Nodal-line Semimetals Research Articles

Topological Nodal Line Electrides: Realization of an Ideal Nodal Line State Nearly Immune from Spin–Orbit Coupling

Nodal line semimetals (NLSs) have attracted broad interest in current research. In most of existing NLSs, the intrinsic properties of nodal lines are greatly destroyed because nodal lines usually suffer sizable gaps induced by non-negligible spin-orbit coupling (SOC). In this work,we propose the topological nodal line electrides (TNLEs), which achieve electronic structures of nodal lines and electrides simultaneously, provide new insight on designing excellent NLSs nearly immune from SOC. Since the states near the Fermi level are most contributed by nonnucleus-bounded interstitial electrons, nodal lines in TNLEs manifest extremely small SOCinduced gap even possessing heavy elements. Especially, we propose the family of A2B (A = Ca, Sr, Ba; B= As, Sb, Bi) materials are realistic TNLEs with negligible SOC-induced gaps, which can play as excellent platforms to study the intrinsic properties of TNLEs

Out-of-plane transport in ZrSiS and ZrSiSe microstructures

A recent class of topological nodal-line semimetals with the general formula MSiX (M = Zr, Hf and X = S, Se, Te) has attracted much experimental and theoretical interest due to their properties, particularly their large magnetoresistances and high carrier mobilities. The plateletlike nature of the MSiX crystals and their extremely low residual resistivities make measurements of the resistivity along the [001] direction extremely challenging. To accomplish such measurements, microstructures of single crystals were prepared using focused ion beam techniques. Microstructures prepared in this manner have very well-defined geometries and maintain their high crystal quality, verified by the observations of quantum oscillations. We present magnetoresistance and quantum oscillation data for currents applied along both [001] and [100] in ZrSiS and ZrSiSe, which are consistent with the nontrivial topology of the Dirac line-node, as determined by a measured π Berry phase. Surprisingly, we find that, despite the three dimensional nature of both the Fermi surfaces of ZrSiS and ZrSiSe, both the resistivity anisotropy under applied magnetic fields and the in-plane angular dependent magnetoresistance differ considerably between the two compounds. Finally, we discuss the role microstructuring can play in the study of these materials and our ability to make these microstructures free-standing.

Band structure engineering of chemically tunable LnSbTe (Ln = La, Ce, Pr)

The ZrSiS family of compounds has garnered interest as Dirac nodal-line semimetals and offers an approach to study structural motifs coupled with electronic features, such as Dirac crossings. CeSbTe, of the ZrSiS/PbFCl structure type, is of interest due to its magnetically tunable topological states. The crystal structure consists of rare earth capped square nets separating the magnetic Ce–Te layers. In this work, we report the single crystal growth, magnetic properties, and electronic structures of LnSb1−xBixTe (Ln = La, Ce, Pr; x ∼ 0.2) and CeBiTe, adopting the CeSbTe crystal structure, and the implication of tuning the electronic properties by chemical substitution.

Topological Phases in Hydrogenated Group 13 Monolayers

Nontrivial topology of Dirac semimetals, Weyl semimetals, and nodal line semimetals (NLSMs) is delineated by the novel band crossings near the Fermi level in the bulk and the appearance of exotic surface states. Among them, NLSMs have gained immense interest because of the formation of a one-dimensional nodal ring near the Fermi level. Using density functional theory calculations and an effective two-band k·p model, we report that a two-dimensional (2D) NLSM phase can be hosted on hydrogen-passivated gallenene (gallenane) and on other group 13 elements, without inclusion of spin–orbit coupling (SOC). NLSM in these 2D systems is protected by the presence of crystalline symmetry along with inversion symmetry and time-reversal symmetry. In the presence of SOC, aluminane preserves its topological NLSM phase, while in other hydrogenated group 13 monolayers, a gap opens at the nodal point because of relatively stronger SOC effect. On applying tensile strain along with the inclusion of SOC, gallenane evolves int...

Observation of a topological nodal-line semimetal in YbMnSb2 through optical spectroscopy

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 the frequency-independent optical conductivity component arises from interband transitions near the Dirac nodal line, thus demonstrating that YbMnSb2 is a Dirac nodal line semimetal.

Fully spin-polarized open and closed nodal lines in β -borophene by magnetic proximity effect

Recently, the experimental realization of Dirac fermions in ${\ensuremath{\beta}}_{12}$- and ${\ensuremath{\chi}}_{3}$-boron sheets has attracted tremendous attention and simulated a broad exploration for the novel topologically nontrivial states in two-dimensional materials. Herein, by combining first-principles and tight-binding calculations, we discover a coexistence of open nodal arc and closed nodal loop produced by three-band touching in the recently synthesized $\ensuremath{\beta}$-boron sheet [Q. Zhong et al., Phys. Rev. Mater. 1, 021001 (2017)]. The symmetry analysis reveals that the nodal lines are protected by both time-reversal symmetry (TRS) and mirror-reflection symmetry (MRS). Intriguingly, when TRS is broken, e.g., via introducing magnetic proximity effect, a topological phase transition occurs, namely, the original spin-degenerate nodal line (loop) decays into fully spin-polarized nodal line (loop). Furthermore, when Rashba spin-orbit coupling (SOC) is turned on to break the MRS, spin-up and -down states are shifted toward opposite momentum directions, leading to the emergence of two new nodal loops around the $\mathrm{\ensuremath{\Gamma}}$ point. In addition, inclusion of both Rashba SOC and exchange field leads to band-gap opening of the Dirac points and nodal lines. Our findings not only reveal a form of nodal line in the $\ensuremath{\beta}$-boron sheet, but also offer an alternative approach to realize spin-polarized nodal line semimetals with promising applications in spintronic devices.

Dirac nodal lines and large spin Hall effect in the 6H -perovskite iridate Ba3TiIr2O9

Nodal line semimetals with symmetry protected band structure offer a platform for the investigation of a number of emerging quantum phenomena. Using first-principles calculation combined with symmetry analysis, we show that ${\mathrm{Ba}}_{3}{\mathrm{TiIr}}_{2}{\mathrm{O}}_{9}$ hosts a Dirac nodal line (DNL) along the $A\text{\ensuremath{-}}L$ direction of the Brillouin zone, protected by the glide reflection symmetry. In the presence of the spin-orbit coupling, even though the DNL along the $A\text{\ensuremath{-}}L$ direction is protected, DNLs along other directions as well as multiple nodal loops present in the system gap out. The gapped out Dirac nodal loops act as a source of spin Berry curvature, resulting in a large spin Hall conductivity ($\ensuremath{\approx}300$ $\frac{\ensuremath{\hbar}}{e}\phantom{\rule{4pt}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}{\phantom{\rule{0.16em}{0ex}}\mathrm{cm}}^{\ensuremath{-}1}$). This suggests the possible application of the material as a spin current detector.

Magnetic Susceptibility of Topological Semimetals

We give a review of theoretical and experimental results concerning the magnetic susceptibility of the Weyl, Dirac, and nodal-line semimetals. In particular, dependences of the susceptibility on the chemical potential, temperature, and magnitude of the magnetic field are discussed. The presented results show that the specific features of the magnetic susceptibility can serve as a hallmark of the topological semimetals, and hence magnetic measurements can be useful in investigating these materials.

Zero-energy Majorana edge modes in the three-dimensional Kitaev model

We obtain analytical solutions for zero-energy Majorana edge modes in the three-dimensional Kitaev model on the hyperhoneycomb lattice. We consider three types of edges (zigzag, bearded, and armchair) and find the regions in parameter space where each type of edge mode exists. In the gapless phase, we obtain edge-state solutions which are the drumhead surface states associated with nodal-line semimetals. We also find a correspondence between noninteracting complex fermions and Majorana fermions on bipartite lattices, which explains the equivalence of energy spectrum and eigenmodes of Kitaev model and a corresponding tight-binding model for complex fermions on the same lattice.

Tuning nodal line semimetals in trilayered systems

We investigate two-dimensional trilayered quantum systems with multi-orbital conduction bands by focusing on the role played by the layer degree of freedom in setting the character of nodal line semimetals. The layer index can label the electronic states where the electrons reside in the unit cell and can enforce symmetry constraints in the electronic structure by protecting bands crossing. We demonstrate that both the atomic spin-orbit coupling and the removal of local orbital degeneracy can lead to different types of electronic transitions with nodal lines that undergo a changeover from a loop structure enclosing the center of the Brillouin zone to pockets winding around multiple high symmetry points. We introduce and employ a criterion to find the nodal lines transitions. On the basis of a zero-dimensional topological invariant that, for a selected electronic and energy manifold, counts the number of bands below the Fermi level with a given layer inversion eigenvalue in high symmetry points of the Brillouin zone, one can determine the structure of the nodal loops and the ensuing topological transitions.

Topological Semimetals from First Principles

We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished on the basis of the degeneracy of the band crossings, their codimension (e.g., point or line nodes), and the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give rise to a wide range of distinct semimetal phases such as Dirac or Weyl semimetals, point or line node semimetals, and type I or type II semimetals. In this review we give a general description of various families of topological semimetals, with an emphasis on proposed material realizations from first-principles calculations. The conceptual framework for studying topological gapless electronic phases is reviewed, with a particular focus on the symmetry requirements of energy band crossings, and the relation between the different families of topological semimetals is elucidated. In addition to the paradigmatic Dirac and Weyl semimetals, we pay particular attention to more recent examples of topological semimetals, which include nodal line semimetals, multifold fermion semimetals, and triple-point semimetals. Less emphasis is placed on their surface state properties, their responses to external probes, and recent experimental developments.

Transport of Topological Semimetals

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 fermions. Experimental studies have shown that relativistic fermions can result in a rich variety of exotic transport properties, e.g., extremely large magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect. In this review, we first briefly introduce band structural characteristics of each topological semimetal phase, then review the current studies on quantum oscillations and exotic transport properties of various topological semimetals, and finally provide a perspective of this area.

Evidence for bulk nodal loops and universality of Dirac-node arc surface states in ZrGeXc ( Xc=S , Se, Te)

We have performed angle-resolved photoemission spectroscopy (ARPES) on layered ternary compounds ZrGeXc (Xc = S, Se, and Te) with square Ge lattices. ARPES measurements with bulk-sensitive soft-x-ray photons revealed a quasi-two-dimensional bulk-band structure with the bulk nodal loops protected by glide mirror symmetry of the crystal lattice. Moreover, high-resolution ARPES measurements near the Fermi level with vacuum-ultraviolet photons combined with first-principles band-structure calculations elucidated a Dirac-node-arc surface state traversing a tiny spin-orbit gap associated with the nodal loops. We found that this surface state commonly exists in ZrGeXc despite the difference in the shape of nodal loops. The present results suggest that the spin-orbit coupling and the multiple nodal loops cooperatively play a key role in creating the exotic Dirac-node-arc surface states in this class of topological line-node semimetals.

Weak Localization and Antilocalization in Nodal-Line Semimetals: Dimensionality and Topological Effects.

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 encircle the nodal loop, yielding a 3D weak localization effect. In contrast, for a long-range impurity potential, the electrons effectively diffuse in various 2D planes and the backscattering is dominated by the interference paths that encircle the nodal loop. The latter leads to weak antilocalization with a 2D scaling law. Our results are consistent with symmetry consideration, where the two regimes correspond to the orthogonal and symplectic classes, respectively. Furthermore, we present weak-field magnetoconductivity calculations at low temperatures for realistic experimental parameters and predict that clear scaling signatures ∝sqrt[B] and ∝-lnB, respectively. The crossover between the 3D weak localization and 2D weak antilocalization can be probed by tuning the Fermi energy, giving a unique transport signature of the nodal-line semimetal.

Bulk Fermi surface of the Weyl type-II semimetallic candidate NbIrTe4

Recently, a new group of layered transition-metal tetra-chalcogenides were proposed, via first principles calculations, to correspond to a new family of Weyl type-II semimetals with promising topological properties in the bulk as well as in the monolayer limit. In this article, we present measurements of the Shubnikov-de Haas (SdH) and de Haas-van Alphen effects under high magnetic fields for the type-II Weyl semimetallic candidate NbIrTe$_{4}$. We find that the angular dependence of the observed Fermi surface extremal cross-sectional areas agree well with our DFT calculations supporting the existence of Weyl type-II points in this material. Although we observe a large and non-saturating magnetoresistivity in NbIrTe$_{4}$ under fields all the way up to 35 T, Hall-effect measurements indicate that NbIrTe$_{4}$ is not a compensated semimetal. The transverse magnetoresistivity displays a four-fold angular dependence akin to the so-called butterfly magnetoresistivity observed in nodal line semimetals. However, we conclude that its field and this unconventional angular-dependence are governed by the topography of the Fermi-surface and the resulting anisotropy in effective masses and in carrier mobilities.

Visualizing Dirac nodal-line band structure of topological semimetal ZrGeSe by ARPES

As a member of ZrHM (H = Si/Ge/Sn; M = O/S/Se/Te) family materials, which were predicted to be the candidates of topological Dirac nodal-line semimetals, ZrGeSe exhibited particular properties, such as magnetic breakdown effect in the transport measurement, different from its other isostructural compounds, informing an unique topology of the electronic band structure. However, the related experimental research is insufficient until now. Here, we present a systematic study of the band structure and Fermi surfaces (FS) of ZrGeSe by angle-resolved photoemission spectroscopy (ARPES). Our Brillouin zone (BZ) mapping shows multiple Fermi pockets such as the diamond-shaped FS around the zone center Γ point, small electron pocket encircling the X point of the BZ, and lenses-shaped FS in the Γ-M direction. The obtained Fermi velocities and effective masses were up to 9.2 eV·Å and 0.42 me, and revealing an anisotropic electronic property along different high-symmetry k-space directions. Moreover, a kink appears near the Fermi level in the linear Dirac bands along the M-X direction, probably originated from the band hybridization and has not been reported in other ZrHM-type materials. Our findings support that the ZrHM-type material family can be a new platform on which to explore exotic states of quantum matter.

Three-Dimensional Crystalline Modification of Graphene in all-sp2 Hexagonal Lattices with or without Topological Nodal Lines.

The discovery of fullerenes, nanotubes, and graphene has ignited tremendous interest in exploring additional all-sp2 carbon networks with novel properties. Here we identify by ab initio calculations a new series of three-dimensional crystalline modification of carbon in all-sp2 bonding networks that comprise trigonal polycyclic benzenoid nanoflakes in a 2 n2 ( n ≥ 4) atom hexagonal cell. The resulting 32-, 50-, 72-, and 98-atom structures (termed as tr32, tr50, tr72, and tr98) in trigonal ( P3̅ m1) symmetry are characterized as the crystalline modification of ( n × n × 1)-graphene in AA stacking, which are energetically more stable than or comparable to the solid fcc-C60 and (5,5) carbon nanotube. Electronic band structure calculations show that tr72 without 2 d (1/3, 2/3, z) symmetric carbon atoms is a semiconductor, while tr32, tr50, and tr98 with 2 d carbon atoms are topological nodal-line semimetals comprising nodal lines on the H-K-H' edge in the hexagonal Brillouin zone, as a three-dimensional extension of the Dirac point at the K-point in two-dimensional graphene. The present findings establish an additional crystalline modification of graphene in the all-sp2 carbon allotrope family and offer insights into its outstanding structural and electronic properties.

Quantum transport in topological semimetals under magnetic fields (II)

We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative magnetoresistance in topological semimetals and topological insulators by using the semiclassical equations of motion with the nontrivial Berry curvature. We show that the negative magnetoresistance can exist without the chiral anomaly. At strong magnetic fields, we establish theories for the quantum oscillations in topological Weyl, Dirac, and nodal-line semimetals. We propose a new mechanism of 3D quantum Hall effect, via the "wormhole" tunneling through the Weyl orbit formed by the Fermi arcs and Weyl nodes in topological semimetals. In the quantum limit at extremely strong magnetic fields, we find that an unexpected Hall resistance reversal can be understood in terms of the Weyl fermion annihilation. Additionally, in parallel magnetic fields, longitudinal resistance dips in the quantum limit can serve as signatures for topological insulators.

Imbert-Fedorov shift in pseudospin−N/2 semimetals and nodal-line semimetals

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 topological fermions. The shift can also be interpreted as a consequence of the conservation of the total angular momentum. For the latter, if the NLSM has both time-reversal and inversion symmetries, the IF shift is zero; otherwise it could be finite. We take the NLSM with a vortex ring, which breaks both symmetries, as an example, and show that the IF shift can be used to detect topological Lifshitz transitions. Finally, we propose experimental designs to detect the IF shift.

Transport properties of topological nodal-line semimetal candidate CaAs3 under hydrostatic pressure**Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0401000 and 2016YFA0300604), the National Key Basic Research Program of China (Grant No. 2015CB921303), the Strategic Priority Research Program (B) of Chinese Academy of Sciences (Grant No. XDB07020100), and the National Natural Science Foundation of China

We report the transport properties of the CaAs3 single crystal, which has been predicted to be a candidate for topological nodal-line semimetals. At ambient pressure, CaAs3 exhibits semiconducting behavior with a small gap, while in some crystals containing tiny defects or impurities, a large “hump” in the resistivity is observed around 230 K. By applying hydrostatic pressure, the samples appear to a tendency towards metallic behavior, but not fully metallized up to 2 GPa. Further high pressure studies are needed to explore the topological characteristics for CaAs3.