinsic anomalous Hall effect is observed in the magnetic state below TC with a maximum of anomalous Hall angle near T_(A). Here, we report an elastic neutron scattering on the crystalline lattice of Co_(3)Sn_(2)S_(2) in a magnetic field up to 10 T. A strongly anisotropic magnetoelastic response is observed, while only a slight enhancement of the Bragg peaks is observed when B//c. The in-plane magnetic field(B//ab) dramatically suppresses the Bragg peak intensity probably by tilting the moments and lattice toward the external field direction. The in-plane magnetoelastic response commences from T_(C), and as it is further strengthened below T_(A), it becomes nonmonotonic against the field between T_(A) and T_(C) because of the competition from another in-plane magnetic order. These results suggest that a magnetic field can be employed to tune the Co_(3)Sn_(2)S_(2) lattice and its related topological states.

自旋输运揭示高阶棱态的拓扑性质

根据高阶拓扑相理论,在三维高阶拓扑材料中,除了常见的三维体态和二维表面态,还存在一维无能隙的拓扑棱态.由于很难通过传统的实验手段(如光谱和量子振荡测量)对一维电子态进行探测,到目前为止,人们对于棱态的拓扑性质仍然知之甚少.本文通过自旋电位测量的手段,揭示了高阶拓扑半金属Cd;As;纳米片中棱态的拓扑特性.实验发现,高阶棱态具有和量子自旋霍尔态类似的电子螺旋性特征,即棱态电子的自旋和动量是相互锁定的.棱态自旋极化信号能稳定维持到室温条件,且可以实现长距离的非局域传输,传输距离超过5μm.棱态自旋信号的温度鲁棒性和长程非局域传输特性,表明棱态由于受拓扑保护具备较强的抗环境干扰能力.该工作不但深化了人们对于高阶拓扑材料输运性质的理解,而且也为实现低功耗自旋电子学器件提供了重要的材料平台.

Spin excitations and spin wave gap in the ferromagnetic Weyl semimetal Co3Sn2S2

We report a comprehensive neutron scattering study on the spin excitations in the magnetic Weyl semimetal Co3Sn2S2 with a quasi-two-dimensional structure.Both in-plane and out-of-plane dispersions of the spin waves were revealed in the ferromagnetic state.Similarly,dispersive but damped spin excitations were found in the paramagnetic state.The effective exchange interactions were estimated using a semi-classical Heisenberg model to consistently reproduce the experimental TCand spin stiffness.However,a full spin wave gap below Eg=2.3 meV was observed at T=4 K.This value was considerably larger than the estimated magnetic anisotropy energy(~0.6 meV),and its temperature dependence indicated a significant contribution from the Weyl fermions.These results suggest that Co3Sn2S2 is a three-dimensional correlated system with a large spin stiffness,and the low-energy spin dynamics can interplay with the topological electron states.