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.

Density-wave tendency from a topological nodal-line perspective

The understanding of density waves is a vital component of our insight into electronic quantum matters. Here, we propose an additional mosaic to the existing mechanisms such as Fermi-surface nesting, electron–phonon coupling, and exciton condensation. In particular, we find that certain two-dimensional(2D) spin density-wave systems are equivalent to three-dimensional(3D) Dirac nodal-line systems in the presence of a magnetic field, whose electronic structure takes the form of Dirac-fermion Landau levels and allows a straightforward analysis of its optimal filling. The subsequent minimumenergy wave vector varies over a continuous range and shows no direct connection to the original Fermi surfaces in 2D.Also, we carry out numerical calculations where the results on model examples support our theory. Our study points out that we have yet to attain a complete understanding of the emergent density wave formalism.

Enhanced and controllable reflected group delay based on Tamm surface plasmons with Dirac semimetals

The reflected group delay from a multilayer structure comprising a one-dimensional photonic crystal coated with a bulk Dirac semimetal(BDS)separated by a spacer layer is investigated theoretically.It is shown that the group delay of the reflected beam in this structure can be significantly negatively enhanced and switched from negative to positive.The enhanced group delay originates from the steep phase change caused by the excitation of the optical Tamm state at the interface between the BDS and spacer layer.Moreover,positive and negative group delays can be actively tuned through the Fermi energy and the relaxation time of the BDS.We believe that this enhanced and tunable delay scheme has important research significance for the fabrication of optical delay devices.

Controllable optical bistability in a Fabry-Pérot cavity with a nonlinear three-dimensional Dirac semimetal

Optical bistability(OB)is capable of rapidly and reversibly transforming a parameter of an optical signal from one state to another,and homologous nonlinear optical bistable devices are core components of high-speed all-optical communication and all-optical networks.In this paper,we theoretically investigated the controllable OB from a Fabry-Pérot(FP)cavity with a nonlinear three-dimensional Dirac semimetal(3D DSM)in the terahertz band.The OB stems from the third-order nonlinear bulk conductivity of the 3D DSM and the resonance mode has a positive effect on the generation of OB.This FP cavity structure is able to tune the OB because the transmittance and the reflectance can be modulated by the Fermi energy of the 3D DSM.We believe that this FP cavity configuration could provide a reference concept for realizing tunable bistable devices.

Negative magnetoresistance in the antiferromagnetic semimetal V_(1/3)TaS_(2)

Intercalated transition metal dichalcogenides(TMDCs)attract much attention due to their rich properties and potential applications.In this article,we grew successfully high-quality V_(1/3)TaS_(2) crystals by a vapor transport method.We measured the magnetization,longitudinal resistivityρxx(T,H),Hall resistivityρxy(T,H),as well as performed calculations of the electronic band structure.It was found that V_(1/3)TaS_(2) is an A-type antiferromagnet with the Neel temperature T_(N)=6.20 K,and exhibits a negative magnetoresistance(MR)near T_(N).Both band structure calculations and Hall resistivity measurements demonstrated it is a magnetic semimetal.

Electric modulation of the Fermi arc spin transport via three-terminal configuration in topological semimetal nanowires

Spin–momentum locking is a key feature of the topological surface state, which plays an important role in spintronics.The electrical detection of current-induced spin polarization protected by the spin–momentum locking in nonmagnetic systems provides a new platform for developing spintronics, while previous studies were mostly based on magnetic materials.In this study, the spin transport measurement of Dirac semimetal Cd_(3)As_(2) was studied by three-terminal geometry, and a hysteresis loop signal with high resistance and low resistance state was observed. The hysteresis was reversed by reversing the current direction, which illustrates the spin–momentum locking feature of Cd_(3)As_(2). Furthermore, we realized the on–off states of the spin signals through electric modulation of the Fermi arc via the three-terminal configuration, which enables the great potential of Cd_(3)As_(2) in spin field-effect transistors.

Saturable absorption and visible pulse modulation of few-layer topological nodal-line semimetal HfGeTe

Topological nodal-line semimetals attract growing research attention in the photonic and optoelectronic fields due to their unique topological energy-level bands and fascinating nonlinear optical responses.Here,to the best of our knowledge,we first report the saturable absorption property of topological nodal-line semimetal HfGeTe and the related pulse modulation in passively Q-switched visible lasers.Few-layer HfGeTe demonstrates outstanding saturable absorption properties in the visible-light band,yielding the saturation intensities of 7.88,12.66,and 6.64μJ/cm^(2)at 515,640,and 720 nm,respectively.Based on an as-prepared few-layer HfGeTe optical switch and a Pr:LiYF_(4)gain medium,Q-switched visible lasers are also successfully achieved at 522,640,and 720 nm.The minimum pulse widths of the green,red,and deep-red pulsed lasers are150,125.5,and 420 ns,respectively.Especially for the green and red pulsed laser,the obtained pulse width is smaller than those of the low-dimensional layered materials.Our work sheds light on the application potential of topological nodal-line semimetals in the generation of visible pulsed lasers.

Two-dimensional tetragonal ZnB: A nodalline semimetal with good transport properties

Nodal-line semimetals have become a research hot-spot due to their novel properties and great potential application in spin electronics. It is more challenging to find 2D nodal-line semimetals that can resist the spin–orbit coupling(SOC)effect. Here, we predict that 2D tetragonal Zn B is a nodal-line semimetal with great transport properties. There are two crossing bands centered on the S point at the Fermi surface without SOC, which are mainly composed of the pxy orbitals of Zn and B atoms and the pz orbitals of the B atom. Therefore, the system presents a nodal line centered on the S point in its Brillouin zone(BZ). And the nodal line is protected by the horizontal mirror symmetry M_(z). We further examine the robustness of a nodal line under biaxial strain by applying up to-4% in-plane compressive strain and 5% tensile strain on the Zn B monolayer, respectively. The transmission along the a direction is significantly stronger than that along the b direction in the conductive channel. The current in the a direction is as high as 26.63 μA at 0.8 V, and that in the b direction reaches 8.68 μA at 0.8 V. It is interesting that the transport characteristics of Zn B show the negative differential resistance(NDR) effect after 0.8 V along the a(b) direction. The results provide an ideal platform for research of fundamental physics of 2D nodal-line fermions and nanoscale spintronics, as well as the design of new quantum devices.

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.

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice

Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional （3D） Weyl semimetals, 3D Dirac semimetMs, and 3D node-line semimetals （NLSs）. In particular, several compounds （e.g., certain 3D graphene networks, Cu3PdN, Ca3P2 ） were discovered to be 3D NLSs, in which the conduction and valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional （2D） Dirac semimetal （e.g., graphene）, 2D topological semimetals are much less investigated. Here we propose a new concept of a 2D NLS and suggest that this state could be realized in a new mixed lattice （named as HK lattice） composed by Kagome and honeycomb lattices. It is found that A3B2 （A is a group-liB cation and B is a group-VA anion） compounds （such as Hg3As2） with the HK lattice are 2D NLSs due to the band inversion between the cation Hg-s orbital and the anion As-pz orbital with respect to the mirror symmetry. Since the band inversion occurs between two bands with the same parity, this peculiar 2D NLS could be used as transparent conductors. In the presence of buckling or spin-orbit coupling, the 2D NLS state may turn into a 2D Dirac semimetal state or a 2D topological crystalline insulating state. Since the band gap opening due to buckling or spin-orbit coupling is small, Hg3As3 with the HK lattice can still be regarded as a 2D NLS at room temperature. Our work suggests a new route to design topological materials without involving states with opposite parities.

Quantum critical duality in two-dimensional Dirac semimetals

Quantum criticality is closely related to the existence of two phases with unrelated symmetry breaking. In this paper,we study Néel and Kekulé valence bond state(VBS) quantum criticality in Dirac semimetals with four-fermion interactions.Our results show that all possible dynamical masses yield the same critical coupling, which exhibits the phenomenon that all possible phases meet at a multicritical point(e.g., a tricritical point for the Néel, Kekulé-VBS and semimetallic phases).In terms of the well-established Wess–Zumino–Witten field theory, we investigate the typical criticality for the transition between Néel and Kekulé-VBS phases, and the compatible Néel–Kekulé-VBS mass matrices imply the existence of a nonLandau transition between the Néel and Kekulé-VBS phases. We show the existence of mutual duality in the defect-driven Néel–Kekulé-VBS transition near the non-Landau critical point and find that this mutual duality results from the presence of a mutual Chern–Simons term. We also study the mutual duality based on dual topological excitations.

Magnetic impurity in hybrid and type-Ⅱ nodal line semimetals

We study the Kondo screening of a spin-1/2 magnetic impurity in the hybrid nodal line semimetals(NLSMs) and the type-Ⅱ NLSMs by using the variational method. We mainly study the binding energy and the spin–spin correlation between magnetic impurity and conduction electrons. We find that in both the hybrid and type-Ⅱ cases, the density of states(DOS) is always finite, so the impurity and the conduction electrons always form bound states, and the bound state is more easily formed when the DOS is large. Meanwhile, due to the unique dispersion relation and the spin–orbit couplings in the NLSMs, the spatial spin–spin correlation components show very interesting features. Most saliently, various components of the spatial spin–spin correlation function decay with 1/r^(2) in the hybrid NLSMs, while they follow 1/r^(3) decay in the type-Ⅱ NLSMs. This property is mainly caused by the special band structures in the NLSMs, and it can work as a fingerprint to distinguish the two types of NLSMs.

High-pressure study of topological semimetals XCd_(2)Sb_(2)(X=Eu and Yb)

Topological materials have aroused great interest in recent years,especially when magnetism is involved.Pressure can effectively tune the topological states and possibly induce superconductivity.Here we report the high-pressure study of topological semimetals XCd_(2)Sb_(2)(X=Eu and Yb),which have the same crystal structure.In antiferromagnetic(AFM)Weyl semimetal EuCd_(2)Sb_(2),the Néel temperature(TN)increases from 7.4 K at ambient pressure to 50.9 K at 14.9 GPa.When pressure is above 14.9 GPa,the AFM peak of resistance disappears,indicating a non-magnetic state.In paramagnetic Dirac semimetal candidate YbCd_(2)Sb_(2),pressure-induced superconductivity appears at 1.94 GPa,then Tc reaches to a maximum of 1.67 K at 5.22 GPa and drops to zero at about 30 GPa,displaying a dome-shaped temperature–pressure phase diagram.High-pressure x-ray diffraction measurement demonstrates that a crystalline-to-amorphous phase transition occurs at about 16 GPa in YbCd_(2)Sb_(2),revealing the robustness of pressure-induced superconductivity against structural instability.Similar structural phase transition may also occur in EuCd_(2)Sb_(2),causing the disappearance of magnetism.Our results show that XCd_(2)Sb_(2)(X=Eu and Yb)is a novel platform for exploring the interplay among magnetism,topology,and superconductivity.

Effect of weak disorder in multi-Weyl semimetals

We study the behaviors of three-dimensional double and triple Weyl fermions in the presence of weak random potential.By performing the Wilsonian renormalization group(RG)analysis,we reveal that the quasiparticle experiences strong renormalization which leads to the modification of the density of states and quasiparticle residue.We further utilize the RG analysis to calculate the classical conductivity and show that the diffusive transport is substantially corrected due to the novel behavior of the quasiparticle and can be directly measured by experiments.

Two-dimensional topological semimetals

The field of two-dimensional topological semimetals,which emerged at the intersection of two-dimensional materials and topological materials,has been rapidly developing in recent years.In this article,we briefly review the progress in this field.Our focus is on the basic concepts and notions,in order to convey a coherent overview of the field.Some material examples are discussed to illustrate the concepts.We discuss the outstanding problems in the field that need to be addressed in future research.

Peierls-phase-induced topological semimetals in an optical lattice:Moving of Dirac points,anisotropy of Dirac cones,and hidden symmetry protection

We propose a square optical lattice in which some of neighbor hoppings have a Peierls phase.The Peierls phase makes the lattice have a special band structure and induces the existence of Dirac points in the Brillouin zone,which means that topological semimetals exist in the system.The Dirac points move with the change of the Peierls phase and the Dirac cones are anisotropic for some vales of the Peierls phase.The lattice has a novel hidden symmetry,which is a composite antiunitary symmetry composed of a translation operation,a sublattice exchange,a complex conjugation,and a local U(1)gauge transformation.We prove that the Dirac points are protected by the hidden symmetry and perfectly explain the moving of Dirac points with the change of the Peierls phase based on the hidden symmetry protection.

High-order harmonic generations in tilted Weyl semimetals

We investigate high-order harmonic generations(HHGs)under comparison of Weyl cones in two types.Due to the hyperboloidal electron pocket structure,strong noncentrosymmetrical generations in high orders are observed around a single type-ⅡWeyl point,especially at zero frequency.Such a remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition.Under weak pulse electric field,the linear optical response of a nontilted Weyl cone is consistent with the Kubo theory.With extensive numerical simulations,we conclude that the non-zero chemical potential can enhance the even-order generations,from the slightly tilted system to the over-tilted systems.In consideration of dynamical symmetries,type-Ⅰand type-ⅡWeyl cones also show different selective responses under the circularly polarized light.Finally,using a more realistic model containing two pairs of Weyl points,we demonstrate that paired Weyl points with opposite chirality can suppress the overall even-order generations.

Broadband strong optical dichroism in topological Dirac semimetals with Fermi velocity anisotropy

Prototypical three-dimensional(3D)topological Dirac semimetals(DSMs),such as Cd3As2 and Na3Bi,contain electrons that obey a linear momentum-energy dispersion with different Fermi velocities along the three orthogonal momentum dimensions.Despite being extensively studied in recent years,the inherent Fermi velocity anisotropy has often been neglected in the theoretical and numerical studies of 3D DSMs.Although this omission does not qualitatively alter the physics of light-driven massless quasiparticles in 3D DSMs,it does quantitatively change the optical coefficients which can lead to nontrivial implications in terms of nanophotonics and plasmonics applications.Here we study the linear optical response of 3D DSMs for general Fermi velocity values along each direction.Although the signature conductivity-frequency scaling,σ(ω)∝ω,of 3D Dirac fermion is well-protected from the Fermi velocity anisotropy,the linear optical response exhibits strong linear dichroism as captured by the universal extinction ratio scaling law,Λi j=(vi/v j)^2(where i=j denotes the three spatial coordinates x,y,z,and vi is the i-direction Fermi velocity),which is independent of frequency,temperature,doping,and carrier scattering lifetime.For Cd3As2 and Na3Bi3,an exceptionally strong extinction ratio larger than 15 and covering a broad terahertz window is revealed.Our findings shed new light on the role of Fermi velocity anisotropy in the optical response of Dirac semimetals and open up novel polarization-sensitive functionalities,such as photodetection and light modulation.

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.

Negative magnetoresistance in Dirac semimetal Cd_(3)As_(2)with in-plane magnetic field perpendicular to current

Topological insulators and semimetals have exotic surface and bulk states with massless Dirac or Weyl fermions,demonstrating microscopic transport phenomenon based on relativistic theory.Chiral anomaly induced negative magnetoresistance(negative MR)under parallel magnetic field and current has been used as a probable evidence ofWeyl fermions in recent years.Here we report a novel negative MR result with mutually perpendicular in-plane magnetic field and current in Cd_(3)As_(2)nanowires.The negative MR has a considerable value of-16%around 1.5 K and could persist to room temperature of 300 K with value of-1%.The gate tuning and angle dependence of the negative MR demonstrate the mechanism of the observed negative MR is different from the chiral anomaly.Percolating current paths induced by charge puddles and disorder might be involved to produce such considerable negative MR.Our results indicate the negative MR effect in topological semimetals involves synergistic effects of many mechanisms besides chiral anomaly.