Dirac Nodal-line Semimetals Research Articles

Synthesis and characterisation of Cu2Ge, a new two-dimensional Dirac nodal line semimetal

Dirac nodal line (DNL) semimetals are a novel class of topological materials in which the valence and conduction bands touch along lines in the reciprocal space, with linear dispersion. These materials attract a growing attention, but the experimental realizations for two-dimensional systems are sparse. This article reports the first experimental realization of a two-dimensional hexagonal monolayer Cu2Ge, grown by evaporation of Ge on a Cu(111) substrate. Through a combination of low-energy electron diffraction XPS and ARPES measurements, it is shown that the surface presents all characteristics expected from calculations for a free-standing Cu2Ge monolayer. More specifically, the preservation of the two concentric nodal lines around the Γ point indicates weak interactions between the Cu2Ge surface and its Cu(111) substrate, making it an ideal system for the study of DNL materials.

Ultrafast Carrier Relaxation Dynamics in a Nodal-Line Semimetal PtSn4.

Topological Dirac nodal-line semimetals host topologically nontrivial electronic structure with nodal-line crossings around the Fermi level, which could affect the photocarrier dynamics and lead to novel relaxation mechanisms. Herein, by using time- and angle-resolved photoemission spectroscopy, we reveal the previously inaccessible linear dispersions of the bulk conduction bands above the Fermi level in a Dirac nodal-line semimetal PtSn4, as well as the momentum and temporal evolution of the gapless nodal lines. A surprisingly ultrafast relaxation dynamics within a few hundred femtoseconds is revealed for photoexcited carriers in the nodal line. Theoretical calculations suggest that such ultrafast carrier relaxation is attributed to the multichannel scatterings among the complex metallic bands of PtSn4 via electron-phonon coupling. In addition, a unique dynamic relaxation mechanism contributed by the highly anisotropic Dirac nodal-line electronic structure is also identified. Our work provides a comprehensive understanding of the ultrafast carrier dynamics in a Dirac nodal-line semimetal.

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.

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.

Two-dimensional Dirac-line semimetals resistant to strong spin–orbit coupling

Several intriguing electronic phenomena and electric properties were discovered in three-dimensional Dirac nodal line semimetals (3D-DNLSM), which are, however, easy to be perturbed under strong spin-orbit coupling (SOC). While two-dimensional (2D) layers are an emerging material category with many advantages, 2D-DNLSM against SOC is yet to be uncovered. Here, we report a 2D-DNLSM in odd-atomic-layer Bi (the brick phase, another Bi allotrope), whose robustness against SOC is protected by the little co-group C_2v \times Z^T_2, the unique protecting symmetry we found in 2D.Specially, (4n+2) valence electrons fill the electronic bands in the brick phase, so that the Dirac nodal line with fourfold degeneracy locates across the Fermi level. There are almost no other low energy states close to the Fermi level; this allows to feasibly observe the neat DNLSM-induced phenomena in transport measurements without being affected by other bands. In contrast, Other VA-group elements also form the brick phases, but their DNL states are mixed with the extra states around the Fermi level. This unprecedented category of layered materials allows for exploring nearly isolated 2DDNL states in 2D.

Photonic Dirac nodal-line semimetals realized by a hypercrystal

Recently, the gapless Dirac/Weyl nodal semimetals with linear dispersion and topologically protected modes degeneracy are rapidly growing frontiers of topological physics. Especially, type-I, type-II, and critical type-III nodal semimetals are discovered according to the tilt angles of the Dirac/Weyl cones. Here, by introducing hyperbolic metamaterials into one-dimensional photonic crystals, we design the "hyper-crystal" and study the photonic four-fold degenerate Dirac nodal line semimetals (DNLSs) with two types of perpendicularly polarized waves. Moreover, the flexibly controlled photonic DNLSs using the phase compensation effect of hyperbolic dispersion are studied. Our results not only demonstrate a new platform to realize the various photonic DNLSs, where the optical polarization plays the role of electron spin in electronic DNLSs, but also may pave a novel way to explore the abundant Dirac/Weyl physics in the simple classical wave systems.

Quasiparticle interference observation of the topologically nontrivial drumhead surface state in ZrSiTe

Drumhead surface states that link together loops of nodal lines arise in Dirac nodal-line semimetals as a consequence of the topologically non-trivial band crossings. We used low-temperature scanning tunneling microscopy and Fourier-transformed scanning tunneling spectroscopy to investigate the quasiparticle interference (QPI) properties of ZrSiTe. Our results show two scattering signals across the drumhead state resolving the energy-momentum relationship through the occupied and unoccupied energy ranges it is predicted to span. Observation of this drumhead state is in contrast to previous studies on ZrSiS and ZrSiSe, where the QPI was dominated by topologically trivial bulk bands and surface states. Furthermore, we observe a near $\mathbf{k} \rightarrow -\mathbf{k}$ scattering process across the $\Gamma$-point, enabled by scattering between the spin-split drumhead bands in this material.

Prediction of novel two-dimensional Dirac nodal line semimetals in Al2B2 and AlB4 monolayers.

Topological semimetal phases in two-dimensional (2D) materials have gained widespread interest due to their potential applications in novel nanoscale devices. Despite the growing number of studies on 2D topological nodal lines (NLs), candidates with significant topological features that combine nontrivial topological semimetal phase with superconductivity are still rare. Herein, we predict Al2B2 and AlB4 monolayers as new 2D nonmagnetic Dirac nodal line semimetals with several novel features. Our extensive electronic structure calculations combined with analytical studies reveal that, in addition to multiple Dirac points, these 2D configurations host various highly dispersed NLs around the Fermi level, all of which are semimetal states protected by time-reversal and in-plane mirror symmetries. The most intriguing NL in Al2B2 encloses the K point and crosses the Fermi level, showing a considerable dispersion and thus providing a fresh playground to explore exotic properties in dispersive Dirac nodal lines. More strikingly, for the AlB4 monolayer, we provide the first evidence for a set of 2D nonmagnetic open type-II NLs coexisting with superconductivity at a rather high transition temperature. The coexistence of superconductivity and nontrivial band topology in AlB4 not only makes it a promising material to exhibit novel topological superconducting phases, but also a rather large energy dispersion of type-II nodal lines in this configuration may offer a platform for the realization of novel topological features in the 2D limit.

Double-bowl state in photonic Dirac nodal line semimetal

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 exhibits double-bowl states (DBS), which comprise two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole-spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.

Anisotropic lattice thermal conductivity in topological semimetal ZrGeX (X = S, Se, Te): a first-principles study

Topological semimetals have attracted significant attentions owing to their potential applications in numerous fields such as low-power electron devices and quantum computation, which are closely related to their thermal transport properties. In this work, the phonon transport properties of topological Dirac nodal-line semimetals ZrGeX (X = S, Se, Te) with the PbClF-type structures are systematically studied using the first-principles calculations combined with the Boltzmann transport theory. The obtained lattice thermal conductivities show an obvious anisotropy, which is caused by the layer structures of ZrGeX (X = S, Se, Te). The room-temperature lattice conductivity of ZrGeTe along c direction is found to be as low as 0.24 W m−1 K−1, indicating that it could be of great significance in the fields of thermal coating materials and solar cell absorber. In addition, we extract each phonon branch from group velocities, phonon scattering rates, Grüneisen parameters, and phase space volumes to investigate the mechanism underlying the low thermal conductivity. It is concluded that the difference of thermal conductivities of three materials may be caused by the number of scattering channels and the effect of anharmonic. Furthermore, the phonon mean free path along a direction is relatively longer. Nanostructures or polycrystalline structures may be effective to reduce the thermal conductivity and improve the thermoelectric properties.

Strain effects on band structure and Dirac nodal-line morphology of ZrSiSe

The Dirac nodal-line semimetals are new promising materials for technological applications due to their exotic properties, which originate from band structure dispersion and nodal-line behavior. We report strain effects on the band structure of ZrSiSe Dirac nodal-line semimetal through the density functional theory calculations. We found that the kz=0 Dirac nodal-line of ZrSiSe is robust to all strains under reasonable magnitude although there are significant changes in the band oscillation amplitude, bandgap, and band occupancy due to orbital interactions and the Fermi energy shift upon strains. We also found that the effective strains to tune the nodal-line and band structure are equi-biaxial tensile, uniaxial (100) tensile, and xz-plane shear strains.

Topological piezoelectric effect and parity anomaly in nodal line semimetals

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 length of the nodal ring, leading to a semi-quantized transport coefficient. Our theoretical proposal can be experimentally realized in various nodal line semimetals, such as CaAgP and Ca$_{_3}$P${_2}$.

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.

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.

Emergence of topological phases by stacking of two-dimensional lattices with nonsymmorphic symmetry

Topological semimetals have a variety of phases, whose Fermi surfaces can be nodal points, nodal lines and nodal loops. Here we construct four classes of 3D minimal models via vertically stacking a 2D nonsymmorphic lattice with and without breaking crystalline symmetries. As a result, four distinct topological phases can be generated in our minimal model, such as Dirac nodal line semimetals, Weyl nodal line semimetals, unconventional Weyl semimetals with topological charge , and weak topological insulators. Unexpectedly, Weyl nodal loops are generated without mirror symmetry protection, where nontrivial ‘drumhead’ surface states emerge within the loops.

Surface termination dependent quasiparticle scattering interference and magneto-transport study on ZrSiS

Dirac nodal line semimetals represent a new state of quantum matters in which the electronic bands touch to form a closed loop with linear dispersion. Here, we report a combined study on ZrSiS by density functional theory calculation, scanning tunnelling microscope (STM) and magneto-transport measurements. Our STM measurements reveal the spectroscopic signatures of a diamond-shaped Dirac bulk band and a surface band on two types of cleaved surfaces as well as a spin-polarized surface band at at E ∼ 0.6 eV on S-surface, consistent with our band calculation. Furthermore, we find the surface termination does not affect the surface spectral weight from the Dirac bulk bands but greatly affect the surface bands due to the change in the surface orbital composition. From our magneto-transport measurements, the primary Shubnikov–de-Haas frequency is identified to stem from the hole-type quasi-two-dimensional Fermi surface between Γ and X. The extracted non-orbital magnetoresistance (MR) contribution D(θ, H) yields a nearly H-linear dependence, which is attributed to the intrinsic MR in ZrSiS. Our results demonstrate the unique Dirac line nodes phase and the dominating role of Zr-d orbital on the electronic structure in ZrSiS and the related compounds.

Distinct multiple fermionic states in a single topological metal

Among the quantum materials that have recently gained interest are the topological insulators, wherein symmetry-protected surface states cross in reciprocal space, and the Dirac nodal-line semimetals, where bulk bands touch along a line in k-space. However, the existence of multiple fermion phases in a single material has not been verified yet. Using angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations, we systematically study the metallic material Hf2Te2P and discover properties, which are unique in a single topological quantum material. We experimentally observe weak topological insulator surface states and our calculations suggest additional strong topological insulator surface states. Our first-principles calculations reveal a one-dimensional Dirac crossing—the surface Dirac-node arc—along a high-symmetry direction which is confirmed by our ARPES measurements. This novel state originates from the surface bands of a weak topological insulator and is therefore distinct from the well-known Fermi arcs in semimetals.

Evidence for a Dirac nodal-line semimetal in SrAs3

Dirac nodal-line semimetals with the linear bands crossing along a line or loop, represent a new topological state of matter. Here, by carrying out magnetotransport measurements and performing first-principle calculations, we demonstrate that such a state has been realized in high-quality single crystals of SrAs3. We obtain the nontrivial π Berry phase by analysing the Shubnikov-de Haas quantum oscillations. We also observe a robust negative longitudinal magnetoresistance induced by the chiral anomaly. Accompanying first-principles calculations identifies that a single hole pocket enclosing the loop nodes is responsible for these observations.

PT-Symmetric Real Dirac Fermions and Semimetals.

Recently, Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here, we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the PT symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, 2D subtopological insulators, and Fermi arcs, are studied in the PT symmetric Dirac semimetals and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about PT symmetric Dirac nodal line semimetals.