Nodal-line Semimetals Research Articles

From Topological Nodal-Line Semimetal to Insulator in ABW-Ge4: A New Member of the Germanium Allotrope.

Topological semimetals have attracted much attention because of their excellent properties, such as ultra-high speed, low energy consumption quantum transport, and negative reluctance. Searching materials with topological semimetallic properties has become a new research field for Group-IV materials. Herein, using first-principles calculations and tight-binding modeling, we proposed a topological nodal-line semimetal ABW-Ge4 when spin-orbit coupling (SOC) is ignored, which is composed of pure germanium atoms in a zeolite framework ABW. It holds excellent dynamic and thermal stability. In its electronic band structure, there exists a stable Dirac linear band crossing near the Fermi energy level, which forms a closed ring in the kx = 0 plane of the Brillouin zone (BZ). Our symmetry analysis reveals that the nodal ring is protected by Mx mirror symmetry. Furthermore, by examining the slope index in all possible k paths through the considered Dirac point, we find that the band dispersion near the Dirac point is greatly anisotropic. In some direction, the Fermi velocity is even larger than that of graphene, being promising for the future ultra-high speed device. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with topological invariants Z2 = 1. Our findings not only identify a new Ge allotrope but also establish a promising topological material in Group-IV materials, which may have the desirable compatibility with the traditional semiconductor industry.

Electrochemical transport in Dirac nodal-line semimetals

Nodal-line semimetals are topological phases where the conduction and the valence bands cross each other along one-dimensional lines in the Brillouin zone, which are symmetry protected by either spatial symmetries or time-reversal symmetry. In particular, nodal lines protected by the combined symmetry exhibits the parity anomaly of 2D Dirac fermions. In this letter, we study the electrochemical transport in Dirac nodal-line semimetals by using the semiclassical Boltzmann equation approach. We derive a general formula for the topological current that includes both the Berry curvature and the orbital magnetic moment. We first evaluate the electrochemical current by introducing a small mass term (which could be induced by inversion-breaking uniaxial strain, pressure, or an external electric field) and apply it to the hexagonal pnictide CaAgP. The electrochemical current vanishes in the zero-mass limit. Introducing a tilting term that does not spoil symmetry that protects the nodal ring, we obtain a finite electrochemical current in the zero-mass limit, which can be regarded as a direct consequence of the parity anomaly. We show that the parity-anomaly–induced electrochemical transport is also present at nonzero temperatures.

Nernst effect in anisotropic four-terminal topological nodal-line semimetals

The Nernst effect is the transverse mode of thermoelectric transport, in which a longitudinal thermal gradient induces a transverse current in the conductor while under a perpendicular magnetic field. Here the Nernst effect in a mesoscopic topological nodal-line semimetals (TNLSMs) system of four-terminal cross-bar with the spin–orbit coupling under a perpendicular magnetic field is studied. The Nernst coefficient N c in two non-equivalen connection modes (k z –y mode and k x –y mode) is calculated based on the tight-binding Hamiltonian combined with the nonequilibrium Green’s function method. When the magnetic field is absent with φ = 0.0, the Nernst coefficient is exactly regardless of the temperature. When the magnetic field is not zero, the Nernst coefficient exhibits a series of densely oscillating peaks. The height of peak strongly depends on the magnetic field, and the Nernst coefficient is an even function of the Fermi energy satisfying the symmetrical property . The Nernst coefficient is also closely related to the temperature . When the temperature is very low (or ), the Nernst coefficient depends linearly on temperature. In the presence of a strong magnetic field, the Nernst coefficient shows peaks when the Fermi energy crosses the Landau levels. Under the weak magnetic field, the influence of spin–orbit coupling in TNLSMs materials on Nernst effect is very obvious. In the presence of the mass term, the PT-symmetry of the system is destroyed, the nodal ring of TNLSMs is broken and an energy gap will be opened. The Nernst coefficient N c has a large value in the energy gap, which is very promising for the application of the transverse thermoelectric transport.

Topological nodal line semimetal with large nodal ring in an all- sp2 hybridized carbon network formed by all-ten-membered carbon rings

Carbon can form versatile allotropes due to its multiple bonding connections and the prediction of new carbon structures and properties has long been a hot topic. In 1983, Hoffmann et al. [J. Am. Chem. Soc. 105, 4831 (1983)] have reported an all-$s{p}^{2}$ hybridized carbon allotrope with a 16-atom body-centered-tetragonal unit cell in $\mathrm{I}{4}_{1}/\mathrm{amd}$ (${D}_{4h}^{19}$) symmetry, which is dubbed as cT16 carbon in this work. Here we report by ab initio calculations a systematical study on the structural, energetic, dynamical, and electronic properties of cT16 carbon. Interestingly, cT16 carbon is linked with all-ten-membered carbon rings. The phonon band spectrum calculations confirm its dynamical stability and ab initio molecular dynamics simulations prove its thermal stability up to 900 K. Previously cT16 carbon was widely considered as a simple metallic carbon. However, our detailed electronic band structures calculations reveal that cT16 is actually a topological nodal line semimetal with a large closed nodal ring centering the high-symmetric $\mathrm{\ensuremath{\Gamma}}$ point. It nearly encloses the entire ${k}_{z}=0$ mirror plane, thus the drumheadlike surface bands can nearly cover the entire projected ($11\overline{1}$) surface Brillouin zone, which makes cT16 carbon an ideal nodal line semimetal. The simulated x-ray diffraction pattern of cT16 carbon matches well with one of the previously unexplained experimental peaks found in the diamond rich coatings grown on the stainless steel substrate. Our findings have provided insight for this well-known cT16 carbon, enriched the family of carbon allotropes with exotic topological electronic properties, suggested a viable route for its synthesis, and also provided an reasonable explanation for previous experimental data.

Topological states in the polymerized carbon nanotubes

In this work, we report by ab initio calculations a systematical study on the energetic, dynamical, and electronic properties of polymerized (2n+1,0) (n=2,3,4) sing wall carbon nanotubes, termed as CNT(5,0), CNT(7,0), and CNT(9,0) carbon. The total energy calculations show that the equilibrium energies of the three carbon allotropes are lower than or comparable to the previously proposed bct-C16, bco-C16, and ors-C16 carbon. Their dynamical stabilities have been confirmed with phonon band spectrum calculations and their thermal stabilities have been confirmed with ab initio molecular dynamics simulations. Despite their unified space group symmetries and similar bonding types, their electronic properties are distinct: CNT(5,0) and CNT(7,0) carbon are topological nodal line semimetals with nodal rings in kx=0 and kz=0 mirror planes respectively, while the CNT(9,0) carbon is a semiconductor. To understand their distinct electronic behaviors, we provide a systematical explanation from the real space crystalline structure perspective. Our work has enriched the family of carbon allotropes with exotic band topologies and provide insights for the relations between real space crystalline structures and momentum space band topologies.

Entanglement entropy as an order parameter for strongly coupled nodal line semimetals

Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which evades the standard Landau paradigm. In the case of Weyl semimetals, the anomalous Hall effect is a good non-local order parameter for the TQPT, as it is proportional to the separation between the Weyl nodes in momentum space. On the contrary, for nodal line semimetals (NLSM), the quest for an order parameter is still open. By taking advantage of a recently proposed holographic model for strongly-coupled NLSM, we explicitly show that entanglement entropy (EE) provides an optimal probe for nodal topology. We propose a generalized c-function, constructed from the EE, as an order parameter for the TQPT. Moreover, we find that the derivative of the renormalized EE with respect to the external coupling driving the TQPT diverges at the critical point, signaling the rise of non-local quantum correlations. Finally, we show that these quantum information quantities are able to characterize not only the critical point but also features of the quantum critical region at finite temperature.

Topological nodal lines in bulk and monolayer W2O3I4

By means of first-principles calculations, we study the topological nontrivial electronic structures and lattice dynamics of bulk and monolayer ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$. We find that both of them are nodal-line semimetals in the absence of spin-orbit coupling (SOC), in which the nodal lines are induced by the band inversion between conduction and valence bands contributed by W $d$ and I p orbitals. Moreover, ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$ bulk and monolayer exhibit excellent mechanical and thermal stability. By studying the external field modulation of topological nodal lines without SOC effect in monolayer ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$, we find that the nodal lines are extremely robust against the biaxial strain but destroyed under vertical electric field due to the breaking of horizonal mirror symmetry. It is studied that the SOC effect here is large and non-negligible, and after considering the SOC effect, ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$ bulk and monolayer undergo change of topological state from a topological nodal-line semimetal to a topological insulator. Our work not only extends the member of inorganic three-dimensional and two-dimensional topological semimetals library but also provides a prototype material candidate to investigate the double nodal-line surface states.

Robust three-dimensional type-II Dirac semimetal state in SrAgBi

Topological semimetals such as Dirac, Weyl or nodal line semimetals are widely studied for their peculiar properties including high Fermi velocities, small effective masses and high magnetoresistance. When the Dirac cone is tilted, exotic phenomena could emerge whereas materials hosting such states are promising for photonics and plasmonics applications. Here we present evidence that SrAgBi is a spin-orbit coupling-induced type-II three-dimensional Dirac semimetal featuring tilted Dirac cone at the Fermi energy. Near charge compensation and Fermi surface characteristics are not much perturbed by 7% of vacancy defects on the Ag atomic site, suggesting that SrAgBi could be a material of interest for observation of robust optical and spintronic topological quantum phenomena.

Dirac nodal line induced anomalous low-energy acoustic plasmons on beryllium (0001) surface

Beryllium is a simple hexagonal metal but exhibits anomalous low-energy acoustic plasmons on its (0001) surface, which are radically distinct from the conventional metal surface plasmons. Although the plasmons on Be(0001) have been extensively studied, the underlying mechanism remains elusive. Here, through first-principles calculations combined with model analysis, we unambiguously demonstrate that it is the topological Dirac nodal line induced surface states that result in the anomalous low-energy acoustic plasmons on Be(0001), rather than the commonly believed Shockley surface states. Our study not only clarifies the origin of the puzzling anomalous plasmons on Be(0001), but also provides a sound theoretical interpretation for the appearance of low-energy acoustic surface plasmons on the noble metal (111) surfaces. This work suggests that the topological nodal line semimetals offer a potential platform for obtaining low-energy acoustic plasmons.

Magnetotransport properties and Fermi surface topology of the nodal line semimetal InBi

In the present study, we have thoroughly characterized the 3D Fermi surface of a topological nodal line semimetal InBi via the Shubnikov--de Haas oscillations and density functional theory. The nitty-gritty of its full 3D Fermi surface has been discussed in detail. The Fermi surface topology and the Hall conductivity emphasized the carrier compensation as a driving force for the observed extremely high magnetoresistance. The magnetotransport revealed a unique magnetic-field-induced metal-semiconducting transition. The origin of such a phenomenon has been elaborated theoretically which has implications for layered topological nodal line semimetals with linearly dispersing bands.

Type‐II Dirac Nodal Lines in a Double‐Kagome‐Layered Semimetal

AbstractLorentz‐violating type‐II Dirac nodal line semimetals (DNLSs), hosting curves of band degeneracy formed by two dispersion branches with the same sign of slope, represent a novel state of matter. While being studied extensively in theory, convincing experimental evidence of type‐II DNLSs remain elusive. Recently, vanadium‐based kagome materials have emerged as a fertile ground to study the interplay between lattice symmetry and band topology. This work studies the low‐energy band structure of double‐kagome‐layered CsV8Sb12 and identifies it as a scarce type‐II DNLS protected by mirror symmetry. This work observes multiple DNLs consisting of type‐II Dirac cones close to or almost at the Fermi level via angle‐resolved photoemission spectroscopy (ARPES), which provides an electronic explanation for the nonsaturating magnetoresistance effect as observed. First‐principles theory analyses show that spin‐orbit coupling only opens a small gap, resulting in effectively gapless ARPES spectra, yet generating large spin Berry curvature. These type‐II DNLs, together with the interaction between a low‐energy van Hove singularity and quasi‐one‐dimensional band as observed in the same material, suggest CsV8Sb12 as an ideal platform for exploring novel transport properties.

Density functional theory investigation on the structural, mechanical, lattice dynamical and thermal properties of nodal-line semimetals CaAgX (X: P, As)

Density functional theory investigation on the structural, mechanical, lattice dynamical and thermal properties of nodal-line semimetals CaAgX (X: P, As)

Observation of gapless nodal-line states in NdSbTe

Lanthanide ($Ln$)-based systems in $\mathrm{ZrSiS}$-type nodal-line semimetals have been subjects of research investigations as grounds for studying the interplay of topology with possible magnetic ordering and electronic correlations that may originate from the presence of $Ln\phantom{\rule{0.28em}{0ex}}4f$ electrons. In this study, we carried out a thorough study of a $Ln\mathrm{SbTe}$ system, $\mathrm{NdSbTe}$, by using angle-resolved photoemission spectroscopy along with first-principles calculations and thermodynamic measurements. We experimentally detect the presence of multiple gapless nodal-line states, which is well supported by first-principles calculations. A dispersive and an almost nondispersive nodal line exist along the bulk $X\text{\ensuremath{-}}R$ direction. Another nodal line is present well below the Fermi level across the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}M$ direction, which is formed by bands with high Fermi velocity that seem to be sensitive to light polarization. Our study provides insight into the electronic structure of an alternative $Ln\mathrm{SbTe}$ material system that will aid towards understanding the connection of $Ln$ elements with topological electronic structures in these systems.

Nodal-line plasmons in ZrSiX ( X=S,Se,Te ) and their temperature dependence

Topological nodal-line semimetals gain extensive attention for their peculiar linear band crossings along closed lines in the Brillouin zone leading to various interesting properties. Here, we systematically study the nodal-line plasmons of prototypical nodal-line semimetals $\mathrm{ZrSi}X$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) by high-resolution electron energy loss spectroscopy, and first-principles calculations. In energy range from near- to mid-infrared frequencies, plasmons induced by the intraband correlations ($\ensuremath{\sim}0.8$ eV) and the interband correlations ($\ensuremath{\sim}0.3$ eV) of surface states related to the nodal-line electrons are universally observed in all the $\mathrm{ZrSi}X$ family. The bulk plasmon ($\ensuremath{\sim}0.6$ eV) is observed in ZrSiS but is indiscernible in both ZrSiSe and ZrSiTe owing to their stronger screening effect from the surface states and large interlayer distance. Although the plasmons in ZrSiS seem to be temperature independent, the frequencies of the intraband plasmons in ZrSiSe and ZrSiTe show large redshifts ($\ensuremath{\sim}10%$) with temperature increasing from 30 K to room temperature, which can be ascribed to the prominent thermal occupation effect of nodal-line electrons when the Fermi level is close to the nodal line.

(Ann. Phys. 4/2023)

Annalen der PhysikVolume 535, Issue 4 2370007 Cover PictureFree Access (Ann. Phys. 4/2023) First published: 13 April 2023 https://doi.org/10.1002/andp.202370007AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract Quantum Pumping When quasiparticles of Weyl/multi-Weyl and nodal-line semimetals are subjected to a time-periodic potential well, the presence of the oscillating potential of frequency ω creates equispaced Floquet side-bands. Using the Floquet theory and the scattering matrix approach, in the zero-temperature non-adiabatic pumping limit, characteristic Fano resonance patterns are found in the transmission coefficients, which depend on the nature of the dispersion. See article number 2200460 for more details. Volume535, Issue4April 20232370007 RelatedInformation

Theoretical analysis of anisotropic upper critical field of superconductivity in nodal-line semimetals

We study the properties of the upper critical field of superconductivity in nodal-line semimetals in a continuous model, which has a nodal line on the ${k}_{z}=0$ plane. Using the semiclassical Green's function method, we calculate the upper critical field for the two limiting cases: the dirty limit with many impurities and the clean limit with few impurities. The results show the large anisotropy of the magnitude of the upper critical field and the unusual temperature dependence. The obtained results are compared with recent experimental data of ${\mathrm{PbTaSe}}_{2}$.

Plasmons in a two-dimensional nonsymmorphic nodal-line semimetal

Recent experiments have established a type of nonsymmorphic symmetry-protected nodal lines in the family of two-dimensional (2D) composition-tunable materials ${\mathrm{NbSi}}_{x}{\mathrm{Te}}_{2}$. Here, we theoretically study the plasmonic properties of such nonsymmorphic nodal-line semimetals. We show that the nonsymmorphic character endows the plasmons with extremely strong anisotropy. There exist both intraband and interband plasmon branches. The intraband branch is gapless and has a ${q}^{1/2}$ dispersion. It is most dispersive and is independent of carrier density in direction normal to the nodal line, whereas along the nodal line, its dispersion is largely suppressed and its frequency scales linearly with carrier density. The interband branches are gapped and their long-wavelength limits are connected with Van Hove singularities of the band structure. We find that the single-particle excitations are strongly suppressed in such systems, which decreases the Landau damping of plasmons. These characters are further verified by first-principles calculations on 2D ${\mathrm{NbSi}}_{x}{\mathrm{Te}}_{2}$. Interesting features in static screening of charged impurity are also discussed. Our result reveals characteristic plasmons in a class of nonsymmorphic topological semimetals and offers guidance for its experimental detection and possible applications.

Competition-induced sign reversal of Casimir-Lifshitz torque: Investigation of topological nodal-line semimetals

The dispersion of quasiparticles in topological node-line semimetals is significantly different in different directions. In a certain direction, the quasiparticles behave like relativistic particles with constant velocity. In other directions, they act as two-dimensional electron gas. The competition between relativistic and nonrelativistic dispersions can induce a sign reversal of Casimir-Lifshitz torque. Three different approaches can be applied to generate this sign reversal, i.e., tuning the anisotropic parameter or chemical potential in node-line semimetal, changing the distance between this material and substrate birefringence. Detailed calculations are illustrated for the system with topological node-line semimetal Ca$_3$P$_2$ and liquid crystal material 4-cyano-4-n-pentylcyclohexane-phenyl.

Symmetry-engineered nodal lines and hourglass fermions in patterned two-dimensional electron gas

In most cases, the formation of topological quantum states requires intrinsic crystalline symmetry to protect either discrete or continuous degeneracies in real materials, which greatly hinders their realization in practice. Patterned two-dimensional electron gas (2DEG), on the other hand, has become a very effective external means to manipulate the symmetry to whatever we want. Here, taking nonsymmorphic symmetries as the focus of attention, based on patterned 2DEG decoration, we reveal rich band-crossing features in two-dimensional systems. It is demonstrated that in the presence of intrinsic spin-orbital coupling (SOC), wallpaper groups $p2mg,p2gg$, and $p4mg$ possess fourfold-degenerate Dirac nodal lines, and if Rashba SOC is further considered, the fourfold-degenerate nodal lines disappear and hourglass Weyl fermions then emerge. Our results not only afford an attractive route for designing robust nodal-line and hourglass Weyl semimetals in reality, but also pave the way for designing ideal macroscale materials through rational extrinsic symmetry engineering.

Negative transverse magnetoresistance due to the negative off-diagonal mass in linear dispersion materials

This study calculated the magnetoresistance (MR) in the Dirac electron system, Dresselhaus–Kip–Kittel (DKK) model, and nodal-line semimetals based on the semiclassical Boltzmann theory, with particular focus on the detailed energy dispersion structure. The negative off-diagonal effective-mass was found to induce negative transverse MR owing to the energy dispersion effect. The impact of the off-diagonal mass was more prominent in case of a linear energy dispersion. Further, Dirac electron systems could realize negative MR even if the Fermi surface was perfectly spherical. The obtained negative MR in the DKK model may explain the long-standing mystery in p-type Si.