We show that hybrid Dirac and Weyl semimetals can be realized in a three-dimensional Luttinger semimetal with quadratic band touching (QBT). We illustrate this using periodic kicking scheme. In particular, we focus on a momentum-dependent drivings (nonuniform driving) and demonstrate the realization of various hybrid Dirac and Weyl semimetals. We identify a unique hybrid dispersion Dirac semimetal with two nodes, where one of the nodes is linear while the other is dispersed quadraticlly. Next, we show that by tilting QBT via periodic driving and in the presence of an external magnetic field, one can realize various single/double hybrid Weyl semimetals depending on the strength of external field. Finally, we note that in principle, phases that are found in this work could also be realized by employing the appropriate electronic interactions.
We study the interaction between elliptically polarized light and a three-dimensional Luttinger semimetal with quadratic band touching using Floquet theory. In the absence of light, the touching bands can have the same or the opposite signs of the curvature; in each case, we show that simply tuning the light parameters allows us to create a zoo of Weyl semimetallic phases. In particular, we find that double and single Weyl points can coexist at different energies, and they can be tuned to be type I or type II. We also find an unusual phase transition, in which a pair of Weyl nodes form at fini…
We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.
Due to strong spin-orbit coupling, charge carriers in three-dimensional quadratic band touching Luttinger semimetals have non-trivial wavefunctions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric screening shows a reduced plasma frequency and an increased spectral weight at small wavevectors, compared to a regular quadratic band. This weakens the effective Coulomb potential, modifying the single-particle self-energy for which we present both ana…
We investigate the response of 3D Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an $1/r^4$ divergence of the responses, and anisotropic behavior. Certain of the spin-orbital signatures are robust to temperature, even if the charge and spin oscillations are smeared out, and give an unusual diamagnetic Pauli susceptibility. We compare our results to the experimental literature on the bismuth-based ha…
$α$-Sn is well known as a typical Luttinger semimetal with a quadratic band touching at the $Γ$ point. Based on the effective $k\cdot p$ analysis as well as first-principles calculations, we demonstrate that multiple topological phases with a rich diagram, including topological insulator, Dirac semimetal, and Weyl semimetal phases, can be induced and engineered in $α$-Sn by external strains, magnetic fields, and circularly polarized light (CPL). Intriguingly, not only the conventional type-I Weyl nodes, but also type-II Weyl nodes and double-Weyl nodes can be generated directly from the quadra…
The Luttinger model of a quadratic-node semimetal for electrons with the $j=\frac32$ angular momentum under cubic symmetry is the parent, highest-symmetry low-energy model for a variety of topological and strongly correlated materials, such as HgTe, $α$-Sn, and iridate compounds. Previously, we have theoretically demonstrated that the Luttinger semimetal exhibits surface states. In the present work, we theoretically study the evolution of these surface states under symmetry-lowering perturbations: compressive strain and bulk-inversion asymmetry (BIA). This system is quite special in that each …
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measure…
Dirac and Weyl semimetals with linearly crossing bands are the focus of much recent interest in condensed matter physics. Although they host fascinating phenomena, their physics can be understood in terms of weakly interacting electrons. In contrast, more than 40 years ago, Abrikosov pointed out that quadratic band touchings are generically strongly interacting. We have performed terahertz spectroscopy on films of the conducting pyrochlore Pr$_2$Ir$_2$O$_7$, which has been shown to host a quadratic band touching. A dielectric constant as large as $\tilde{\varepsilon }/ε_0 \sim 180 $ is observe…
Luttinger semimetals have quadratic band crossings at the Brillouin zone-center in three spatial dimensions. Coulomb interactions in a model that describes these systems stabilize a non-trivial fixed point associated with a non-Fermi liquid state, also known as the Luttinger-Abrikosov-Beneslavskii phase. We calculate the optical conductivity $σ(ω) $ and the dc conductivity $σ_{dc} (T) $ of this phase, by means of the Kubo formula and the Mori-Zwanzig memory matrix method, respectively. Interestingly, we find that $σ(ω) $, as a function of the frequency $ω$ of an applied ac electric field, is c…
We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by {\em chiral symmetry} and characterized by the topological winding number $N$. We derive the asymptotic chiral-symmetric boundary conditions and find that there are $N+1$ universal classes of them. The class determines the numbers of flat-band edge states on either side off the node in the 1D spe…
We consider theoretically surface plasmon polaritons in Weyl semimetals. These materials contain pairs of band touching points - Weyl nodes - with a chiral topological charge, which induces an optical anisotropy and anomalous transport through the chiral anomaly. We show that these effects, which are not present in ordinary metals, have a direct fundamental manifestation in the surface plasmon dispersion. The retarded Weyl surface plasmon dispersion depends on the separation of the Weyl nodes in energy and momentum space. For Weyl semimetals with broken time-reversal symmetry, the distance bet…
We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity $ρ$ that depends on the current $\boldsymbol{I}$ and the magnetic field $\boldsymbol{B}$ as $ρ=ρ_0 (1 + γ\boldsymbol{I} \cdot \boldsymbol{B})$, and can be applied to rectifier devices controlled by $\boldsymbol{B}$. We derive the formula for the coefficient $γ$ in noncentrosymmetric Weyl semimetals. The obtained formula for $γ$ shows that the magnetochiral anisotropy…
Weyl points with monopole charge $\pm 1$ have been extensively studied, however, real materials of multi-Weyl points, whose monopole charges are higher than $1$, have yet to be found. In this Rapid Communication, we show that nodal-line semimetals with nontrivial line connectivity provide natural platforms for realizing Floquet multi-Weyl points. In particular, we show that driving crossing nodal lines by circularly polarized light generates double-Weyl points. Furthermore, we show that monopole combination and annihilation can be observed in crossing-nodal-line semimetals and nodal-chain semi…
When a Dirac semimetal is subject to a circularly polarized laser, it is predicted that the Dirac cone splits into two Weyl nodes and a nonequilibrium transient state called the Floquet Weyl semimetal is realized. We focus on the previously unexplored low-frequency regime, where the upper and lower Dirac bands resonantly couple with each other through multi-photon processes, which is a realistic situation in solid state ultrafast pump-probe experiments. We find a series of new Weyl nodes emerging in pairs when the Floquet replica bands hybridize with each other. The nature of the Floquet Weyl …
We construct an exactly solvable lattice model of a fractional Weyl semimetal (FWS). The low energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect (CPGE) and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function they provide strong experimental signatures for this exotic gapless state of matter.
For first-order topological semimetals, non-Hermitian perturbations can drive the Weyl nodes into Weyl exceptional rings having multiple topological structures and no Hermitian counterparts. Recently, it was discovered that higher-order Weyl semimetals, as a novel class of higher-order topological phases, can uniquely exhibit coexisting surface and hinge Fermi arcs. However, non-Hermitian higher-order topological semimetals have not yet been explored. Here, we identify a new type of topological semimetals, i.e, a higher-order topological semimetal with Weyl exceptional rings. In such a semimet…
We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays sing…
Weyl semimetals have been classified into type-I and type-II with respect to the geometry of their Fermi surfaces at the Weyl points. Here, we propose a new class of Weyl semimetal, whose unique Fermi surface contains two electron or two hole pockets touching at a multi-Weyl point, dubbed as type-III Weyl semimetal. Based on first-principles calculations, we first show that quasi-one-dimensional compound (TaSe4)2I is a type-III Weyl semimetal with larger chiral charges. (TaSe4)2I can support four-fold helicoidal surface states with remarkably long Fermi arcs on the (001) surface. Angle-resolve…
The recent explosion of research interest in Weyl semimetals has led to many proposed Weyl semimetal candidates and a few experimental observations of a Weyl semimetal in real materials. Through this experience, we have come to appreciate that typical Weyl semimetals host many Weyl points. For instance, the first Weyl semimetal observed in experiment, TaAs, hosts 24 Weyl points. Similarly, the Mo$_x$W$_{1-x}$Te$_2$ series, recently under study as the first Type II Weyl semimetal, has eight Weyl points. However, it is well-understood that for a Weyl semimetal without inversion symmetry but with…
A relativistic spinor with spin 3/2 is historically called Rarita-Schwinger spinor. The right- and left-handed chiral degrees of freedom for the massless Rarita-Schwinger spinor are independent and are thought of as the left- and right-Weyl fermion with helicity \pm3/2. We study three orbital spin-1/2 Weyl semimetals in the strong spin-orbital coupling limit with time reversal symmetry breaking. We find that in this limit the systems can be a J_{eff}=1/2 Weyl semimetal or a J_{eff}=3/2 semimetal, depending on the Fermi level position. The latter near Weyl points includes both degrees of freedo…
It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topologica…
Kramers Weyl semimetals are Weyl semimetals that have Weyl points pinned at the time reversal invariant momenta. Recently it has been discovered that all chiral crystals host Weyl points at time reversal invariant momenta, so metals with chiral lattice symmetry all belong to the category of Kramers Weyl semimetals. In this work, we show that due to the chiral lattice symmetry, Kramers Weyl semimetals have the unique longitudinal magnetoelectric effect in which the charge current induced spin and orbital magnetization is parallel to the direction of the current. This feature allows Kramers Weyl…
Magnetotransport and magneto-optics experiments offer a very powerful probe for studying the physical properties of materials. Here, we investigate the second-order nonlinear magnetoconductivity of tilted type-I Weyl and multi-Weyl semimetal. In contrast to the presence of chiral anomaly in the linear response regime, we show that Weyl semimetal do not host chiral charge pumping in the nonlinear transport regime. We predict that an inversion symmetry broken and tilted Weyl semimetal can support finite longitudinal nonlinear magnetoconductivity, which is otherwise absent in untilted Weyl semime…
Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation betw…
There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional (3D) spin-orbit (SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propos…
We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed "hybrid Weyl semimetal", in which one Weyl node is of type-I while the other is of type-II. For the hybrid Weyl semimetal, we further demonstrate the bulk Fermi surfaces and the topologically protected surface states, analyze the unique Landau level structure and quantum oscillation, and discuss the material realization.
We present a new switching mechanism that utilizes the proximity coupling between the surface spin texture of a Weyl semimetal and a superconductor, in a Weyl semimetal/superconductor/Weyl semimetal trilayer heterostructure. We show that the superconductivity in the middle layer can be fully suppressed by the surface spin texture of the Weyl semimetals in the presence of an external magnetic field, but it can be recovered again by only changing the field direction. The restoration of the middle-layer superconductivity indicates a sharp transition to a low-resistance state. This sharp switching…
Multi-band touchings such as 3-band, 6-band and 8-band touchings together with the emergence of high pseudospin fermions were predicted recently at high-symmetry points in three-dimensional space. In this paper, we propose a simple cubic model whose unit cell contains three atoms. There are 6 bands in the system due to the spin degrees of freedom. The 4-band and 2-band touchings are realized at high-symmetry points, where we derive low-energy theories, demonstrating the emergence of pseudospin-3/2 fermions and Weyl fermions, respectively. Away from the high-symmetry points, we find critical We…
Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of …
We study a general phase transition between spinless topological nodal-line semimetal and Weyl semimetal phases. We classify topological nodal lines into two types based on their positions and shapes, and their phase transitions depends on their types. We show that the topological nodal-line semimetal becomes the Weyl semimetal by breaking time-reversal symmetry when the nodal lines enclose time-reversal invariant momenta (type-A nodal lines). We also discuss an effect of crystallographic symmetries determining the band structure of the topological nodal-line semimetals. Thanks to protection b…
Weyl semimetals possess low energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the extensive novel transport properties that Weyl semimetals exhibit. The singular nature of the Berry curvature around the nodal points in Weyl semimetals allows for the possibility of large anomalous transport coefficients in zero applied magnetic field. Recently a new class, termed type-II Weyl semimetals, has been demonstrated in a variety of materials, where the Weyl nodes are tilted. We present here a study of anomalous transport in thi…
We report the discovery of a time-reversal symmetric Weyl semimetal obtained by modifying a model Hamiltonian describing the electronic properties of conventional alkali metals. The artificially generated Weyl semimetal features four isolated Weyl nodes in its bulk band structure and displays characteristic surface Fermi arcs arising from topologically protected surface states. The Weyl semimetal occurs as an intermediate state between a conventional band insulator and a three-dimensional topological insulator. The generation of topological Weyl semimetals from conventional metals opens a new …
The separation of the Weyl nodes in a broken time-reversal symmetric Weyl semimetal leads to helical quasi-particle excitations at the Weyl nodes, which, when coupled with overall spin conservation allows only inter-nodal transport at the junction of the Weyl semimetal with a superconductor. This leads to an unusual periodic oscillation in the Josephson current as a function of $k_0L$, where $L$ is the length of the Weyl semimetal and $2k_0$ is the inter-nodal distance. This oscillation is robust and should be experimentally measurable, providing a direct path to confirming the existence of ch…
Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work, we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quant…
Classification of topological insulators and superconductors is manifested in terms of spin cobordism groups for lower dimensions. It is discussed that the periodic table of topological insulators is a result of the possible choices of spin structures on Brillouin zones of relevant topological materials. This framework is extended to the case of Weyl semimetals. It is shown that the classification of Weyl semimetals can be managed in terms of spin$^c$ cobordism groups via the extension of spin structures to spin$^c$ structures. Topological invariants of Weyl semimetals are connected to the top…
Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2 and ZnPbAs2 are ideal Weyl semimetals, having largely separated Weyl points (~ 0.05/A) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-powe…
We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have non-trivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated Doubling Theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that…
Multi-Weyl semimetals are new types of Weyl semimetals which have anisotropic non-linear energy dispersion and a topological charge larger than one, thus exhibiting a unique quantum response. Using a unified lattice model, we calculate the optical conductivity numerically in the multi-Weyl semimetal phase and in its neighboring gapped states, and obtain the characteristic frequency dependence of each phase analytically using a low-energy continuum model. The frequency dependence of longitudinal and transverse optical conductivities obeys scaling relations that are derived from the winding numb…
We experimentally compare two types of interface structures with magnetic and non-magnetic Weyl semimetals. They are the junctions between a gold normal layer and magnetic Weyl semimetal Ti$_2$MnAl, and a ferromagnetic nickel layer and non-magnetic Weyl semimetal WTe$_2$, respectively. Due to the ferromagnetic side of the junction, we investigate spin-polarized transport through the Weyl semimetal surface. For both structures, we demonstrate similar current-voltage characteristics, with hysteresis at low currents and sharp peaks in differential resistance at high ones. Despite this behavior re…
A new type of Weyl semimetal state, in which the energy values of Weyl nodes are not the local extrema, has been theoretically proposed recently, namely type II Weyl semimetal. Distinguished from type I semimetal (e.g. TaAs), the Fermi surfaces in a type II Weyl semimetal consist of a pair of electron and hole pockets touching at the Weyl node. In addition, Weyl fermions in type II Weyl semimetals violate Lorentz invariance. Due to these qualitative differences distinct spectroscopy and magnetotransport properties are expected in type II Weyl semimetals. Here, we present the direct observation…
The term Weyl semimetal originates from the fact that its energy dispersion obeys a Weyl equation. However, a Weyl equation itself cannot fully describe the electron states in an actual bounded geometry. For example, the appearance of chiral surface states, which is a characteristic feature of a Weyl semimetal, cannot be captured with a Weyl equation. This indicates that some degree of freedom is lost when a Weyl equation is derived from a microscopic model of a Weyl semimetal. To overcome this difficulty, we present a framework consisting of a Weyl equation and a supplementary equation, which…
We investigate multilayer systems of a normal insulator and a Weyl semimetal. We calculate the bulk band structure and determine phase diagrams by changing the thickness of the normal insulator and that of the Weyl semimetal layer using two models; one is from the effective model for a Weyl semimetal, and the other is the lattice model. We compare the results between the two models, and found that they agree well. As a result, we find that the multilayer system shows a qualitatively different behavior depending on the stacking direction relative to the displacement vector connecting between tw…
The Fermi arcs of topological surface states in the three-dimensional multi-Weyl semimetals on surfaces by a continuum model are investigated systematically. We calculated analytically the energy spectra and wave function for bulk quadratic- and cubic-Weyl semimetal with a single Weyl point. The Fermi arcs of topological surface states in Weyl semimetals with single- and double-pair Weyl points are investigated systematically. The evolution of the Fermi arcs of surface states variating with the boundary parameter is investigated and the topological Lifshitz phase transition of the Fermi arc co…
The magnetotransport properties of disordered ferromagnetic Weyl semimetals are investigated numerically. We found an extraordinarily stable and huge magnetoresistance effect in domain walls of Weyl semimetals. This effect originates from the helicity mismatch of Weyl fermions and is a specific property of Weyl semimetals. Although conventional magnetoresistance effects are strongly suppressed in domain walls where local magnetization varies gradually, the helicity-protected magnetoresistance in Weyl semimetals maintains almost $100\%$ of the magnetoresistance ratio for any kind of thick domai…
We report the electrical transport properties for Weyl semimetal TaAs in an intense magnetic field. Series of anomalies occur in the longitudinal magnetoresistance and Hall signals at ultra-low temperatures when the Weyl electrons are confined into the lowest Landau level. These strongly temperature-dependent anomalies are ascribed to the electron-hole pairing instability. Our measurements show that the Weyl semimetal TaAs in the ultraquantum regime provides a good platform for studying electron-electron interaction in topological nontrivial semimetals.
