We investigate the effect of a vertical electric field on a Dirac semimetal thin film. We show that through the interplay between the quantum confinement effect and the field-induced coupling between sub-bands, the sub-band gap can be tuned and inverted, during which the system undergoes a topological phase transition between a trivial band insulator and a quantum spin Hall insulator. Consequently, one can electrically switch the topological edge channels on and off, making the system a promising platform for constructing a topological field effect transistor.
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…
In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular step-like anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized theory), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the li…
The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness. We present the study of disorder effects in thin film of Dirac semimetals. It is found that moderate Anderson …
We theoretically study the electric polarization in magnetic topological nodal semimetal thin films. In magnetically doped topological insulators, topological nodal semimetal phases emerge once the exchange coupling overcomes the band gap. Changing the magnetization direction, nodal structure is modulated and the system becomes topological nodal point or line semimetals. We find that nodal line semimetals are characterized by non-linear electric polarization, which is not observed in nodal point semimetals. The non-linear response originates from the existence of the surface states. Screening …
We demonstrate that, apart from the chiral anomaly, Dirac semimetals possess another quantum anomaly, which we call the mirror anomaly, and which manifests in a singular response of the Dirac semimetal to an applied magnetic field. Namely, the anomalous Hall conductivity exhibits step-function singularities when the field is rotated. We show that this phenomenon is closely analogous to the parity anomaly of (2+1)-dimensional Dirac fermions, but with mirror symmetry, which we demonstrate emerges near any Dirac point at a time reversal invariant momentum, replacing the parity symmetry.
The Datta-Das-type spin field-effect transistor, using a two-dimensional electron gas in a semiconductor heterostructure as a channel, plays a key role in spintronics. Here, we theoretically present a type of spin field-effect transistor based on massless birefringent Dirac fermions in polar Dirac semimetals. The manipulation of spin arises from the existence of the strong spin-orbit coupling, polar space groups, and Dirac cones in a single phase. The oscillatory channel conductance can be controlled by the sign of gate voltage in addition to its magnitude due to the gapless band structures of…
Recently, crystalline-symmetry-protected three-dimensional (3D) bulk Dirac semimetal phase has been experimentally identified in a stoichiometric high-mobility compound, Cd3As2. The Dirac state observed in Cd3As2 has been attributed to originate mostly from the bulk state while calculations show that the bulk and surface states overlap over the entire Dirac dispersion energy range. In this study, we unambiguously reveal doping induced evolution of the ground state of surface and bulk electron dynamics in a 3D Dirac semimetal. We develop a systematic technique to isolate the surface and bulk st…
We demonstrate that topological Dirac semimetals, which possess two Dirac nodes, separated in momentum space along a rotation axis and protected by rotational symmetry, exhibit an additional quantum anomaly, distinct from the chiral anomaly. This anomaly, which we call the $ \mathbb Z_2$ anomaly, is a consequence of the fact that the Dirac nodes in topological Dirac semimetals carry a $\mathbb Z_2$ topological charge. The $\mathbb Z_2$ anomaly refers to nonconservation of this charge in the presence of external fields due to quantum effects and has observable consequences due to its interplay …
We propose an unconventional type of Hall effect in a topological Dirac semimetal with ferromagnetic electrodes. The topological Dirac semimetal itself has time-reversal symmetry, whereas attached ferromagnetic electrodes break it, causing the large Hall response. This induced Hall effect is a characteristic of the helical surface/edge states that arise in topological materials, such as topological Dirac semimetals or quantum spin Hall insulators. We compute the Hall conductance/resistance and the Hall angle by using a lattice model with four-terminal geometry. For topological Dirac semimetals…
The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. In this paper, we propose the concept of a three-dimensional type-II Dirac fermion and identify a new topological semimetal state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predict …
We theoretically investigate surface plasmon polaritons propagating in the thin-film Weyl semimetals. We show how the properties of surface plasmon polaritons are affected by hybridization between plasmons localized at the two metal-dielectric interfaces. Generally, this hybridization results in new mixed plasmon modes, which are called short-range surface plasmons and long-range surface plasmons, respectively. We calculate dispersion curves of these mixed modes for three principle configurations of the axion vector describing axial anomaly in Weyl semimetals. We show that the partial lack of …
We study correlations and magnetic textures of localized spins, doped in three-dimensional Dirac semimetals. An effective field theory for magnetic moments is constructed by integrating out the fermionic degrees of freedom. The spin correlation shows a strong anisotropy, originating from spin-momentum locking of Dirac electrons, in addition to the conventional Heisenberg-like ferromagnetic correlation. The anisotropic spin correlation allows topologically nontrivial magnetic excitation textures such as a transient hedgehog state, as well as the ferromagnetic ground state. The spin-wave dispers…
We show that, under the effect of an external magnetic field, a photogalvanic effect and the generation of second harmonic wave can be induced in inversion-symmetric and time reversal invariant Dirac semimetals. The mechanism responsible of these non linear optical responses is the magnetochiral effect. The origin of this magnetochiral effect is the band bending of the dispersion relation in real Dirac semimetals. Some observable consequences of this phenomenon are the appearance of a dc current on the surface of the system when it is irradiated with linearly polarized light or a rotation of t…
We theoretically study the spin susceptibility of Dirac semimetals using the linear response theory. The spin susceptibility is decomposed into an intraband contribution and an interband contribution. We obtain analytical expressions for the intraband and interband contributions of massless Dirac fermions. The spin susceptibility is independent of the Fermi energy while it depends on the cutoff energy, which is introduced to regularize the integration. We find that the cutoff energy is appropriately determined by comparing the results for the Wilson-Dirac lattice model, which approximates the …
Using first principles pseudopotential density functional theory calculations, we find that terminating zigzag graphene nanoribbons (ZGNR) with monovalent alkali atoms at a reduced concentration has a dramatic impact on their properties. In particular, using sodium atoms for the saturation of ZGNR edges at half the concentration of edge-carbon atoms make it a one dimensional, perfect semimetal, where the valance and conduction bands meet at only a single, Dirac-like point. Unlike pristine graphene, the Dirac-"cones" of Na-ZGNR is not symmetric with respect to wave vector, but rather it is tilt…
We theoretically study a tunneling effect in a two-dimensional Dirac semimetal with two Dirac points protected by non-symmorphic symmetries. The tunnel barrier can be arranged by a magnetic exchange potential which opens a gap at the Dirac points which can be induced by a magnetic proximity effect of a ferromagnetic insulator. We found that the tunnel decay length increases with a decrease in the strength of the spin-orbit coupling, and moreover the dependence is attributed to the correlation of sublattice and spin degree of freedoms which lead to symmetry-protected Dirac points. The tunnel pr…
We study the photoresponse of two-dimensional semi-Dirac semimetals and three-dimensional Dirac semimetals to off-resonant circularly polarized light. For two-dimensional semi-Dirac semimetals we find that incident light does not open a gap in the spectrum, in contrast to the case of purely linear dispersion. For the three-dimensional case we find that applying a circularly polarized light, one can tune from a trivial insulator to three-dimensional Dirac semimetal with an inverted gap. We propose and show that application of light leads to an intriguing platform for generation, motion and merg…
We study the current of chiral charge density in a Dirac semimetal with two Dirac points in momentum space, subjected to an externally applied time dependent electric field and in the presence of a magnetic field. Based on the kinetic equation approach, we find contributions to the chiral charge current, that are proportional to the second power of the electric field and to the first and second powers of the magnetic field, describing the interplay of the chiral anomaly and the drift motion of electrons moving under the action of electric and magnetic fields.
In the Fermi liquid description of metals, electrical and thermoelectric transport coefficients are linked by robust relations which can be challenged by strong interactions or when the electron liquid enters a different regime. These relations have been very powerful in the characterisation of novel materials. We show that Dirac and Weyl semimetals at zero doping and zero temperature (the conformal limit) have a very singular behavior due to a quantum anomaly. Away from this point, a Mott relation can be established.
Nodal-line semimetals with magnetic orders have been theoretically predicted and experimentally observed in only few compounds. We theoretically explore the electronic structure in bulk and boundary of such a magnetic nodal-line state by introducing magnetism in topological Dirac semimetal (TDSM). TDSMs, such as $\mathrm{Cd_3 As_2}$ and $\mathrm{Na_3 Bi}$, are characterized by a pair of spin-degenerate Dirac points protected by rotational symmetries of crystals. By introducing local magnetic moments coupled to the electron spins in the lattice model of TDSM, we show that the TDSM can turn into…
Revealing the ultrafast dynamics of three-dimensional (3D) Dirac fermions upon photoexcitation is critical for both fundamental science and device applications. So far, how the cooling of 3D Dirac fermions differs from that of two-dimensional (2D) Dirac fermions and whether there is population inversion are fundamental questions that remain to be answered. Here we reveal the ultrafast dynamics of Dirac fermions in a model 3D Dirac semimetal Cd$_3$As$_2$ by ultrafast time- and angle-resolved photoemission spectroscopy (TrARPES) with a tunable probe photon energy from 5.3 - 6.9 eV. The energy- a…
Recent transport experiments have revealed the activation of longitudinal magnetoresistance of Weyl semimetals in the quantum limit, suggesting the breakdown of chiral anomaly in a strong magnetic field. Here we provide a general mechanism for gapping the zeroth chiral Landau levels applicable for both Dirac and Weyl semimetals. Our result shows that the zeroth Landau levels anticross when the magnetic axis is perpendicular to the Dirac/Weyl node separation and when the inverse magnetic length $l_B^{-1}$ is comparable to the node separation scale $Δk$. The induced bulk gap increases rapidly be…
Realizing stable two-dimensional (2D) Dirac points against spin-orbit coupling (SOC) has attracted much attention because it provides a platform to study the unique transport properties. In previous work, Young and Kane [Phys. Rev. Lett. \textbf{115}, 126803 (2015)] proposed stable 2D Dirac points with SOC, in which the Berry curvature and edge states vanish due to the coexistence of inversion and time-reversal symmetries. Herein, using the tight-binding model and k$\cdot$p effective Hamiltonian, we present that 2D Dirac points can survive in the presence of SOC without inversion symmetry. Suc…
Anisotropic magnetoresistance is the change tendency of resistance of a material on the mutual orientation of the electric current and the external magnetic field. Here, we report experimental observations in the Dirac semimetal Cd3As2 of giant anisotropic magnetoresistance and its transverse version, called the planar Hall effect. The relative anisotropic magnetoresistance is negative and up to -68% at 2 K and 10 T. The high anisotropy and the minus sign in this isotropic and nonmagnetic material are attributed to a field-dependent current along the magnetic field, which may be induced by the…
Weak topological insulators and Dirac semimetals are gapped and nodal phases with distinct topological properties, respectively. Here, we propose a novel topological phase that exhibits features of both and is dubbed composite Dirac semimetal (CDSM). In its bulk, the CDSM has a pair of Dirac points and a pair of bands inverted along a high-symmetry path. At side surfaces, a pair of Fermi arcs connecting the projected Dirac points coexist with a pair of Fermi loops traversing the surface Brillouin zone. A nonsymmorphic symmetry dictates degeneracies between the Fermi arcs and the Fermi loops. W…
Motivated by recent transport experiments, we theoretically study the quantum Hall effect in topological semimetal films. Owing to the confinement effect, the bulk subbands originating from the chiral Landau levels establish energy gaps that have quantized Hall conductance and can be observed in relatively thick films. We find that the quantum Hall state is strongly anisotropic for different confinement directions not only due to the presence of the surface states but also because of the bulk chiral Landau levels. As a result, we re-examine the quantum Hall effect from the surface Fermi arcs a…
We investigate the topological phase derived by time-reversal breaking fields in a nonsymmorphic symmetry-protected two-dimensional Dirac semimetal. When the nonsymmorphic symmetry is preserved even in the presence of the field, the two-dimensional electronic states change into two distinct topological phases with the insulating gap. One phase is well-known as quantum Hall states with chiral edge modes accompanying the Hall current, but the other one is an unconventional topological phase with helical edge modes in the absence of time-reversal symmetry.
We connect between the problem of thermodynamics of localized magnetic moments in a Dirac semimetal, the interaction with relativistic electrons leading to the effective ferromagnetic exchange between the moments, and the existing theories dealing with long--range exchange interaction. We point out that the results of high--temperature expansion for the free energy of a dilute ensemble of magnetic impurities in the semimetal performed by V. Cheianov et al. (Phys. Rev. B {\bf 86}, 054424 (2012)) give an indication to the existence of a new disordered fixed point in such model.
We consider the effective coupling between impurity spins on surfaces of a thin-film Weyl semimetal within Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory. If the spins are on the same surface, their coupling reflects the anisotropy and the spin-momentum locking of the Fermi arcs. By contrast when the spins are on opposite surfaces, their coupling is mediated by the Fermi arcs as well as by bulk states. In this case the coupling is both surprisingly strong and strongly thickness dependent, with a maximum at an optimum thickness. We demonstrate our results using analytical solutions of states in t…
It is shown that the convective instability in electron fluids in three- and two-dimensional (3D and 2D) Dirac and Weyl semimetals is strongly inhibited. The major obstacles for electron convection are the effects of the Coulomb forces and the momentum relaxation related to the interaction with impurities and phonons. The effect of the Coulomb forces is less pronounced in 2D materials, such as graphene. However, momentum relaxation still noticeably inhibits convection making it very difficult to achieve in practice.
Here we demonstrate the Shubnikov de Haas oscillation in high-quality Cd3As2 nanowires grown by a chemical vapor deposition approach. The dominant transport of topological Dirac fermions is evident by the nontrivial Berry phase in the Landau Fan diagram. The quantum oscillations rise at a small field of 2 Tesla and preserves till up to 100K, revealing a sizeable Landau level gap and a mobility of over 2000 cm2/V-1s-1. The angle-variable oscillations indicates the isotropy of the bulk Dirac transport. The large estimated mean free path appeals the one-dimensional transport of Dirac semimetals.
The tunable carrier density plays a key role in the investigation of novel transport properties in three-dimensional topological semimetals. Here we demonstrate that the carrier density as well as the mobility of Dirac semimetal Cd3As2 nanoplates can be effectively tuned by the in-situ thermal treatment at 350 K for one hour, both showing a non-monotonic evolution with the thermal cycling treatments. The upward shift of Fermi level relative to the Dirac nodes blurs the surface Fermi-arc states, accompanying with an anomalous phase shift of oscillations of bulk states due to the change of topol…
A tight-binding model of 8-Pmmn borophene, a two-dimensional boron crystal, is developed. We confirm that the crystal hosts massless Dirac fermions and the Dirac points are protected by symmetry. Strain is introduced into the model, and it is shown to induce a pseudomagnetic field vector potential and a scalar potential. The dependence of the potentials on the strain tensor is calculated. The physical effects controlled by pseudomagnetic field are discussed.
The recent discovery of Dirac semimetals represents a new achievement in our fundamental understanding of topological states of matter. Due to their topological surface states, high mobility, and exotic properties associated with bulk Dirac points, these new materials have attracted significant attention and are believed to hold great promise for fabricating novel topological devices. For nanoscale device applications, effects from finite size usually play an important role. In this report, we theoretically investigate the electronic properties of Dirac semimetal nanostructures. Quantum confin…
We investigate the effect of Coulomb interactions on the electromagnetic response of three-dimensional Dirac and Weyl semimetals. In a calculation reminiscent of Schwinger's seminal work on quantum electrodynamics, we find three physically distinct effects for the anomalous magnetic moment of the relativisticlike quasiparticles in the semimetal. In the case of nonzero doping, the anomalous magnetic moment is finite at long wavelengths and typically orders of magnitude larger than Schwinger's result. We also find interesting effects of one of the three new Hamiltonian terms on the topological s…
We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find that the internode process, as well as the unique three-dimensional spin-momentum locking, has significant influences on the RKKY interaction, resulting in both a Heisenberg and an Ising term, and an additional Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These interactions can lead to rich spin textures and possible ferromagnetism in Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic Dirac and Wey…
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest possible application of our theory to recently discovered superconducting …
The search for symmetry-protected 2D Dirac semimetals analogous to graphene is important both for fundamental and practical interest. The 2D Dirac cones are protected by crystalline symmetries and magnetic ordering may destroy their robustness. Here we propose a general framework to classify stable 2D Dirac semimetals in spin-orbit coupled systems having the combined time-reversal and inversion symmetries, and show the existence of the stable Dirac points in 2D antiferromagnetic semimetals. Compared to 3D Dirac semimetals which fall into two distinct classes, Dirac semimetals in 2D with combin…
Electronic structures of Ge$_{1-x}$Sn$_{x}$ alloys (0 $\leq$ $x$ $\leq$ 1) are theoretically studied by nonlocal empirical pseudopotential method. For relaxed Ge$_{1-x}$Sn$_{x}$, a topological semimetal is found for $\textit x$ $>$ 41$\%$ with gapless and band inversion at $Γ$ point, while there is an indirect-direct bandgap transition at $x$ = 8.5$\%$. For strained Ge$_{1-x}$Sn$_{x}$ on a Ge substrate, semimetals with a negative indirect bandgap appear for $x$ $>$ 43$\%$, and the strained Ge$_{1-x}$Sn$_{x}$ on Ge is always an indirect bandgap semiconductor for $x$ $<$ 43$\%$. With appropriate…
We discuss the Schwinger pair creation process for the system of massless Dirac fermions in the presence of constant external magnetic and electric fields. The pair production rate remains finite unlike the vacuum decay rate. In the recently discovered Dirac semimetals, where the massless Dirac fermions emerge, this pair production may be observed experimentally through the transport properties. We estimate its contribution to the ordinary conductivity of the semimetals.
Three dimensional (3D) Dirac semimetals are 3D analogue of graphene, which display Dirac points with linear dispersion in k-space, stabilized by crystal symmetry. Cd3As2 and Na3Bi were predicted to be 3D Dirac semimetals and were subsequently demonstrated by photoemission experiments. As unveiled by transport measurements, several exotic phases, such as Weyl semimetals, topological insulators, and topological superconductors, can be deduced by breaking time reversal or inversion symmetry. Here, we reported a facile and scalable chemical vapor deposition method to fabricate high-quality Dirac s…
We study the time-development processes of spin and charge transport phenomena in a topological Dirac semimetal attached to a ferromagnetic insulator with a precessing magnetization. Compared to conventional normal metals, topological Dirac semimetals manifest a large inverse spin Hall effect when a spin current is pumped from the attached ferromagnetic insulator. It is shown that the induced charge current is semi-quantized, i.e., it depends only on the distance between the two Dirac points in momentum space and hardly depends on the disorder strength when the system remains in the topologica…
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are \emph{not} gapped by spin-orbit interactions, and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases, and show that single symmetry-protected Dirac points are impossible in two d…
We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135, showing that 135 can host an intrinsic double Dirac semimetal -- one with no additional degeneracies at the Fermi energy. We consider symmetry-lowering perturbations and show that uniaxial compressive strain in different directions leads to topologically distinct insulating phases. In addition, the do…
Three dimensional (3D) Dirac semimetal is a novel state of quantum matter, characterized by the gapless bulk four-fold degeneracy near Fermi energy. Soon after its discovery, the classification of stable 3D Dirac semimetals with inversion and rotational symmetry have been studied. However, only ten out of thirty-two point groups have both inversion and rotational symmetry, and we need a more complete classification of stable 3D Dirac semimetals. Here we classify stable 3D Dirac semimetals with reflection symmetry and rotational symmetry in the presence of time reversal symmetry, which belong t…
Weyl and Dirac semimetals recently stimulate intense research activities due to their novel properties. Combining first-principles calculations and effective model analysis, we predict that nonmagnetic compounds BaYBi (Y=Au, Ag and Cu) are Dirac semimetals. As for the magnetic compound EuYBi, although the time reversal symmetry is broken, their long-range magnetic ordering cannot split the Dirac point into pairs of Weyl points. However, we propose that partially substitute Eu ions by Ba ions will realize the Weyl semimetal.
Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu$_3$PdN can host a three-dimensional (3D) topological nodal line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by coexistence of time-reversal and inversion symmetry. There are three nodal line circles in total due to the cubic symmetry. "Drumhead"-like surface flat bands are also derived. When SOC is included, each nodal line evolves into a pair of stable 3D Dirac points as protected by C$_4$ crystal symmetry. This is remarkably distinguished …
We propose that the noncentrosymmetric LiGaGe-type hexagonal $ABC$ crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. The symmetry-protected Dirac points arise due to a band inversion and are located on the sixfold rotation $z$-axis, whereas the six pairs of Weyl points related by sixfold symmetry are located on the perpendicular $k_z=0$ plane. By studying the electronic structure as a function of the buckling of the HgPb layer, which is the origin of inversion symmetry breaking, we establish that the coexistence of Dirac and We…
We calculate the extremal cross sectional areas and cyclotron masses for the Fermi-surface pockets in Dirac and Weyl topological semimetals. The calculation is carried out for the most general form of the electron energy bands in the vicinity of the Weyl and Dirac points. Using the obtained formulas, one can find parameters characterizing the Dirac and Weyl electrons in the topological semimetals from appropriate experimental data. As an example, we consider the W1 electrons in TaAs.
Black phosphorus (BP), a layered van der Waals material, reportedly has a band gap sensitive to external perturbations and manifests a Dirac-semimetal phase when its band gap is closed. Previous studies were focused on effects of each perturbation, lacking a unified picture for the band-gap closing and the Dirac-semimetal phase. Here, using pseudospins from the glide-reflection symmetry, we study the electronic structures of mono- and bilayer BP and construct the phase diagram of the Dirac-semimetal phase in the parameter space related to pressure, strain, and electric field. We find that the …
We present a new type of three-dimensional essential Dirac semimetal with magnetic ordering. The Dirac points are protected by the magnetic space groups and cannot be gapped without lowering such symmetries, where the combined antiunitary symmetry of half-translation operator and time-reversal plays an essential role. We introduce two explicit tight-binding models for space groups $16$ and $102$, which possesses Dirac point at time-reversal-invariant momenta of surface Brillouin zone. In contrast to the time-reversal-invariant essential Dirac semimetal, the magnetic space groups here can be ei…
