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We present the pressure dependence of the electronic and dynamical properties of six different CoGe phases with orthorhombic Cmmm, hexagonal P6/mmm and P 6 ̄ 2m, monoclinic C2/m, cubic P2 1 3, and orthorhombic Pnma symmetries. Using first-principles DFT calculations and the direct force-constants method, we study the dynamical stability of individual phases under external pressure. We show that the orthorhombic (Cmmm) and hexagonal (P6/mmm) structures are unstable over a broad pressure range and most pronounced imaginary phonon soft mode in both cases leads to a stable hexagonal (P 6 ̄ 2m) structure of the lowest ground-state energy of all studied phases at ambient and low (below ∼ 3 GPa) external pressure. Under these conditions, the cubic structure has the highest energy, however, together with monoclinic and orthorhombic phases, it is dynamically stable and all these three structures can potentially coexist as meta-stable phases. Above ∼ 3 GPa , the cubic phase becomes the most energetically favorable. Fitting the Birch–Murnaghan equation of state, we derive bulk modulus for all mentioned phases. The results indicate relatively high resistance of CoGe to compression. Such conclusions are confirmed by band structure calculations. Additionally, we show that electronic bands of the hexagonal (P 6 ̄ 2m) phase reveal characteristic features of the kagome-like structure, while in the cubic phase the electronic bands contain spin-1 and double Weyl fermions. In both cases, the external pressure induces the Lifshitz transition, related to the modification of the Fermi surface topology. [Display omitted] • The P 6 ̄ 2m phase is most energetically favored in the absence of pressure. • All investigated phases possess similar mechanical properties, while the Cmmm and P6/mmm phases are unstable in a dynamic sense. • Above approximately 3 GPa, the P2 1 3 phase has the lowest energies. • External pressure induces the Lifshitz transition for both the P 6 ̄ 2m and P2 1 3 phases. [ABSTRACT FROM AUTHOR]

[Display omitted] Based on irreducible representations (or symmetry eigenvalues) and compatibility relations (CR), a material can be predicted to be a topological/trivial insulator (satisfying CR) or a topological semimetal (violating CR). However, Weyl semimetals (WSMs) usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy CR, or if the symmetry indicators are zero. In this work, we propose a new topological invariant χ for the systems with S 4 symmetry (i.e., the improper rotation S 4 (≡ IC 4 z) is a proper fourfold rotation ( C 4 z ) followed by inversion (I)), which can be used to diagnose the WSM phase. Moreover, χ can be easily computed through the one-dimensional Wilson-loop technique. By applying this method to the high-throughput screening in our first-principles calculations, we predict a lot of WSMs in both nonmagnetic and magnetic compounds. Various interesting properties (e.g., magnetic frustration effects, superconductivity and spin-glass order, etc.) are found in predicted WSMs, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states. [ABSTRACT FROM AUTHOR]

Ternary compound HfCuP is a potential Weyl semimetal coexisting both type-I and type-II Weyl nodes. In most Weyl semimetal (WSMs), the Weyl nodes with opposite chiralities usually have the same type of band dispersions (either type-I or type-II), whereas realistic candidate materials hosting different types of Weyl nodes have not been identified to date. Here we report for the first time that, a ternary compound HfCuP, is an excellent WSM with the coexistence of type-I and type-II Weyl nodes. Our results show that, HfCuP totally contains six pairs of type-I and six pairs of type-II Weyl nodes in the Brillouin zone, all locating at the H-K path. These Weyl nodes situate slightly below the Fermi level, and do not coexist with other extraneous bands. The nontrivial band structure in HfCuP produces clear Fermi arc surface states in the (1 0 0) surface projection. Moreover, we find the Weyl nodes in HfCuP can be effectively tuned by strain engineering. These characteristics make HfCuP a potential candidate material to investigate the novel properties of type-I and type-II Weyl fermions, as well as the potential entanglements between them. [ABSTRACT FROM AUTHOR]

[Display omitted] Two-dimensional (2D) topological materials have attracted extensive attention due to the discovery of graphene. In addition, their counterparts in magnetic materials are also a fascinating subject of research. However, it remains challenging to find 2D materials that have the desired topological phases. Here, based on first-principles calculations, we investigate the properties of a newly synthesized 2D material, monolayer/bilayer (ML/BL) ZnSb. We find that the ML ZnSb is antiferromagnetic (AFM) and that its magnetism can be changed by an external strain, from AFM to ferromagnetic. Without any external strain, the ML ZnSb can be considered as an almost ideal 2D type-II Weyl material with a pair of type-II Weyl fermions exactly located at the Fermi level. When taking into account spin–orbit coupling (SOC), a gap can be introduced at the Weyl point. We further show that by applying a biaxial strain to the BL ZnSb material, it is possible to open different gaps at the Weyl points, leading to a topological phase transition without breaking symmetry. When SOC is included, these Weyl points become topological insulators with a large bandgap, where the helical edge states can be identified. Overall, this study provides an example of a material that can be used to explore the physical consequences of 2D topological phases and provide a promising candidate for future research in this field. [ABSTRACT FROM AUTHOR]

Abstract Projecting measurements of the interactions of the known Standard Model (SM) states into an effective field theory (EFT) framework is an important goal of the LHC physics program. The interpretation of measurements of the properties of the Higgs-like boson in an EFT allows one to consistently study the properties of this state, while the SM is allowed to eventually break down at higher energies. In this review, basic concepts relevant to the construction of such EFTs are reviewed pedagogically. Electroweak precision data is discussed as a historical example of some importance to illustrate critical consistency issues in interpreting experimental data in EFTs. A future precision Higgs phenomenology program can benefit from the projection of raw experimental results into consistent field theories such as the SM, the SM supplemented with higher dimensional operators (the SMEFT) or an Electroweak chiral Lagrangian with a dominantly J P = 0 + scalar (the HEFT). We discuss the developing SMEFT and HEFT approaches, that are consistent versions of such EFTs, systematically improvable with higher order corrections, and comment on the pseudo-observable approach. We review the challenges that have been overcome in developing EFT methods for LHC studies, and the challenges that remain. [ABSTRACT FROM AUTHOR]

Abstract We introduce the quantum-field-theory (QFT) derivation of chiral kinetic theory (CKT) from the Wigner-function approach, which manifests side jumps and non-scalar distribution functions associated with Lorentz covariance and incorporates both background fields and collisions. The formalism is utilized to investigate second-order responses of chiral fluids near local equilibrium. Such non-equilibrium anomalous transport is dissipative and affected by interactions. Contributions from both quantum corrections in anomalous hydrodynamic equations (EOM) of motion and those from the CKT and Wigner functions (WF) are considered in a relaxation-time approximation (RTA). Anomalous charged Hall currents engendered by background electric fields and temperature/chemical-potential gradients are obtained. Furthermore, chiral magnetic/vortical effects (CME/CVE) receive viscous corrections as non-equilibrium modifications stemming from the interplay between side jumps, magnetic-moment coupling, and chiral anomaly. [ABSTRACT FROM AUTHOR]

Abstract For a general λ -deformation of current algebra CFTs we compute the exact Weyl anomaly coefficient and the corresponding metric in the couplings space geometry. By incorporating the exact β -function found in previous works we show that the Weyl anomaly is in fact the exact Zamolodchikov's C -function interpolating between exact CFTs occurring in the UV and in the IR. We provide explicit examples with the anisotropic S U (2) case presented in detail. The anomalous dimension of the operator driving the deformation is also computed in general. Agreement is found with special cases existing already in the literature. [ABSTRACT FROM AUTHOR]

Graphical abstract Based on the cryogenic point contact system as shown in the schematic, the detection of tip-induced superconductivity (TISC) has been successfully realized in different topological materials. The observation of unconventional superconducting feature in these non-superconducting materials makes TISC a new way to investigate the topological superconductivity. Abstract Topological materials, hosting topological nontrivial electronic band, have attracted widespread attentions. As an application of topology in physics, the discovery and study of topological materials not only enrich the existing theoretical framework of physics, but also provide fertile ground for investigations on low energy excitations, such as Weyl fermions and Majorana fermions, which have not been observed yet as fundamental particles. These quasiparticles with exotic physical properties make topological materials the cutting edge of scientific research and a new favorite of high tech. As a typical example, Majorana fermions, predicted to exist in the edge state of topological superconductors, are proposed to implement topological error-tolerant quantum computers. Thus, the detection of topological superconductivity has become a frontier in condensed matter physics and materials science. Here, we review a way to detect topological superconductivity triggered by the hard point contact: tip-induced superconductivity (TISC) and tip-enhanced superconductivity (TESC). The TISC refers to the superconductivity induced by a non-superconducting tip at the point contact on non-superconducting materials. We take the elaboration of the chief experimental achievement of TISC in topological Dirac semimetal Cd 3 As 2 and Weyl semimetal TaAs as key components of this article for detecting topological superconductivity. Moreover, we also briefly introduce the main results of another exotic effect, TESC, in superconducting Au 2 Pb and Sr 2 RuO 4 single crystals, which are respectively proposed as the candidates of helical topological superconductor and chiral topological superconductor. Related results and the potential mechanism are conducive to improving the comprehension of how to induce and enhance the topological superconductivity. [ABSTRACT FROM AUTHOR]

We discuss our recent optical investigation of YbMnBi 2 , a representative type II Weyl semimetal, by considering a simple scheme for the electronic structure, which can be embedded within a recent theoretical approach for the calculation of the excitation spectrum. Our study allows us disentangling the generic optical fingerprints of Weyl fermions, which are in broad agreement with the theoretical predictions but also challenge the present understanding of their electrodynamic response. [ABSTRACT FROM AUTHOR]

We study theoretically the features of impurity-induced states on the surface of a three-dimensional Weyl semimetal in this work. For calculating the impurity-induced local density of states based on T -matrix formulation, we found that for different Weyl semimetal phases the behaviors of a local impurity exhibit distinguishable prominent features for the surface Fermi arc states. Due to two opposite-directional and -chirality surface currents for a surface, a bound state appears at the unitary limit of scattering intensity near the impurity site. Then the resonance condition for different Weyl semimetal phases and scattering intensity is investigated. Our results can be used to identify distinctive topological phases of Weyl semimetal. Furthermore, the relevance of topological nodal-point and -line systems is discussed. Some relation between our theoretical results and current experimental scheme are also discussed. [ABSTRACT FROM AUTHOR]

We propose a method of realizing an effective beam splitter for Dirac–Weyl fermions through the Goos–Hänchen-like shift. It is implemented via the birefringence of a wave packet of pseudospin-3/2 Dirac–Weyl fermions impinging upon a potential barrier. It is shown that experimentally observable spatial separation between the transmitted fermions with helicity-1/2 and 3/2 can be generated by the Goos–Hänchen-like shift. The dependence of Goos–Hänchen-like shift and the corresponding transmission probability on the incident angle, the height and width of the potential barrier are carefully studied. [ABSTRACT FROM AUTHOR]

In this research, firstly, by using the new form of Dirac-Weyl equation and the series method with submitting more suitable details, the energy spectrum and wave functions of the massless Dirac fermions are calculated under the inhomogeneous and q-deformed spatially magnetic fields. Although, we discussed about the results of the energy levels, further, we obtained the wave function as the Hessenberg determinant with calculating the elements of it as exact. On the other hand, by using the Mellin-Barnes integral representation and Hurwitz zeta function, we have achieved the thermodynamic physical quantities of the Dirac-Weyl fermions in the absence of a magnetic field for inside of the graphene quantum dot. Finally, our numerical results for the wave functions and probability densities are presented too. [ABSTRACT FROM AUTHOR]

In semimetals with time-reversal symmetry, the interplay between Weyl points and Fu–Kane–Mele indices results in coexisting surface Dirac cones and Fermi arcs that are transmutable without a topological phase transition. We show that Weyl points act as a new type of monopole, and that their connectivity is essential for capturing the full topology of semimetals and their role as intermediaries of topological insulator transitions. The history of Weyl point creation–annihilation provides a simple and mathematically equivalent way to classify semimetals, and directly prefigures the surface state topology. We further predict the possibility of a topological Dirac cone on the interface between two Weyl semimetals. [ABSTRACT FROM AUTHOR]

Weyl fermions are characterized by definite helicity, a relation between orientation of the spin and momentum. We investigate controlling helicity utilizing helicity-dependent dynamics due to separation between the Weyl points. We study transport properties of a multilayer structure formed by piece-wise constant scalar and vector potentials and separations between the Weyl points. We show that the transmission spectrum is determined by a relation between the electron momentum and momenta corresponding to Klein tunneling, when the barrier is fully transparent regardless of its width. The helicity dependence of the “Klein momenta” is shown to yield a helicity filtering effect. [ABSTRACT FROM AUTHOR]

This a pedagogical introduction to scattering amplitudes in gauge theories. It proceeds from Dirac equation and Weyl fermions to the two pivot points of current developments: the recursion relations of Britto, Cachazo, Feng and Witten, and the unitarity cut method pioneered by Bern, Dixon, Dunbar and Kosower. In ten lectures, it covers the basic elements of on-shell methods. [ABSTRACT FROM AUTHOR]

Abstract Weyl fermion is a massless Dirac fermion with definite chirality, which has been long pursued since 1929. Though it has not been observed as a fundamental particle in nature, Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal, which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal, TaAs crystal possesses 12 pairs of Weyl points in the momentum space, which are topologically protected against small perturbations. Here, we report for the first time the tip induced superconductivity on TaAs crystal by point contact spectroscopy. The zero bias conductance peak as well as a conductance plateau with double conductance peaks and sharp double dips are observed in the point contact spectra simultaneously, indicating unconventional superconductivity. Our further theoretical study suggests that the induced superconductivity may have nontrivial topology. The present work opens a new route in investigating the novel superconducting states based on Weyl materials. [ABSTRACT FROM AUTHOR]

Wide ranging interest in Dirac Hamiltonian is due to the emergence of novel materials, namely, graphene, topological insulators and superconductors, the newly-discovered Weyl semimetals, and still actively-sought after Majorana fermions in real materials. We give a brief review of the relativistic Dirac quantum mechanics and its impact in the developments of modern physics. The quantum band dynamics of Dirac Hamiltonian is crucial in resolving the giant diamagnetism of bismuth and Bi-Sb alloys. Quantitative agreement of the theory with the experiments on Bi-Sb alloys has been achieved, and physically meaningful contributions to the diamagnetism has been identified. We also treat relativistic Dirac fermion as an interband dynamics in uniform magnetic fields. For the interacting Bloch electrons, the role of translation symmetry for calculating the magnetic susceptibility avoids any approximation to second order in the field. The expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results. The unified treatment of all the above calculations is based on the lattice Weyl-Wigner formulation of discrete phase-space quantum mechanics. For completeness, the magnetic susceptibility of Kondo alloys is also given since Dirac fermions in conduction band and magnetic impurities exhibit Kondo effect. [ABSTRACT FROM AUTHOR]

The chiral magnetic effect (CME) is the generation of electrical current induced by chirality imbalance in the presence of magnetic field. It is a macroscopic manifestation of the quantum chiral anomaly [S. L. Adler. Axial-vector vertex in spinor electrodynamics . Physical Review, 177, 2426 (1969), J. S. Bell and R. Jackiw. A PCAC puzzle: π 0 γ γ in the σ-model . Il Nuovo Cimento A, 60, 47–61 (1969)] in systems possessing charged chiral fermions. In quark-gluon plasma containing nearly massless quarks, the chirality imbalance is sourced by the topological transitions. In condensed matter systems, the chiral quasiparticles emerge in gapless semiconductors with two energy bands having pointlike degeneracies opening the path to the study of chiral anomaly [H. B. Nielsen and M. Ninomiya. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal . Physics Letters B, 130, 389–396 (1983)]. Recently, these novel materials – so-called Dirac and Weyl semimetals have been discovered experimentally, are suitable for the investigation of the CME in condensed matter experiments. Here we report on the first experimental observation of the CME in a 3D Dirac semimetal ZrTe 5 [Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosić, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla. Chiral magnetic effect in Z r T e 5 . Nature Physics (2016) doi:10.1038/nphys3648 ]. [ABSTRACT FROM AUTHOR]

Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy. [ABSTRACT FROM AUTHOR]

In this study, we are predicting a new class of materials obtained by substituting a magnetic transition metal ion in quaternary Heusler alloys with the formula LiMgXSb (X = Co, Cr, Fe, Mn). We found that all the studied alloys exhibit a ferromagnetic ground state except LiMgCoSb. The phonon dispersions of the studied alloys computed within spin-polarized density functional perturbation theory (DFPT) do not exhibit any imaginary frequencies indicating that the proposed alloys are dynamically stable. The band structure calculations show that the studied alloys are metallic and exhibit the states near Fermi level for both spins. The fixed spin moment (FSM) calculations have been employed to exclude the possibility of other ferromagnetic ground states. One of the most interesting aspects of the band structure of these compounds is the existence of multiple band crossings leading to multiple Weyl points in the Brillouin zone. We have also computed the spin-polarized transport properties of these alloys. Our results find that doping charge carriers in the unit cell can significantly enhance the power factor and ZT. Electron doping is more effective for improving the power factor. Our findings show that among all the alloys LiMgFeSb has the highest ZT value with electron doping. Our studied materials constitute a new family of three-dimensional materials exhibiting band degeneracies that lead to Weyl points. • The quaternary Heusler alloys with formula LiMgXSb (X = Co, Cr, Fe, Mn) have been studied. • The dynamical stability of these alloys is predicted by spin-polarized lattice dynamics. • These alloys exhibit ferromagnetic ground state and multiple Weyl points in the band structure. • The electronic and lattice thermal conductivity have been investigated. • The studied compounds can find applications in spintronics and thermoelectrics. [ABSTRACT FROM AUTHOR]

We propose and demonstrate a wavevector filter for Weyl fermion based on evanescent wave or the interference effect in the barrier. It is shown that a perfect wavevector filter through a Weyl semimetal-based junction can be efficiently controlled by the barrier strength, the length of the barrier, and the incident energy of the Weyl fermion. Furthermore, the crystal structure oration is also vital in determining the wavevector filter effect. Those numerical results can be found in a good agreement with the theoretical analysis. It is anticipated that this property would receive wide applications in various Weyl semimetal-based electronic devices. [ABSTRACT FROM AUTHOR]

We present a holographic model of a Weyl semi-metal. We show the evidences that upon varying a mass parameter the model undergoes a sharp crossover at small temperature from a topologically non-trivial state to a trivial one. The order parameter is the anomalous Hall effect (AHE) and we find that it is very strongly suppressed above a critical value of the mass parameter. This can be taken as a hint for an underlying topological quantum phase transition. We give an interpretation of the results in terms of a holographic RG flow and compare to a weakly coupled field theoretical model. Since there are no fermionic quasiparticle excitations in the strongly coupled holographic model the presence of an anomalous Hall effect cannot be bound to notions of topology in momentum spaces. [ABSTRACT FROM AUTHOR]

We study predictions of orbifold family unification models with SU ( 9 ) gauge group on a six-dimensional space–time including the orbifold T 2 / Z 2 , and obtain relations among sfermion masses in the supersymmetric extension of models. The models have an excellent feature that just three families of the standard model fermions exist in a pair of Weyl fermions in the 84 representation as four-dimensional zero modes, without accompanying any mirror particles. [ABSTRACT FROM AUTHOR]

[Display omitted] We suggest a new Janus-like Weyl semimetal (WSM) candidate MoTeSe with only four Weyl points (WPs) by alloying route from prototype T d -phase WSM MoTe 2 with twelve WPs. The topological properties and topological responses under external uniform magnetic field B and strain of MoTeSe have been investigated by Wannier-function-based tight-binding Hamiltonian and first-principles method. Our calculations show WSM state is robust in a large B with the magnitude of order 10 meV and the separation distance of WPs can be effectively modulated by changing the direction and strength of B . The four WPs move away from the k z = 0 plane and the energy of WP changes parabolically with the increase of c -axial B . By contrast, the energy of WP varies linearly and approaches to the Fermi level with the increasing a -/ b -axial B . We further consider the influence of in-plane B on the topological response of MoTeSe and reveal a more complex and diverse behavior. In addition, four-WP MoTeSe displays good robustness within the moderate strain and can be transit into other multi-node WSM or non-WSM under larger strain. Our findings provide an excellent few-node WSM platform for understanding the behavior of Weyl fermion under external magnetic or strain field and a potential candidate for applications of WSM in topological electronic devices. [ABSTRACT FROM AUTHOR]

Using the first-principles calculations, we predict the 2D monolayer MXene Mn 2 NT 2 (T=-OH, -F, =O) is a half-metallic Weyl semimetal. Without spin–orbit coupling, multiple types Weyl fermions and Fermi arc edge state are observed, and there are abundant topological phases under biaxial strain in the a – b plane. Considering the spin–orbit coupling, the Weyl points are gapped, and the quantum anomalous Hall effect is observed, which is also proved by the chiral edge state in the gap and Chern number. In addition, a tight-binding model is applied to understand the origin of the non-trivial electronic properties of the quantum anomalous Hall phase. Finally, we calculate the Berry curvature and abnormal Hall conductivity of Mn 2 NT 2 , and find that they are a non-zero energy point near the Fermi level. Our results indicate that monolayer Mn 2 NT 2 have a potential application in magnetoelectronic devices. [ABSTRACT FROM AUTHOR]

Topological state in two-dimensional (2D) magnetic system has attracted widespread attention due to its potential application in spintronics and quantum computing fields. As a novel topological states of matter, Weyl semimetals with multiple topological phases have been studied. However, realizing multiple topological phases in 2D magnetic system and studying their entanglement still face great challenges. In this work, using first-principles calculations, we predict that 2D monolayer Cr 2 NT 2 (T = -OH, -F, =O) has multiple Weyl fermions (WFs) and large spin-down gap. Ferromagnetic ground states of monolayer Cr 2 NT 2 meet the dynamic, thermal and mechanical stabilities. Without spin-orbit coupling (SOC), these WPs are fully spin-polarized. When considering SOC, apart from WP3 in Cr 2 NO 2 , all WPs are opened the gap, and the chiral edge states are observed in Cr 2 NT 2. In particular, there is a quantum anomalous Hall effect in Cr 2 NF 2. Further, a biaxial strain in the a - b plane leads to the emergence of rich topological phases without SOC. In addtion, an effective four-band tight-binding model is constructed to clarify the origin of WFs in the non-trivial band topology. Finally, we calculate the Berry curvature and abnormal Hall conductivity of Cr 2 NT 2 , and find that they are a non-zero energy points around the Fermi level, indicating that monolayer Cr 2 NT 2 are promising candidates for spintronic applications. Therefore, it is necessary to explore 2D magnetic materials with multiple types of WFs and QAH phases. • The Cr2NT2 satisfies the dynamic, thermal and mechanical stabilities. • Multiple Wyle fermions are observed in 2D half-metallic Cr 2 NT 2 without SOC. • Biaxial strain in the a-b plane leads to a rich topological phase diagram in Cr 2 NT 2. • All WPs except for WP3 in Cr 2 NO 2 are opened the gap with SOC. • Quantum anomalous Hall effect is observed in Cr 2 NF 2. [ABSTRACT FROM AUTHOR]

We show that geometric torsion does not lead to new chiral dissipationless transport effects. Instead apparent response to torsion can be viewed as a manifestation of the chiral vortical effect. [ABSTRACT FROM AUTHOR]

The spin-orbit coupling field, an atomic magnetic field inside a Kramers' system, or discrete symmetries can create a topological torus in the Brillouin Zone and provide protected edge or surface states, which can contain relativistic fermions, namely, Dirac and Weyl Fermions. The topology-protected helical edge or surface states and the bulk electronic energy band define different quantum or topological phases of matters, offering an excellent prospect for some unique device applications. Device applications of the quantum materials rely primarily on understanding the topological properties, their mutual conversion processes under different external stimuli, and the physical system for achieving the phase conversion. There have been tremendous efforts in finding new topological materials with exotic topological phases. However, the application of the topological properties in devices is still limited due to the slow progress in developing the physical structures for controlling the topological phase conversions. Such control systems often require extreme tuning conditions or the fabrication of complex multi-layered topological structures. This review article highlights the details of the topological phases, their conversion processes, along with their potential physical systems, and the prospective application fields. A general overview of the critical factors for topological phases and the materials properties are further discussed to provide the necessary background for the following sections. [ABSTRACT FROM AUTHOR]

[Display omitted] • Monolayer EuO 2 shows multiple Weyl fermions, which have 100% spin-polarization. • Monolayer EuO 2 achieves the quantum anomalous Hall effects both in-plane and out-of-plane magnetization. • Monolayer EuO 2 shows clearly the Fermi arc edge states of these WFs and the single chiral edge states of QAHE phases. Topological states of matter in two-dimensional (2D) system, especially those combined with magnetism have received special attention currently, because of their new physics and the potential applications in spintronics and nanoscale. At present, realizing multiple topological phases in a single 2D Magnetic material and studying their potential entanglement still face great challenges. Here, we predict a novel 2D topological material namely monolayer EuO 2 , which can realize multiple types of topological states, namely, type-I Weyl point (WP), type-II WP, critical-type WP, and Quantum anomalous Hall (QAH) effect. Specifically, Without considering Spin-orbit coupling (SOC), these Weyl points perfectly possess the 100% spin-polarization because monolayer EuO 2 is a half metal phase with huge spin-related energy gap as large as 6.2 eV. Remarkably, With considering SOC, the topological states in monolayer EuO 2 can be tuned by direction of magnetization. Under out-plane magnetization, monolayer EuO 2 can realize the QAH effect with single chiral edge state occurring inside the energy gap. Under in-plane magnetization, the system can remain 2D Weyl states at special directions. In other in-plane magnetization, the system shows the in-plane QAH effect with the Chern number of −1 or 1. Therefore, Our work promotes the realization of tunable topological phase in 2D half metals. [ABSTRACT FROM AUTHOR]

We used first-principles density functional theory to study the physical properties of TaAs sheet. The effect of the strain on the energy band structure and transport properties was investigated. The results show that the Weyl point of TaAs can be destroyed by the strain, and new Weyl points are generated as the strain increases. The electron transmission and the strain resistance were used to describe the transport properties of TaAs. Under the effect of the strain, a significant negative strain resistance appears, and its energy range increases as the strain increases. The band structure and transport properties present anisotropic behaviors when the strain is exerted along two different directions. In terms of the numerical results, we known that the transport properties of TaAs sheet can be effectively modulated by adjusting the strength and direction of the strain. • Weyl points of TaAs can be destroyed by the strain, and new Weyl points can be generated as the strain increases. • An efficient way is proposed to achieve the modulation of the band structure of the Weyl fermions by utilizing the strain. • The band structure and transport properties present anisotropic behaviors when the strain is exerted along two different directions. [ABSTRACT FROM AUTHOR]

We consider four-dimensional quadratic gravity coupled to infinite towers of free massive scalar fields, Weyl fermions and vector bosons. We find that for specific numbers of towers, finite cosmological and Newton constants are induced in the 1-loop effective action. This is derived both in Adler's approach and by using the heat kernel method, which yield identical results. If the infinite number of massive states may be regarded as Kaluza–Klein modes arising from fields in higher dimensions, there are no Kaluza–Klein states associated with the four-dimensional graviton. Hence gravity is intrinsically four-dimensional. [ABSTRACT FROM AUTHOR]

We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study gravitational anomalies, i.e. anomalies in the conservation of the stress tensor. We use the path integral method to compute the coefficients related to the gravitational anomalies of theories in a non-abelian gauge background and flat space of dimensions 2, 4, and 6. In 4 dimensions one does not expect to have genuine gravitational anomalies. However, they may be induced at intermediate stages by regularization schemes that fail to preserve the corresponding symmetry. A case of interest has recently appeared in the study of the trace anomalies of Weyl fermions. [ABSTRACT FROM AUTHOR]

Magnetic topological materials have attracted increasingly attentions in recent years due to their exotic electronic behaviors emerging from the couplings of topological, magnetic, and crystalline symmetries. In this work, based on the first-principles calculations, we propose that hexagonal wurtzite MnO is a magnetic topological spin-gapless semi-half-metal with two pairs of type-I Weyl fermions near the Fermi level in ferromagnetic state, which is a promising candidate material in spintronic and piezoelectric applications. In the absence of spin-orbit coupling (SOC), it hosts one triple degeneracy point (TP) in the irreducible Brillouin zone. Owing to weak SOC, the TP splits into two type-I Weyl points that are very close to each other. The Fermi arc surface states connecting the projected Weyl points with opposite chirality are observed. Our results therefore provide a wonderful platform to study the interplay of magnetism and topology. • A novel magnetic topological semi-half-metal, ferromagnetic wz-MnO, is proposed. • Two pairs of Weyl fermions are hosted near the Fermi level. • It could generate 100% spin polarization, which is of profound value for spintronics. • The system is an ideal platform to explore the interplay of topology and magnetism. [ABSTRACT FROM AUTHOR]

Topological nodal line semimetals with protected 1-D Fermi lines have continuously attracted great interest. In this study, based on first-principles calculations, we demonstrate that type-I and type-II nodal lines can coexist in the dynamically stable monolayer TiBF. Both types of nodal lines are protected by mirror symmetry in the absence of spin-orbital coupling. Besides, we find that the closed nodal lines can be effectively tuned by applying biaxial tensile strain. Interestingly, with a moderate compressive biaxial strain, a novel metal-semimetal-semiconductor phase transition can be induced, during which a 2-D double Weyl fermion emerges. The 2-D double Weyl fermion features a single Fermi point, where the conduction and the valence bands contact quadratically. We construct an effective Hamiltonian to characterize the 2-D double Weyl fermion. Additionally, we show that TiBX (X = Cl, Br, I) monolayers possess similar properties. Our findings show that the monolayer TiBF is a fascinating platform to investigate unique topological phases and that it demonstrates a great potential for nanoscale device applications. • We predict that type-I and type-II nodal lines (NL) coexist in the monolayer TiBF, and reveal that these NLs are close to Fermi level. • The electronic structure can be effectively tuned by applying biaxial strain, which can drive a n interesting semiconductor-semimetal-metal quantum phase transition. • We propose for the first time a realistic 2-D material that realizes the quantum phase transition from 2-D NL fermions to 2-D double Weyl fermions. • The monolayer TiBF features a thickness of five atomic layers, facilitating the experimental demonstration. [ABSTRACT FROM AUTHOR]

• The calculated Tc is two orders of magnitude smaller than the experimental value. • The dependence of Tc with pressure is inverse with experiment. • Superconductivity in MoP can not be explained by electron-phonon pairing mechanism. Different from Dirac and Weyl fermion, three-component fermions have no analogue in high-energy physics. Recently, this new fermion was experimentally observed in topological semimetal MoP (Nature 546 (2017), 627). Later, MoP is found to be superconducting below 2.5 K at 30 GPa, and the transition temperature increases with the increasing of pressure. The microscopic paring mechanism in MoP is crucial to topological superconductor but so far unexplored. In this work, we investigate the variation of electron–phonon coupling (EPC) and superconducting critical temperature T c of MoP with pressures by first-principles calculations. On the one hand, the calculated transition temperature T c is two orders of magnitude smaller than the experimental value. On the other hand, the calculated EPC strength and T c decrease monotonically with the increasing of pressure, which is in contradiction with the relation established in experiment. Our results demonstrate that the superconductivity in pressurized MoP cannot be explained within the framework of the conventional electron–phonon pairing mechanism. [ABSTRACT FROM AUTHOR]

We report optical transmission measurements through a single crystal of the Weyl semimetal TaAs at terahertz frequencies. The measurements were performed at T = 1.6 K using intense coherent light from a free-electron laser in high magnetic fields. We detected small but measurable changes in the sample's transparency upon applying dc voltage (current) to the sample. In a constant magnetic field, the sign of the transmission change depends on the current direction. The effect disappears in zero magnetic field. These observations are qualitatively consistent with theory predictions for optical signatures of the chiral anomaly in a Weyl semimetal. [ABSTRACT FROM AUTHOR]

We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of N = 2 superconformal field theories with deformation parameter γ and prove that bi-fermion models emerge in the limit of large imaginary γ and vanishing 't Hooft coupling g , with g e − i 2 γ fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any γ and in presence of double-trace deformations. [ABSTRACT FROM AUTHOR]