Dirac nodal line semimetals (DNLSs) host relativistic quasiparticles in their one-dimensional (1D) Dirac nodal line (DNL) bands that are protected by certain crystalline symmetries. Their novel low-energy fermion quasiparticle excitations and transport properties invite studies of relativistic physics in the solid state where their linearly dispersing Dirac bands cross at continuous lines with four-fold degeneracy. In materials studied up to now, the four-fold degeneracy, however, has been vulnerable to suppression by the ubiquitous spin-orbit coupling (SOC). Despite the current effort to discover 3D DNLSs that are robust to SOC by theory, positive experimental evidence is yet to emerge. In 2D DNLSs, because of the decreased total density of states as compared with their 3D counterparts, it is anticipated that their physical properties would be dominated by the electronic states defined by the DNL. It has been even more challenging, however, to discover robust 2D DNLSs against SOC because of their lowered symmetry; no such materials have yet been predicted by theory. By combining molecular beam epitaxy growth, STM, nc-AFM characterisation, with DFT calculations and space group theory analysis, here we reveal a novel class of 2D crystalline DNLSs that host the exact symmetry that protects them against SOC. The discovered quantum material is a brick phase 3-AL Bi(110), whose symmetry protection and thermal stability are imparted by the compressive vdW epitaxial growth on black phosphorus substrates. The BP substrate templates the growth of 3-AL Bi(110) nano-islands in a non-symmorphic space group structure. This crystalline symmetry protects the DNL electronic phase against SOC independent of any orbital or elemental factors. We theoretically establish that this intrinsic symmetry imparts a general, robust protection of DNL in a series of isostructural 2D quantum materials.
Band-crossings occurring on a mirror plane are compelled to form a nodal loop in the momentum space without spin-orbit coupling (SOC). In the presence of other equivalent mirror planes, multiple such nodal loops can combine to form interesting nodal-link structures. Here, based on first-principles calculations and an effective $\mathbf{k.p}$ model analysis, we show that CaAuAs hosts a unique starfruit-like nodal-link structure in the bulk electronic dispersion in the absence of SOC. This nodal-link is comprised of three nodal loops, which cross each other at the time-reversal-invariant momentu…
Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial $π$ Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W=Zr/Hf, H=Si/Ge, M=S/Se/Te). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity unde…
Nodal-line semimetals, one of the topological semimetals, have degeneracy along nodal lines where the band gap is closed. In many cases, the nodal lines appear accidentally, and in such cases it is impossible to determine whether the nodal lines appear or not, only from the crystal symmetry and the electron filling. In this paper, for spinless systems, we show that in specific space groups at $4N+2$ fillings ($8N+4$ fillings including the spin degree of freedom), presence of the nodal lines is required regardless of the details of the systems. Here, the spinless systems refer to crystals where…
We investigate the optical activity of tilted nodal loop semimetals. We calculate the full conductivity matrix for a band structure containing a nodal loop with possible tilt in the $x-y$ plane, which allows us to study the Kerr rotation and ellipticity both for a thin film and a bulk material. We find signatures in the Kerr signal that give direct information about the tilt velocity and direction, the radius of the nodal loop and the internal chemical potential of the system. These findings should serve as guide to understanding optical measurements of nodal loop semimetals and as an addition…
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 study what kind of topological crystalline insulator phase emerges from nodal line semimetal phases in the face-centered cubic system which is not indicated by topological indices when spin-orbit coupling (SOC) is introduced. We construct an effective model which hosts two different nodal lines phases, and calculated mirror Chern numbers in it by introducing SOC. As a result, we find that the two nodal line phases with different nodal line configurations are mapped to different topological crystalline insulator phases. This result shows that turning off SOC and checking the nodal line confi…
The distinct over-tilting of band crossings in topological semimetal generates the type-I and typeII classification of Dirac/Weyl and nodal-line fermions, accompanied by the exotic electronic and magnetic transport properties. In this work, we propose a concept of hybrid nodal-chain semimetal, which is identified by the linked type-I and type-II nodal rings in the Brillouin zone. Based on first-principles calculations and swarm-intelligence structure search technique, a new ternary nitride MgCaN2 crystal is proposed as the first candidate to realize a novel 3D hybrid nodal-chain state. Remarka…
We propose that CaP3 family of materials, which include CaP3, CaAs3, SrP3, SrAs3 and BaAs3 can host a three-dimensional topological nodal line semimetal states. Based on first-principle calculations and kp model analysis, we show that a closed topological nodal line exists near the Fermi energy, which is protected by the coexistence of time-reversal and spatial inversion symmetry when the band inversion happens. A drumhead-like surface states are also obtained on the c-direction surface of these materials.
The topological nodal-line semimetal state, serving as a fertile ground for various topological quantum phases, where a topological insulator, Dirac semimetal, or Weyl semimetal can be realized when the certain protecting symmetry is broken, has only been experimentally studied in very few materials. In contrast to discrete nodes, nodal lines with rich topological configurations can lead to more unusual transport phenomena. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we provide compelling evidence of nodal-line fermions in centrosymmetric semime…
Nodal-line semimetals are characterized by a kind of topologically nontrivial bulk-band crossing, giving rise to almost flat surface states. Yet, a direct evidence of the surface states is still lacking. Here we study theoretically impurity effects in topological nodal-line semimetals based on the T-matrix method. It is found that for a bulk impurity, some in-gap states may be induced near the impurity site, while the visible resonant impurity state can only exist for certain strength of the impurity potentials. For a surface impurity, robust resonant impurity states exist in a wide range of i…
Lattice deformations act on the low-energy excitations of Dirac materials as effective axial vector fields. This allows to directly detect quantum anomalies of Dirac materials via the response to axial gauge fields. We investigate the parity anomaly in Dirac nodal line semimetals induced by lattice vibrations, and establish a topological piezoelectric effect; i.e., periodic lattice deformations generate topological Hall currents that are transverse to the deformation field. The currents induced by this piezoelectric effect are dissipationless and their magnitude is completely determined by the…
The peculiar shape of the Fermi surface of topological nodal line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three and two-dimensional nodal line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal line semimetal is anisotropic. Along the axial direction (\textit{i.e.}, the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial d…
In topological semimetals, the valence band and conduction band meet at zero-dimensional nodal points or one-dimensional nodal rings, which are protected by band topology and symmetries. In this Rapid Communication, we introduce "nodal-link semimetals", which host linked nodal rings in the Brillouin zone. We put forward a general recipe based on the Hopf map for constructing models of nodal-link semimetal. The consequences of nodal ring linking in the Landau levels and Floquet properties are investigated.
We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spin-orbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by spacetime inversion symmetry and sublattice symmetry and characterized by a $\mathbb{Z}_2$ index, while another …
Magnetic susceptibility of the topological Weyl, type-II Weyl, Dirac, and line node semimetals is theoretically investigated. Dependences of this susceptibility on the chemical potential, temperature, direction and magnitude of the magnetic field are found. The obtained results show that magnetic measurements can be very useful in investigating these semimetals. As an example, we calculate magnetic susceptibility of Cd$_3$As$_2$, Na$_3$Bi, and Ca$_3$P$_2$.
We study three-dimensional nodal line semimetals (NLSMs) with magnetic ordering and strong spin-orbit interaction. Two distinct classes of magnetic NLSMs are proposed. The first class is band-inversion NLSM where the accidental line node is induced by band inversion and locally protected by glide mirror plane and the combined time-reversal and inversion symmetries. This can be viewed as a trivial stacking of the two-dimensional antiferromagnetic Dirac semimetals. The second class is essential NLSM where the nodal features are filling-enforced by specific magnetic symmetry group. We further pro…
ZrSiS is one of the strong candidates for realistic nodal-line semimetal. We theoretically investigate the dynamical conductivity in ZrSiS by using a multi-orbital theoretical model based on the first-principles band calculation. We find that the dynamical conductivity in the clean limit is actually not frequency independent unlike the ideal Dirac model, while nearly flat dependence is achieved by introducing the energy broadening possibly induced by the disorder. The results can be applied to other compounds with the similar crystal structure, such as ZrSiSe, ZrSiTe, and HfSiS.
Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds $AX_2$ ($A$=Ca, Sr, Ba; $X$=Si, Ge, Sn). Taking BaSn$_2$ as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snake-like nodal loop in three-dimensional momentum space. Drumhead-like surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated …
Topological semimetals, extending the topological classification from insulators to metals, have greatly enriched our understanding of topological states in condensed matter. This is particularly true for topological nodal-line semimetals (TNLSs). In the present paper, we identify layered materials as promising candidates for hosting TNLSs. Based on first-principles calculations and effective model analysis, we propose that layered ferromagnetic rare-earth-metal monohalides LnX (Ln=La, Gd; X=Cl, Br) exhibit long pursued topological phases. Specifically, single-layer LaX and single-layer GdX ar…
The Berry phase and curvature are studied for the Dirac nodal line semimetal of single-component molecular conductor [Pd(dddt)$_2$]. Using two-band model on the basis of a tight-binding model, it is shown that the Berry curvature, $\bm{B}(\bm{k})$, exists along a loop of the nodal line, on which the Berry phase is obtained from surface integral of $\bm{B}(\bm{k})$. The Berry phase, which is called Zak phase, is also calculated from one-dimensional integral of the Berry connection along a line between two equivalent points of boundaries of Brillouin zone. The possible experiment is discussed in…
Recently discovered high-quality nodal chain spin-gapless semimetals $M$F$_3$ ($M$ = Pd, Mn) feature an ultra-clean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100\% spin-polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly …
The optical properties of YbMnSb2 have been measured in a broad frequency range from room temperature down to 7 K. With decreasing temperature, a flat region develops in the optical conductivity spectra at about 300cm-1, which can not be described by the well-known Drude-Lorentz model. A frequency-independent component has to be introduced to model the measured optical conductivity. Our first-principles calculations show that YbMnSb2 possesses a Dirac nodal line near the Fermi level. A comparison between the measured optical properties and calculated electronic band structures suggests that th…
We study the temperature relaxation dynamics of nodal-line semimetals after a sudden excitation in the presence of acoustic and optical phonon modes. We find that the nodal line constrains the electron momenta in scattering processes and, as a result, the temperature relaxation due to acoustic phonons is exponential as a function of time. However, depending on initial conditions, other functional forms are possible. In typical pump-probe experiments, the temperature relaxation is linear due to acoustic phonons with rates that vary as $\sim n^{1/2}$ with density. The temperature relaxation due …
Topological nodal-line semimetals are characterized by the line-contact bulk band crossings and the topological surface states. Breaking certain protecting symmetry turns this system into a Dirac semimetal or Weyl semimetal that hosts zero-dimensional isolated nodal points. Recent advances in band theory predicted a topological nodal-line semimetal state possessing a new type of nodal line in AlB$_2$-type diborides. Here, we report an experimental realization of nodal-line fermions and associated surface states near the Fermi energy in ZrB$_2$ by angle-resolved photoemission spectroscopy combi…
The Imbert-Fedorov (IF) shift is the transverse shift of a beam at a surface or an interface. It is a manifestation of the three-component Berry curvature in three dimensions, and has been studied in optical systems and Weyl semimetals. Here we investigate the IF shift in two types of topological systems, topological semimetals with pseudospin-$N/2$ for an arbitrary integer $N$, and nodal-line semimetals (NLSMs). For the former, we find the IF shift depends on the components of the pseudospin, with the sign depending on the chirality. We term this phenomenon the pseudospin Hall effect of topol…
We propose a simple scheme to construct a model whose Fermi surface is comprised of crossing-line nodes. The Hamiltonian consists of a normal hopping term and an additional term which is odd under the mirror reflection. The line nodes appear along the mirror-invariant planes, where each line node carries the quantized Berry magnetic flux. We explicitly construct a model with the $N$-fold rotational symmetry, where the $2N$ line nodes merge at the north and south poles. Photoirradiation induces a topological phase transition. When we apply photoirradiation along the $k_z$ axis, there emerge poi…
We propose a class of nodal line semimetals that host an eight-fold degenerate double Dirac nodal line (DDNL) with negligible spin-orbit coupling. We find only 5 of the 230 space groups host the DDNL. The DDNL can be considered as a combination of two Dirac nodal lines, and has a trivial Berry phase. This leads to two possible but completely different surface states, namely, a torus surface state covering the whole surface Brillouin zone and no surface state at all. Based on first-principles calculations, we predict that the hydrogen storage material LiBH is an ideal DDNL semimetal, where the …
Owing to the natural compatibility with current semiconductor industry, silicon allotropes with diverse structural and electronic properties provide promising platforms for the next-generation Si-based devices. After screening 230 all-silicon crystals in the zeolite frameworks by first-principles calculations, we disclose two structurally stable Si allotropes (AHT-Si24 and VFI-Si36) containing open channels as topological node-line semimetals with Dirac nodal points forming a nodal loop in the kz=0 plane of Brillouin zone. Interestingly, their nodal loops protected by inversion and time-revers…
Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated. The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermi…
Despite being the most studied nodal line semimetal, a clear understanding of the transient state relaxation dynamics and the underlying mechanism in ZrSiS is lacking. Using time and angle resolved photoemission spectroscopy, we study the ultrafast relaxation dynamics in ZrSiS and reveal a unique relaxation in the bulk nodal-line state which is well captured by a simple model based on optical and acoustic phonon cooling. We find linear decay processes for both optical and acoustic phonon relaxations with acoustic cooling suppressed at high temperatures. Our results reveal different decay mecha…
Using a tight-binding model, we theoretically examine the anisotropic conductivity of the nodal line semimetal of a three-dimensional Dirac electron in a single-component molecular conductor [Pd(dddt)$_2$], which consists of four molecules with HOMO and LUMO orbitals per unit cell. The conductivity shows an anisotropy given by $σ_y > σ_x > σ_z$ in accordance with that of the velocity of the Dirac cone where $z$ is the interlayer direction and $y$ is the molecular stacking direction. With increasing pressure, the nodal line semimetal emerges, followed by a loop of the Dirac point where $σ_x$ ta…
We show by first-principles calculations that the Dirac nodal-line semimetal phase can co-exist with the ferromagnetic order at room temperature in chromium dioxide, a widely used material in magnetic tape applications, under small tensile hydrostatic strains. An ideally flat Dirac nodal ring close to the Fermi energy is placed in the reflection-invariant boundary of the Brillouin zone perpendicular to the magnetic order, and is topologically protected by the unitary mirror symmetry of the magnetic group $D_{4h}(C_{4h})$, which quantizes the corresponding Berry phase into integer multiples of …
We study impurity scattering in the normal and d-wave superconducting states of line nodal semimetals and show that, due to additional scattering phase space available for impurities on the surface, the quasiparticle interference pattern acquires an extended character instead of a discrete collection of delta function peaks. Moreover, using the T-matrix formalism, we demonstrate that the conventional behavior of a scalar impurity in a d-wave superconductor breaks down on the surface of a line nodal semimetal in the quasi flat band limit.
Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line re…
While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superco…
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…
Topological semimetals, including Dirac semimetals, Weyl semimetals, and nodal line semimetals, receive enormous research interest due to their intrinsic topological nature and fascinating properties. In present work, with the help of density functional theory (DFT), we find that nodal line semimetals and Dirac semimetals can coexist in the low energy electron of two dimensional (2D) monolayer B2C. Intriguingly, besides type-I and type-II Dirac fermions, a kind of open nodal line appears around the Fermi level. The low energy electronic nature of B2C sheet can be described by a tight-binding (…
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…
Based on first-principles calculations and effective model analysis, we propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can host a three-dimensional nodal chain semimetal state. Distinguished from the previous material IrF4 [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal chain here is protected by mirror reflection symmetries of a simple space group, while in IrF4 the nonsymmorphic space group with a glide plane is a necessity. Moreover, in the presence of SOC, the nodal chain in WC type HfC evolves into Weyl points. In the Brillouin zone, a total of 30 pairs o…
The chain-type nodal loops in the reciprocal space can generate exotic nodal chain fermions. Here, we report that Li2XY (X = Ca, Ba; Y = Si, Ge) compounds are ideal inner nodal chain semimetals. Their band structures are composed of two connecting nodal loops with either hybrid or type-I band dispersion. The signatures of the nodal chain, such as the nontrivial surface states, are quite pronounced in these Li2XY compounds since there is only a single inner nodal chain without other extraneous bands near the Fermi level. These compounds are existing materials and ambient-stable, which is availa…
New materials such as nodal-line semimetals offer a unique setting for novel transport phenomena. Here, we calculate the quantum correction to conductivity in a disordered nodal-line semimetal. The torus-shaped Fermi surface and encircled $π$ Berry flux carried by the nodal loop result in a fascinating interplay between the effective dimensionality of electron diffusion and band topology, which depends on the scattering range of the impurity potential relative to the size of the nodal loop. For a short-range impurity potential, backscattering is dominated by the interference paths that do not …
The conventional k.p method fails to capture the full and essential physics of many symmetry enriched multiple nodal line structures in the three dimensional Brillouin zone. Here we present a new and systematical method to construct the effective lattice model of mirror symmetry protected three-dimensional multiple nodal line semimetals, when the spin-orbit interaction is ignored. For systems with a given pair of perpendicular nodal rings, we obtain all the effective lattice models and eleven inequivalent nodal line Fermi surfaces together with their related constraints. By means of first-prin…
In topological semimetals the Dirac points can form zero-dimensional and one-dimensional manifolds, as predicted for Dirac/Weyl semimetals and topological nodal line semimetals, respectively. Here, based on first-principles calculations, we predict a topological nodal line semimetal phase in the two-dimensional compounds $X_2Y$ ($X$=Ca, Sr, and Ba; $Y$=As, Sb, and Bi) in the absence of spin-orbit coupling (SOC) with a band inversion at the M point. The mirror symmetry as well as the electrostatic interaction, that can be engineered via strain, are responsible for the nontrivial phase. In addit…
The nodal line semimetals have attracted much attention due to their unique topological electronic structure and exotic physical properties. A genuine nodal line semimetal is qualified by the presence of Dirac nodes along a line in the momentum space that are protected against the spin-orbit coupling. In addition, it requires that the Dirac points lie close to the Fermi level allowing to dictate the macroscopic physical properties. Although the material realization of nodal line semimetals have been theoretically predicted in numerous compounds, only a few of them have been experimentally veri…
Topological nodal semimetals are known to host a variety of fascinating electronic properties due to the topological protection of the band-touching nodes. Neutron scattering, despite its power in probing elementary excitations, has not been routinely applied to topological semimetals, mainly due to the lack of an explicit connection between the neutron response and the signature of topology. In this work, we theoretically investigate the role that neutron scattering can play to unveil the topological nodal features: a large magnetic neutron response with spectral non-analyticity can be genera…
Nodal line semimetals in two-dimensional (2-D) materials have attracted intense attention currently. From fundamental physics and spintronic applications points of view, high Curie temperature ferromagnetic (FM) ones with nodal lines robust against spin-orbit coupling (SOC) are significantly in desirable. Here, we propose that FM K2N monolayer is such Weyl nodal line semimetal. We show that K2N monolayer is dynamically stable, and has a FM ground magnetic state with the out-of-plane [001] magnetization. It shows two nodal lines in the low-energy band structures. Both nodal lines are robust aga…
We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetiza…
Nodal-line semimetals (NLSs) represent a new type of topological semimetallic beyond Weyl and Dirac semimetals in the sense that they host closed loops or open curves of band degeneracies in the Brillouin zone. Parallel to the classification of type-I and type-II Weyl semimetals, there are two types of NLSs. The conventional NLS phase, in which the two bands forming the nodal line have opposite signs for their slopes along any direction perpendicular to the nodal line, has been proposed and realized in many compounds, whereas the exotic type-II NLS is very rare. Our first-principles calculatio…
Topological nodal-line semimetals with exotic quantum properties are characterized by symmetry-protected line-contact bulk band crossings in the momentum space. However, in most of identified topological nodal-line compounds, these topological non-trivial nodal lines are enclosed by complicated topological trivial states at the Fermi energy ($E_F$), which would perplex their identification and hinder further applications. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, we provide compelling evidence for the existence of Dirac nodal-line fermions in the mo…
