In recent years, the exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in seeking for new topological phases and material realization. In this work, we propose a new family of TSMs which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE) at half-filling. Meanwhile, the CICE at half-filling guarantees the presence of a second pair of CICE beyond half-filling. Both CICEs are linked at four-fold degenerate points (FDPs) at zone boundaries. In addition, we identify the generic criteria for the existence of the CICE in a time reversal invariant {\it spinless} fermion system or a spinfull system with negligible spin-orbital coupling (SOC). Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICE whose location centers in the first Brillouin zone (BZ) are identified. We provide a simplest model with SG $Pbam$ (No. 55) which exhibits CICE, and the exotic intertwined drumhead surface states, induced by double-band-inversions. Finally, we propose a series of material candidates that host butterfly-like CICE NLs, such as, ZrX$_2$ (X=P,As), GeTe$_5$Tl$_2$, CYB$_2$ and Al$_2$Y$_3$.
Most topological insulators discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped TI phases and the gapless TSMs. Recently, we have proposed a new family of TSMs in time-reversal invariant {\it spinless} systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semim…
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 (…
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…
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…
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…
We reveal a class of three-dimensional $d$-orbital topological materials in the antifluorite Cu$_2$S family. Derived from the unique properties of low-energy $t_{2g}$ states, their phases are solely determined by the sign of spin-orbit coupling (SOC): topological insulator for negative SOC, whereas topological semimetal for positive SOC; both having Dirac-cone surface states but with contrasting helicities. With broken inversion symmetry, the semimetal becomes one with a nodal box consisting of butterfly-shaped nodal lines that are robust against SOC. Further breaking the tetrahedral symmetry …
Weyl semimetal emerges as a new topologically nontrivial phase of matter, hosting low-energy excitations of massless Weyl fermions. Here, we present a comprehensive study of the type-II Weyl semimetal WP2. Transport studies show a butterfly-like magnetoresistance at low temperature, reflecting the anisotropy of the electron Fermi surfaces. The four-lobed feature gradually evolves into a two-lobed one upon increasing temperature, mainly due to the reduced relative contribution of electron Fermi surfaces compared to hole Fermi surfaces for the magnetoresistance. Moreover, angle-dependent Berry p…
ZrSiS is the most intensively studied topological nodal-line semimetal candidate, which is proposed to host multiple nodal lines in its bulk electronic structure. However, previous angle-resolved photoemission spectroscopy (ARPES) experiments with vacuum ultraviolet lights mainly probed the surface states. Here using bulk-sensitive soft X-ray ARPES, we acquire the bulk electronic states of ZrSiS without any interference from surface states. Our results clearly show two groups of three-dimensional bulk nodal lines located on high-symmetry planes and along high-symmetry lines in the bulk Brillou…
Topological semimetals in ferromagnetic materials have attracted enormous attention due to the potential applications in spintronics. Using the first-principles density functional theory together with an effective lattice model, here we present a new family of topological semimetals with a fully spin-polarized nodal loop in alkaline-metal monochalcogenide $MX$ ($M$ = Li, Na, K, Rb, Cs; $X$ = S, Se, Te) monolayers. The half-metallic ferromagnetism can be established in $MX$ monolayers, in which one nodal loop formed by two crossing bands with the same spin components is found at the Fermi energ…
The application of pressure has been demonstrated to induce intriguing phase transitions in topological nodal-line semimetals. In this work we analyze how uniaxial pressure affects the topological character of BaSn2 , a Dirac nodal-line semimetal in the absence of spin-orbit coupling. Using calculations based on the density functional theory and a model tight-binding Hamiltonian, we find the emergence of a second nodal line for pressures higher than 4 GPa. We examine the topological features of both phases demonstrating that a nontrivial character is present in both of them. Thus, providing ev…
We report the electronic properties of single crystals of candidate nodal-line semimetal CaAgP. The transport properties of CaAgP are understood within the framework of a hole-doped nodal-line semimetal. In contrast, Pd-doped CaAgP shows a drastic increase of magnetoresistance at low magnetic fields and a strong decrease of electrical resistivity at low temperatures probably due to weak antilocalization. Hall conductivity data indicated that the Pd-doped CaAgP has not only hole carriers induced by the Pd doping, but also high-mobility electron carriers in proximity of the Dirac point. Electric…
Nodal-loop semimetals are materials in which the conduction and valence bands cross on a one-dimensional loop in the reciprocal space. For the nodal-loop character to manifest in physical properties, it is desired that the loop is close to the Fermi level, relatively flat in energy, simple in its shape, and not coexisting with other extraneous bands. Here, based on the first-principles calculations, we show that the monoclinic CuTeO$_3$ is a realistic nodal-loop semimetal that satisfies all these requirements. The material features only a single nodal loop around the Fermi level, protected by …
Topological nodal-line semimetals support protected band crossings which form nodal lines or nodal loops between the valence and conduction bands and exhibit novel transport phenomena. Here we address the topological state of the nodal-line semimetal candidate material, CaCdSn, and report magnetotransport properties of its single crystals grown by the self-flux method. Our first-principles calculations show that the electronic structure of CaCdSn harbors a single nodal loop around the $Γ$ point in the absence of spin-orbit coupling (SOC) effects. The nodal crossings in CaCdSn are found to lie …
Based on first-principles study, we report the finding of a new topological semimetal LiBaBi in half-Heusler phase. The remarkable feature of this nonmagnetic, inversion-symmetry-breaking material is that it consists of only simple $s$- and $p$-block elements. Interestingly, the material is ordinary insulator in the absence of spin-orbit coupling (SOC) and becomes nodal-surface topological semimetal showing drumhead states when SOC is included. This is in stark contrast to other nodal-line and nodal-surface semimetals, where the extended nodal structure is destroyed once SOC is included. Impor…
NaAlSi and NaAlGe are isostructural and isoelectronic semimetals with topological nodal lines close to the Fermi level. Despite having virtually identical electronic structures, NaAlSi exhibits superconductivity below Tc = 6.8 K, whereas NaAlGe does not. We investigate NaAlGe by measuring its electrical resistivity, Hall effect, magnetic susceptibility, and heat capacity using single crystals. It is revealed that NaAlGe is not a simple semimetal but rather has an unusual ground state with a small pseudogap of approximately 100 K close to the Fermi level. We argue that the formation of the pseu…
We investigate systematically the bulk and surface electronic structure of the candidate nodal-line semimetal CaAgAs by angle resolved photoemission spectroscopy and density functional calculations. We observed a metallic, linear, non-$k_z$-dispersive surface band that coincides with the high-binding-energy part of the theoretical topological surface state, proving the topological nontriviality of the system. An overall downshift of the experimental Fermi level points to a rigid-band-like $p$-doping of the samples, due possibly to Ag vacancies in the as-grown crystals.
Based on first-principles calculations and symmetry analysis, we report that the three-dimensional (3D) nodal line (NL) semimetal phases can be realized in the lead dioxide family (\emph{$α$}-PbO$_2$ and \emph{$β$}-PbO$_2$) and its derivatives. The \emph{$β$}-PbO$_2$ features two orthogonal nodal rings around the Fermi level, protected by the mirror reflection symmetry. The effective model is developed and the related parameters are given by fitting with the HSE06 band structures. The NLs mainly come from the $p$ orbitals of the light element O and are rather robust against such tiny spin-orbi…
Topological semimetals represent a new class of quantum materials hosting Dirac/Weyl fermions. The essential properties of topological fermions can be revealed by quantum oscillations. Here we present the first systematic de Haas-van Alphen (dHvA) oscillation studies on the recently discovered topological Dirac nodal-line semimetal ZrSiS. From the angular dependence of dHvA oscillations, we have revealed the anisotropic Dirac bands in ZrSiS and found surprisingly strong Zeeman splitting at low magnetic fields. The Landé g-factor estimated from the separation of Zeeman splitting peaks is as lar…
Topological semimetals (TSMs) have attracted numerous attention due to their exotic physical properties and great application potentials. Silicon-based TMSs are of particularly importance because of their high abundance, nontoxicity and natural compatibility with current semiconductor industry. In this work, an ideal low-energy topological nodal-line semimetal (TNLSM) silicon (I4/mcm-Si$_{48}$) with a clean band crossing at Fermi level is screened from thousands of silicon allotropes by the transferable tight-binding and DFT-HSE calculations. The results of formation energy, phonon dispersion,…
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…
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.
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 …
Topological semimetals are characterized by protected crossings between conduction and valence bands. These materials have recently attracted significant interest because of the deep connections to high-energy physics, the novel topological surface states, and the unusual transport phenomena. While Dirac and Weyl semimetals have been extensively studied, the nodal-line semimetal remains largely unexplored due to the lack of an ideal material platform. In this paper, we report the magneto-transport properties of two nodal-line semimetal candidates CaAgAs and CaCdGe. First, our single crystallin…
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…
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…
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 past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal lines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS ex…
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…
The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the k space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the c axis, and magnetic field rotating in the ab plane. The extremal orbits identified through th…
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…
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$_2$.
A nodal-line semimetal phase which is enforced by the symmetries of the material is interesting from fundamental and application standpoints. We demonstrate that such a phase of matter can be engineered by a simple method: Introducing vacancies in certain configurations in common symmorphic materials leads to nonsymmorphic polymorphs with symmetry-enforced nodal lines which are immune to symmetry-preserving perturbations, such as spin-orbit coupling. Furthermore, the spectrum acquires also accidental nodal lines with enhanced robustness to perturbations. These phenomena are explained on the ba…
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…
PbTaSe$_2$ is a unique topological material, in which the number of nodal lines is expected to change at the structural transition between the lower temperature/pressure "L" phase and the higher temperature/pressure "H" phase. We report the anomalous Nernst effect attributed to the Berry curvature of nodal lines and its change with the structural transition. In the L phase, the Nernst coefficient ($S_{yx}$) shows the step-like magnetic field dependence reminiscent of the anomalous Nernst effect of nonmagnetic Dirac/Weyl semimetals. By applying hydrostatic pressure, we discovered that the ampli…
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…
