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.

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.

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.

Rational design of superior catalysts from topological semimetals with nontrivial energy window

Materials featuring topological energy bands and nontrivial surface states hold significant promise in unlocking unprecedented opportunities for innovating electrocatalytic mechanism.However,it remains a challenge to realize superior topological catalysts which can carry both high catalytic activity and excellent catalytic stability.Here,we propose that a family of Ni-based binary materials hosting fantasying topological conjunct-nodalpoint state and a large nontrivial energy window(NEWD)represents an ideal choice for such superior topological catalysts in hydrogen evolution reaction.The presence of conjunct-nodal-points ensures long Fermi arcs on the surface,thereby enabling an extremely high catalytic activity.The NEWD plays a crucial role in stabilizing the high catalytic activity against external perturbations,such as strain and electron/hole injection.The roles for conjunctnodal-points and NEWD are substantiated by the observable weakening of catalytic performance during topological phase transitions,which result in the removal of the conjunct-nodal-points,NEWD and their corresponding long Fermi arcs.Our work unveils a hidden mechanism and opens a feasible route for developing superior quantum catalysts from novel topology point of view.

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topo- logical semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity nmy not be a com- pelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.

Quantum transport in topological semimetals under magnetic fields (III)

We review our most recent research on quantum transport,organizing the review according to the intensity of the magnetic field and focus mostly on topological semimetals and topological insulators.We first describe the phenomenon of quantum transport when a magnetic field is not present.We introduce the nonlinear Hall effect and its theoretical descriptions.Then,we discuss Coulomb instabilities in 3D higher-order topological insulators.Next,we pay close attention to the surface states and find a function to identify the axion insulator in the antiferromagnetic topological insulator MnBi2Te4.Under weak magnetic fields,we focus on the decaying Majorana oscillations which has the correlation with spin−orbit coupling.In the section on strong magnetic fields,we study the helical edge states and the one-sided hinge states of the Fermi-arc mechanism,which are relevant to the quantum Hall effect.Under extremely large magnetic fields,we derive a theoretical explanation of the negative magnetoresistance without a chiral anomaly.Then,we show how magnetic responses can be used to detect relativistic quasiparticles.Additionally,we introduce the 3D quantum Hall effect’s charge-density wave mechanism and compare it with the theory of 3D transitions between metal and insulator driven by magnetic fields.

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.

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.

First-Principles Calculation of the Topological Nodal-Line Semimetal FeGe_(2)

The electronic and topological properties of FeGe2 with a tetragonal crystal structure were investigated via first-principles calculations.The results demonstrate that FeGe2 in this structure exhibits anti-ferromagnetism,with two bands crossing the Fermi level nesting each other at high-symmetry points in the Brillouin zone,forming a nodal ring where the nodes intersect in momentum space.Additionally,it possesses nontrivial topological surface states.Upon inclusion of SOC(spin-orbit coupling),there are no significant changes observed in the band structure,nodal features,or surface states,indicating the persistence of its topological nodal-line characteristics.

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.

Topological Nodal Line Semimetal in Non-Centrosymmetric PbTaS2

Topological semimetals are a new type of matter with one-dimensional Fermi lines or zero-dimensional Weyl or Dirac points in momentum space. Here using first-principles calculations, we find that the non-centrosymmetric PbTaS2 is a topological nodal line semimetal. In the absence of spin-orbit coupling （SOC）, one band inversion happens around a high symmetrical H point, which leads to forming a nodal line. The nodal line is robust and protected against gap opening by mirror reflection symmetry even with the inclusion of strong SOC. In addition, it also hosts exotic drumhead surface states either inside or outside the projected nodal ring depending on surface termination. The robust bulk nodal lines and drumhead-like surface states with SOC in PbTaS2 make it a potential candidate material for exploring the freakish properties of the topological nodal line fermions in condensed matter systems.

Topological transport in Dirac electronic systems： A concise review

Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters pro- tected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase and Berry curvature, which provide precise definitions of the topological phases. In this topical review, transport properties of topological insulator （Bi2Se3）, topological Dirac semimetal （Cd3As2）, and topological insulator-graphene heterojunc- tion are presented and discussed. Perspectives about transport properties of two-dimensional topological nontrivial systems, including topological edge transport, topological valley transport, and topological Weyl semimetals, are provided.

High-resolution angle-resolved photoemission study of large magnetoresistance topological semimetal CaAl4

Extremely large magnetoresistance(XMR)has been explored in many nonmagnetic topologically nontrivial/trivial semimetals,while it is experimentally ambiguous which mechanism should be responsible in a specific material due to the complex electronic structures.In this paper,the magnetoresistance origin of single crystal CaAl4 with C2/m structure at low temperature is investigated,exhibiting unsaturated magnetoresistance of~3000%at 2.5 K and 14 T as the fingerprints of XMR materials.By the combination of ARPES and the first-principles calculations,we elaborate multiband features and anisotropic Fermi surfaces,which can explain the mismatch of isotropic two-band model.Although the structural phase transition from I4/mmm to C2/m has been recognized,the subtle impact on electronic structure is revealed by our ARPES measurements.Considering that both charge compensation and potential topologically nontrivial band structure exist in CaAl4,our findings report CaAl4 as a new reference material for exploring the XMR phenomena.

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.

Topological nodal line semimetals predicted from first-principles calculations

Topological semimetals are newly discovered states of quantum matter, which have extended the con- cept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimet- als, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin-orbit coupling （SOC） or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay-Terrones crystal （MTC）, anti-perovskite Cu3PdN, pressed black phosphorus, and the CaP3 family of materials, and we present the design principles for obtaining such novel states of matter.

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.

Nonlinear current response and electric quantum oscillations in the Dirac semimetal Cd_(3)As_(2)

Chiral anomaly is a distinct quantum anomaly associated with chiral fermions in Dirac or Weyl semimetals.The use of negative magnetoresistance(negative MR)as a signature for this anomaly remains contentious,as trivial mechanisms such as current jetting and weak localization can also induce negative MR.In this study,we report a novel nonlinear behavior of the chiral anomaly in the longitudinal direction,which we observed by applying parallel current and magnetic field to the Dirac semimetal Cd_(3)A_(s_(2)).This nonlinear characteristic peaks at an intermediate magnetic field of approximately5 T,displaying a resistance-increasing property concomitant with strengthening of the current source.Through angledependence experiments,we were able to rule out trivial factors,such as thermal effects,geometric artifacts,and anisotropy.Furthermore,additional electric quantum oscillations were observed when the direct current(DC)was applied as high as300μA.Such an unusual phenomenon is ascribed to the formation of quantized levels due to Bloch oscillation in the high DC regime,suggesting that an oscillatory density distribution may arise as the electric field increases.The non-Ohmic electric quantum oscillations open a new avenue for exploring chiral anomaly and other nontrivial topological properties,which is also one of the salient features of nonequilibrium steady states in condensed matter physics.

Memristive switching in the surface of a charge-density-wave topological semimetal

Owing to the outstanding properties provided by nontrivial band topology,topological phases of matter are considered as a promising platform towards low-dissipation electronics,efficient spin-charge conversion,and topological quantum computation.Achieving ferroelectricity in topological materials enables the non-volatile control of the quantum states,which could greatly facilitate topological electronic research.However,ferroelectricity is generally incompatible with systems featuring metallicity due to the screening effect of free carriers.In this study,we report the observation of memristive switching based on the ferroelectric surface state of a topological semimetal(TaSe_(4))2I.We find that the surface state of(TaSe_(4))2I presents out-of-plane ferroelectric polarization due to surface reconstruction.With the combination of ferroelectric surface and charge-density-wave-gapped bulk states,an electric-switchable barrier height can be achieved in(TaSe_(4))2I-metal contact.By employing a multi-terminal-grounding design,we manage to construct a prototype ferroelectric memristor based on(TaSe_(4))2I with on/off ratio up to 103,endurance over 103 cycles,and good retention characteristics.The origin of the ferroelectric surface state is further investigated by first-principles calculations,which reveal an interplay between ferroelectricity and band topology.The emergence of ferroelectricity in(TaSe_(4))2I not only demonstrates it as a rare but essential case of ferroelectric topological materials,but also opens new routes towards the implementation of topological materials in functional electronic devices.

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.

Predication of topological states in the allotropes of group-IV elements

Three-dimensional(3D)topological insulators(TIs)have been studied for approximately fifteen years,but those made from group-IV elements,especially Ge and Sn,seem particularly attractive owing to their nontoxicity,sizable intrinsic spin–orbit coupling(SOC)strength and natural compatibility with the current semiconductor industry.However,group-IV elemental TIs have rarely been reported,except for the low temperature phase ofα-Sn under strain.Here,based on first-principles calculations,we propose new allotropes of Ge and Sn,named T5-Ge/Sn,as desirable TIs.These new allotropes are also highly anisotropic Dirac semimetals if the SOC is turned off.To the best of our knowledge,T5-Ge/Sn are the first 3D allotropes of Ge/Sn that possess topological states in their equilibrium states at room temperature.Additionally,their isostructures of C and Si are metastable indirect and direct semiconductors.Our work not only reveals two promising TIs,but more profoundly,we justify the advantages of group-IV elements as topological quantum materials(TQMs)for fundamental research and potential practical applications,and thus reveal a new direction in the search for desirable TQMs.