Topological Nodal Line Semimetals Research Articles

From topological nodal-line semimetals to quantum spin Hall insulators in tetragonal SnX monolayers (X=F, Cl, Br, I)

Abstract Two-dimensional (2D) topological materials have recently garnered significant interest due to their profound physical properties and promising applications for future quantum nanoelectronics. Achieving various topological states within one type of materials is, however, seldom reported. Based on first-principles calculations and tight-binding models, we investigate topological electronic states in a novel family of 2D halogenated tetragonal stanene (T-SnX, X = F, Cl, Br, I). All the four monolayers are found being unusual topological nodal-line semimetals (NLSs), protected by a glide mirror symmetry. When spin-orbit coupling (SOC) is turned on, T-SnF and TSnCl are still ascertained as topological NLSs due to the remaining band inversion, primarily composed of Sn pxy orbitals, while T-SnBr and T-SnI become quantum spin Hall insulators. The phase transition is ascribed to moving up in energy of Sn s orbitals and increasing of SOC strengths. The topology origin in the materials is uniformly rationalized through elementary band representations. The robust and diverse topological states found in the 2D T-SnX monolayers position them as an excellent material platform for the development of innovative topological electronics.

Nonsymmorphic symmetry protected nodal lines in layered topological semimetal Ta3GeTe6

Topological semimetals have garnered significant attention due to their distinctive physical properties. However, the ideal material platforms for studying these phenomena remain limited. Here, we report the synthesis and nontrivial topological properties of high-quality van der Waals material Ta3GeTe6. Angle-resolved photoemission spectroscopy studies performed systematically on the as-grown Ta3GeTe6 single crystal along different high-symmetry directions reveal the formation of two nodal lines located near 0.07 and 0.55 eV below EF along the loop X-U-R-S, which arises from band crossings protected by nonsymmorphic symmetry. Furthermore, the nodal lines near the Fermi level along the S-R and S-X directions exhibit a flat feature. The discovery of this material enriches the family of topological nodal line semimetals and provides a promising platform for future investigations into exotic electronic correlation phenomena and potential device applications.

Magnetoelectric transport properties in topological nodal-line semimetals

We study the impact of the size effect and the varying perpendicular magnetic field B on the transport properties of topological nodal-line semimetals (TNLSMs) by using the Landauer–Büttiker formula combined with the nonequilibrium Green’s function. We theoretically calculate the band structure, conductance G and local density of states (LDOS) of TNLSMs nanowire. The results show that both the size effect and the application of varying magnetic field play a crucial role in the electron transport of TNLSMs. We find that both the step height and width of the conductance plateau in TNLSMs are closely related to the size effect of the system. For the system with a large TNLSMs, the low energy states are dominated by flat bands, leading to a series of quantized conductance plateaus. Furthermore, it has been observed that the presence of a magnetic field leads to the formation of the Landau levels in the TNLSMs, which exhibit sensitivity to the direction of the applied magnetic field. A perpendicular magnetic field parallel to the transport direction forms a linearly dispersed Landau level in the TNLSMs system, which leads to an increase in its conductance G and LDOS. At the same time, when the magnetic field perpendicular to the transport direction is applied, a series of the Landau levels with the flat bands are formed near the Fermi energy level EF of the system, resulting in a significant decrease of its conductance G and a rapid decay of LDOS. These unique physical properties of the TNLSMs nanowire offer a wide range of the applications in magnetoelectric transport.

Magnetoinduced spin Nernst effect in topological nodal-line semimetals

The spin Nernst effect (SNE) of a topological nodal-line semimetals (TNLSMs) nanowire in a four-terminal cross-bar device is studied. Based on the nonequilibrium Green’s function method combining with the tight-binding Hamiltonian, the spin Nernst coefficients Ns3z, Ns3x and Ns3y of the two thermal transport models (kz-y case and kx-y case) under a perpendicular magnetic field are obtained. The traditional SNE describes the transverse voltage and spin current caused by the longitudinal thermal gradient. The transverse spin current is generated by the spin–orbit interaction rather than the perpendicular magnetic field. Here we find that the spin Nernst coefficients are equal to zero at the zero-magnetic field, but have finite values for non-zero magnetic fields in TNLSMs. The spin Nernst coefficient is closely related to the strength of the magnetic field and temperature. With the increase of the magnetic field strength, the peak height of the spin Nernst coefficient increases. These results indicate that the SNE is induced by the perpendicular magnetic field in the present TNLSMs system, which can be considered as an anomalous spin Nernst phenomenon. In addition, we find that Ns3z displays a series of peaks when the transmission coefficient TLR jumps from one integer plateau to another, and the spin Nernst coefficient Ns3i (i=x,y,z) is an odd function of the Fermi energy EF with Ns3z/x/y(−EF)=−Ns3z/x/y(EF) in connection mode kz-y. For the kx-y connection mode, due to the presence of the mass term m opening the energy gap, a sudden jump of the transmission coefficient TLR in the vicinity of the energy gap edge causes a very larger peak for the spin Nernst coefficient Ns3z/x/y, and the symmetrical properties of the spin Nernst coefficient Ns3z/x/y are completely broken in the strong magnetic field. These results indicate that the spin Nernst coefficient in TNLSMs strongly depends on the thermal gradient direction and the transverse lead connection direction. The spin Nernst coefficient in TNLSMs has strongly spatial anisotropy, which can be used as the characterization of the experimental detection of TNLSMs.

Quantum transport on the surfaces of topological nodal-line semimetals

Topological nodal-line semimetals are always characterized by the drumhead surface states at the open boundaries. In this paper we first derive an analytical expression for the surface Green’s function of a nodal-line semimetal. By making use of this result, we explore the charge and spin transport properties of a metallic chain on the surface of a nodal-line semimetal, as functions of the gate voltage applied on the top of the material. According to the size of the nodal loop, due to the coupling to the surface modes, the charge conductance in the chain is found to show a robust plateau at e2/h , or to exhibit multiple valleys at e2/h . Correspondingly, the spin polarization of the transmitted current is 100% at the plateau region, or exhibits multiple peaks at nearly 100% . This feature can be viewed as a transport signature of the topological nodal-line semimetals.

Anisotropic optical conductivities of model topological nodal-line semimetals

With the use of simple models, we investigated the optical conductivity of a nodal-line semimetal (NLSM) whose crossing of the conduction and valence bands near the origin (O point) in the () plane of a small cubic region can be adjusted by a parameter α. The Hamiltonian of the NLSM is based on the model for the low-lying energy bands. When α = 0, these bands touch each other along a continuous closed loop but the opening of a band gap corresponding to finite values of α and the varying of the carrier concentration can be adjusted. This provides a tunable semiconductor gap, around the O point and the valence and conduction bands can meet at a pair of points within the small cubic region in k space. The optical conductivity of such a NLSM is calculated using the Kubo formula with emphasis on the optical spectral weight redistribution, deduced from appropriate Green’s functions, brought about by changes in gap and chemical potential due to modifying α. We derived closed-form semi-analytic expressions for the longitudinal components of the optical conductivity for these model systems of NLSM and compare results for chosen α and chemical potential. We also present results for the heat capacity when the system is in thermal equilibrium for various chosen α and chemical potential.

Magnetic Field-Induced Resistivity Upturn and Non-Topological Origin in the Quasi-One-Dimensional Semimetals

As a layered topological nodal line semimetals hosting a quasi-one-dimensional (quasi-1D) crystalline structure, TaNiTe5 has attracted intensive attention. In this research, we analyze the low temperature (low-T) transport properties in single crystals of TaNiTe5. The high anisotropic transport behaviors confirm the anisotropic electronic structure in quasi-1D TaNiTe5. The resistivity shows a magnetic field-induced resistivity upturn followed by a plateau at low temperatures when current is parallel to the c axis and magnetic field is parallel to the b axis. An extremely large magnetoresistance of 1000% has been observed at 2 K and 13 T. Such a magnetic field-induced phenomenon can be generally explained using the topological theory, but we find that the behaviors are well accounted with the classical Kohler’s rule. The analysis of the Hall resistivity points to carrier compensation in TaNiTe5, fully justifying Kohler’s rule. Our findings imply that analogous magnetic field-induced low-T properties in nodal line semimetals TaNiTe5 can be understood in the framework of classical magnetoresistance theories that do not require to invoke the topological surface states.

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.

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 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.

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.

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.

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.

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.

Engineering second-order nodal-line semimetals by breaking PT symmetry and periodic driving

Hosting unique drumhead surface states enclosed by nodal lines, topological nodal-line semimetals exhibit novel transport phenomena. Thus, the exploration of topological semimetals with different nodal-line structures has attracted much attention. In this paper, we first find a second-order nodal line semimetal (SONLS), which has coexisting hinge Fermi arcs and drumhead surface states, in a $\mathcal{PT}$-symmetry broken system. Then, without changing the intrinsic parameters, we artificially create exotic hybrid-order nodal-line semimetals hosted by different quasienergy gaps and rich nodal-line structures including nodal chains, crossing ring nodal nets, crossing line nodes, and nodal nets by applying a periodic driving on our SONLS. Enriching the classification of topological semimetals, such Floquet engineered high tunability of the orders and nodal-line structures of the SONLS sets up a foundation for exploring its further applications.

Spin-dependent scattering induced by surface states in spin-degenerate nodal-line semimetal

The topological nodal-line semimetal is characterized by the conduction band and valence band of electrons crossing along a one-dimensional line or closed loop in reciprocal space, with each nodal line carrying Π Berry phase. According to bulk-boundary correspondence, there exist drumheadlike surface states with weak dispersion at the boundary of system, surrounded by the projection of nodal loops onto the surface Brillouin zone. In most of nodal-line semimetals, the spin orbit coupling effect is weak, leading to the absence of a spin configuration for surface states under the single-particle picture. However, the featured weak dispersion of drumheadlike surface states enhances the electron-electron interaction effect, which triggers out ferromagnetic instability and causes spin splitting in the surface state. In this work, spin-dependent scattering caused by ferromagnetic surface states in spin-degenerate nodal-line semimetals is considered. It is found that both spin-splitting drumheadlike surface states can lead to resonant spin-flipped reflection. This physical process is reflected in a double-peak structure in the spin conductance spectrum. Specifically, we deal with the scattering problem induced by surface states in normal metal and nodal-line semimetal heterojunctions by using the scattering matrix and the Green’s functions theory, respectively, and obtain consistent conclusions. The result points out that spin-degenerate nodal-line semimetal surface states can still lead to spin-dependent transport, which provides a new perspective for the detection and potential application of spintronics in nodal-line semimetals.

Nodeless superconductivity in the topological nodal-line semimetal CaSb2

CaSb2 is a topological nodal-line semimetal that becomes superconducting below 1.6 K, providing an ideal platform to investigate the interplay between topologically nontrivial electronic bands and superconductivity. In this work, we investigated the superconducting order parameter of CaSb2 by measuring its magnetic penetration depth change {\Delta}{\lambda}(T) down to 0.07 K, using a tunneling diode oscillator (TDO) based technique. Well inside the superconducting state, {\Delta}{\lambda}(T) shows an exponential activated behavior, and provides direct evidence for a nodeless superconducting gap. By analyzing the temperature dependence of the superfluid density and the electronic specific heat, we find both can be consistently described by a two-gap s-wave model, in line with the presence of multiple Fermi surfaces associated with distinct Sb sites in this compound. These results demonstrate fully-gapped superconductivity in CaSb2 and constrain the allowed pairing symmetry.

Giant phonon anomaly in topological nodal-line semimetals

The band topology has been revealed to bring a wide array of novel electronic transport phenomena, but its interaction with phonon properties remains largely unexplored. Here we propose that continuous topological singularities with variable Fermi wave vectors can lead to giant effects on phonon transport in nodal-line semimetals. Using first-principles calculations, we show that such an exotic feature is present in a well-known topological semimetal ZrSiSe, in which the unique nodal-line can guarantee considerable momentum-continuous phonons to satisfy the stringent condition of Kohn anomaly and thereby dramatically strengthen the electron-phonon coupling. Moreover, the momentum-continuous anomaly phonons with eight arms of vertical Fermi surface drive intense phonon-electron scattering that is even comparable with intrinsic phonon-phonon scattering, giving rise to a reduction of ∼45% on room temperature lattice thermal conductivity. Our findings not only uncover giant phonon anomaly in topological nodal-line semimetals but also provide guidance for exploring the vital influence of electronic band topology on thermal transport bridged by the electron-phonon coupling.

Quantum transport evidence of isolated topological nodal-line fermions

Anomalous transport responses, dictated by the nontrivial band topology, are the key for application of topological materials to advanced electronics and spintronics. One promising platform is topological nodal-line semimetals due to their rich topology and exotic physical properties. However, their transport signatures have often been masked by the complexity in band crossings or the coexisting topologically trivial states. Here we show that, in slightly hole-doped SrAs3, the single-loop nodal-line states are well-isolated from the trivial states and entirely determine the transport responses. The characteristic torus-shaped Fermi surface and the associated encircling Berry flux of nodal-line fermions are clearly manifested by quantum oscillations of the magnetotransport properties and the quantum interference effect resulting in the two-dimensional behaviors of weak antilocalization. These unique quantum transport signatures make the isolated nodal-line fermions in SrAs3 desirable for novel devices based on their topological charge and spin transport.

I4/mcm-Si48: An Ideal Topological Nodal-Line Semimetal

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, ab initio molecular dynamics and elastic constants show that I4/mcm-Si48 possesses good stability and is more stable than several synthetized silicon structures. By analyzing the symmetry, it reveals that the topological nodal-line of I4/mcm-Si48 is protected by mirror symmetry and inversion, time-reversal and SU(2) spin-rotation symmetries, and the nearly flat drumhead-like surface spectrum is observed. Furthermore, I4/mcm-Si48 exhibits exotic photoelectric properties and the Dirac fermions with high Fermi velocity (3.4$\sim$4.36$\times$10$^5$ m/s) can be excited by low energy photons. Our study provides a promising topological nodal-line semimetal for fundamental research and potential practical applications in semiconductor-compatible high-speed photoelectric devices.