Dirac Nodes Research Articles

Two-dimensional Tunable Dirac/Weyl Semimetal in Non-Abelian Gauge Field

Three-dimensional(3D) Weyl semimetal(WSM) with linear energy spectra has attracted significant interest. Especially they have been observed experimentally in several solid materials with the breaking of inversion symmetry. Here we predict a new family of particle-hole({mathscr{C}}) invariant 2D WSMs in the non-Abelian gauge field, which can emerge in the low energy bands being close to Fermi energy (dubbed Weyl-I) and the high energy bands being away from Fermi energy (dubbed Weyl-II), only when the time-reversal symmetry({mathscr{T}}) of the 2D Dirac semimetal is broken in the presence of in-plane Zeeman fields. Moreover, a 2D Dirac node can split into a pair of Weyl nodes showing the same Berry phase, and the 2D WSM, being protected by {mathscr{T}} symmetry, exhibits four Weyl-I nodes, whose energies are invariant with the variation of the magnetic field. The corresponding Fermi velocity and Berry connection have been calculated. Based on the 2D WSMs, we also examine inhomogeneous pairings of attractive Fermi gases and find a new kind of the LO states with the beat frequency. This 2D WSM provides a realistic and promising platform for exploring and manipulating exotic Weyl physics, which may increase the experimental feasibility in the context of ultracold atoms.

Reorientation of antiferromagnetism in cobalt doped FeSn

FeSn is an itinerant antiferromagnet that hosts electronic Dirac states and ordered magnetic moments lying within its Fe Kagome-lattice planes. We present magnetization measurements of single crystals of $({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})\text{Sn}$, revealing the evolution and suppression of this magnetic order with Co substitution. We interpret the dramatic changes in magnetic anisotropy to indicate a reorientation of the moments from perpendicular to parallel to the hexagonal $c$ axis and confirm this with neutron diffraction. It has been proposed that the Dirac nodes observed in FeSn should become gapped if the moments rotate as our data suggests. We identify Co-substituted compositions that adopt both antiferromagnetic configurations at different temperatures. This system provides a unique opportunity to study how the details of magnetic order impact Dirac electron states.

Signatures for spinons in the quantum spin liquid candidate Ca10Cr7O28

We present new experimental low-temperature heat capacity and detailed dynamical spin-structure factor data for the quantum spin liquid candidate material Ca$_{10}$Cr$_7$O$_{28}$. The measured heat capacity shows an almost perfect linear temperature dependence in the range $0.1$ K $\lesssim T\lesssim0.5$ K, reminiscent of fermionic spinon degrees of freedom. The spin structure factor exhibits two energy regimes of strong signal which display rather different but solely diffuse scattering features. We theoretically describe these findings by an effective spinon hopping model which crucially relies on the existence of strong ferromagnetically coupled triangles in the system. Our spinon theory is shown to naturally reproduce the overall weight distribution of the measured spin structure factor. Particularly, we argue that various different observed characteristic properties of the spin structure factor and the heat capacity consistently indicate the existence of a spinon Fermi surface. A closer analysis of the heat capacity at the lowest accessible temperatures hints towards the presence of weak $f$-wave spinon pairing terms inducing a small partial gap along the Fermi surface (except for discrete nodal Dirac points) and suggesting an overall $\mathbb{Z}_2$ quantum spin liquid scenario for Ca$_{10}$Cr$_7$O$_{28}$.

Observation of bulk states and spin-polarized topological surface states in transition metal dichalcogenide Dirac semimetal candidate NiTe2

Using spin- and angle- resolved photoemission spectroscopy (spin-ARPES) together with ${\it ab~initio}$ calculations, we demonstrate the existence of a type-II Dirac semimetal state in NiTe$_2$. We show that, unlike PtTe$_2$, PtSe$_2$, and PdTe$_2$, the Dirac node in NiTe$_2$ is located in close vicinity of the Fermi energy. Additionally, NiTe$_2$ also hosts a pair of band inversions below the Fermi level along the $\Gamma-A$ high-symmetry direction, with one of them leading to a Dirac cone in the surface states. The bulk Dirac nodes and the ladder of band inversions in NiTe$_2$ support unique topological surface states with chiral spin texture over a wide range of energies. Our work paves the way for the exploitation of the low-energy type-II Dirac fermions in NiTe$_2$ in the fields of spintronics, THz plasmonics and ultrafast optoelectronics.

Large transverse thermoelectric figure of merit in a topological Dirac semimetal

Thermoelectric (TE) conversion in conducting materials is of eminent importance for providing renewable energy and solid-state cooling. Although traditionally, the Seebeck effect plays a key role for the TE figure of merit zST, it encounters fundamental constraints hindering its conversion efficiency. Most notably, there are the charge compensation of electrons and holes that diminishes this effect, and the intertwinement of the corresponding electrical and thermal conductivities through the Wiedemann-Franz (WF) law which makes their independent optimization in zST impossible. Here, we demonstrate that in the Dirac semimetal Cd3As2 the Nernst effect, i.e., the transverse counterpart of the Seebeck effect, can generate a large TE figure of merit zNT. At room temperature, zNT = 0.5 in a small field of 2 T; it significantly surmounts its longitudinal counterpart zST for any field and further increases upon warming. A large Nernst effect is generically expected in topological semimetals, benefiting from both the bipolar transport of compensated electrons and holes and their high mobilities. In this case, heat and charge transport are orthogonal, i.e., not intertwined by the WF law anymore. More importantly, further optimization of zNT by tuning the Fermi level to the Dirac node can be anticipated due to not only the enhanced bipolar transport, but also the anomalous Nernst effect arising from a pronounced Berry curvature. A combination of the former topologically trivial and the latter nontrivial advantages promises to open a new avenue towards high-efficient transverse thermoelectricity.

Large Variation of Dirac Semimetal State in Perovskite CaIrO_{3} with Pressure-Tuning of Electron Correlation.

The impact of electron correlation on the Dirac semimetal state is investigated for perovskite CaIrO_{3} in terms of the magnetotransport properties under varying pressures. The reduction of electron correlation with a pressure of 1GPa enhances the Fermi velocity as much as 40%, but it reduces the mobility by an order of magnitude by detuning the Dirac node from the Fermi energy. Moreover, the giant magnetoresistance at the quantum limit due to the one-dimensional confinement of Dirac electrons is critically suppressed under pressure. These results indicate that the electron correlation is a crucial knob for controlling the transport of a correlated Dirac semimetal.

Photon-Induced Weyl Half-Metal Phase and Spin Filter Effect from Topological Dirac Semimetals.

Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as Na_{3}Bi and Cd_{2}As_{3}, are regarded as carrying the Z_{2} topological charge in addition to the chiral charge. We study the Floquet phase transition of Z_{2} topological DSMs subjected to a beam of circularly polarized light. Owing to the resulting interplay of the chiral and Z_{2} charges, the Weyl nodes are not only chirality dependent but also spin dependent, which constrains the behavior in creation and annihilation of the pair of Weyl nodes. Interestingly, we find a novel phase: One spin band is in the Weyl semimetal phase while the other is in the insulator phase, and we dub it the Weyl half-metal (WHM) phase. We further study the spin-dependent transport in a Dirac-Weyl semimetal junction and find a spin filter effect as a fingerprint of the existence of the WHM phase. The proposed spin filter effect, based on the WHM bulk band, is highly tunable in a broad parameter regime and robust against magnetic disorder, which is expected to overcome the shortcomings of the previously proposed spin filter based on the topological edge or surface states. Our results offer a unique opportunity to explore the potential applications of topological DSMs in spintronics.

Interacting topological bound states and Majorana fermions in strained nodal superconductors

Landau levels (LL) have been predicted to emerge in systems with Dirac nodal points under applied non-uniform strain. We consider 2D, $d_{xy}$ singlet (2D-S) and 3D $p \pm i p$ equal-spin triplet (3D-T) superconductors (SCs). We demonstrate the spinful Majorana nature of the bulk gapless zeroth-LLs. Strain along certain directions can induce two topologically distinct phases in the bulk, with zeroth LLs localized at the the interface. These modes are unstable toward ferromagnetism for 2D-S cases. Emergent real-space Majorana fermions in 3D-T allow for more exotic possibilities.

Determination of the crystal field splitting energy in Cd3As2 using magnetooptics

Symmetry considerations are of extreme importance to the topological properties of crystals. A crystal field splitting {\delta} yields Dirac nodes near the Brillouin zone center in Cd3As2, but its value has yet to be determined with precision. We study the band structure of Cd3As2 using magnetooptical infrared spectroscopy measurements on epilayers with low carrier density grown by molecular beam epitaxy. By combining angular dependent cyclotron resonance with Landau level spectroscopy measurements in the Faraday geometry, we determine that {\delta} is positive and equal to 15+/-5 meV in Cd3As2. Our results lead to a more accurate knowledge of the details of the band structure of this Dirac semimetal such as the position its Dirac nodes in momentum space and their splitting into Weyl nodes under a magnetic field.

Topological band crossings in epitaxial strained SnTe

Epitaxial SnTe (111) is grown by molecular-beam epitaxy on $\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{3}$ substrates. Structural evaluation indicates that SnTe deviates from cubic due to in-plane compressive strain, which induces significant changes in the electronic band structure. More specifically, a pair of gapless crossings between the two uppermost valence bands occurs in $k$ space along the out-of-plane \ensuremath{\Gamma}Z direction of the Brillouin zone, associated with a band inversion, thus defining topological three-dimensional Dirac nodes. Combined first-principles calculations and angle-resolved photoelectron spectroscopy reveal an overtilted Dirac cone indicating that the crossing is a topological type-III Dirac node at the borders between type-I and type-II Dirac nodes.

Magnetotransport properties of compensated semimetal HfB2 with high-density light carriers

We present a detailed magnetotransport study on HfB2, a possible topological nodal-line semimetal. HfB2 exhibits field-induced resistivity upturn and plateau behaviors at low temperature and high field, accompanying rather large magnetoresistance. The analysis of the field dependence of Hall and longitudinal resistivity shows that there are two kinds of carriers (electrons and holes) with almost same carrier concentrations and rather high mobilities in HfB2. Above field-induced phenomena can be well explained by using the two-band model with compensation condition. Even the carrier concentration is significantly high (∼1.8 1021 cm−3) in HfB2, much larger than other known topological semimetals with discrete Dirac nodal points, the electron-type carriers still have relatively small effective masses. In contrast to ZrB2, the slightly increased effective mass in HfB2 manifests the effect of enhanced spin–orbit coupling due to the large atomic number of Hf.

Underlying Topological Dirac Nodal Line Mechanism of the Anomalously Large Electron-Phonon Coupling Strength on a Be (0001) Surface.

Beryllium has recently been discovered to harbor a Dirac nodal line (DNL) in its bulk phase and the DNL-induced nontrivial surface states (DNSSs) on its (0001) surface, rationalizing several already-existing historic puzzles [Phys. Rev. Lett. 117, 096401 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.096401]. However, to date the underlying mechanism as to why its (0001) surface exhibits an anomalously large electron-phonon coupling effect (λ_{e-ph}^{s}≈1.0) remains unresolved. Here, by means of first-principles calculations, we show that the coupling of the DNSSs with the phononic states mainly contributes to its novel surface e-ph enhancement. Besides the fact that the experimentally observed λ_{e-ph}^{s} and the main Eliashberg coupling function (ECF) peaks are reproduced well in our current calculations, we decompose the ECF α^{2}F(k,q;v) and the e-ph coupling strength λ(k,q;v) as a function of each electron momentum (k), each phonon momentum (q), and each phonon mode (v), evidencing the robust connection between the DNSSs and both α^{2}F(k,q;v) and λ(k,q;v). The results reveal the strong e-ph coupling between the DNSSs and the phonon modes, which contributes over 80% of the λ_{e-ph}^{s} coefficient on the Be (0001) surface. It highlights that the anomalously large e-ph coefficient on the Be (0001) surface can be attributed to the presence of its DNL-induced DNSSs, clarifying the long-debated mechanism.

Si-Cmma: A silicon thin film with excellent stability and Dirac nodal loop

Silicon thin film with both remarkable stability and graphenelike properties attract many research interests in materials science and condensed matter physics. In this paper, two new two-dimensional silicon allotropes (Si-Cmma and Si-Pmma) with excellent energetic stability and positive dynamical stability are proposed and investigated by first-principles calculations. Si-Pmma possesses the energy of about 203 meV/atom lower than that of silicene and it is a normal metallic phase. Si-Cmma is of about 198 meV/atom lower than silicene in energy and it is confirmed to be a nodal loop semimetallic material. Symmetry analysis reveals that the nodal loop in Si-Cmma is protected by the glide mirror and it belongs to class AI $+$ R of Altland-Zirnbauer symmetry classes. A further three-band $k\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{p}$ model is constructed to understand the formation of the nodal loop and its strong anisotropy.

Tip-induced superconductivity coexisting with preserved topological properties in line-nodal semimetal ZrSiS

ZrSiS was recently shown to be a new material with topologically non-trivial band structure that exhibits multiple Dirac nodes and a robust linear band dispersion up to an unusually high energy of 2 eV. Such a robust linear dispersion makes the topological properties of ZrSiS insensitive to perturbations like carrier doping or lattice distortion. Here, we show that a novel superconducting phase with a remarkably high of 7.5 K can be induced in single crystals of ZrSiS by a non-superconducting metallic tip of Ag. From first-principles calculations, we show that the observed superconducting phase might originate from a dramatic enhancement of density of states due to the presence of a metallic tip on ZrSiS. Our calculations also show that the emerging tip-induced superconducting phase co-exists with the well preserved topological properties of ZrSiS.

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.

Interplay of Dirac Nodes and Volkov-Pankratov Surface States in Compressively Strained HgTe

Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Due to the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.

Excitonic effects in twisted bilayer graphene

In the present work, we consider the excitonic effects in the twisted bilayer graphene (tBLG) within the rotated bilayer Hubbard model. Both, intralayer and interlayer Coulomb interactions have been considered and the half-filling condition is imposed for the electronic densities is both layers of the bilayer. We calculate the excitonic pairing gap parameter and the chemical potential for different twist angles and different values of the interlayer Coulomb interaction parameter. Furthermore, we show the appearance of the electronic flat bands in the electronic band structure, mediated by the excitonic effects. We show that there is a doubling effect of the Dirac's $K$-point at the low interaction limit and one of Dirac's nodes is stable and the other one changes its position as a function of rotation angle. At the large twist angle limit, there appear two additional Dirac-like nodes at the $M$-point in the Brillouin zone. We show the excitonic red-shift effect of the principal Dirac's point $K$, in the low interaction limit, while, at the strong interactions, we get also the blue-shift effect at the $M$-point. Apart from the mentioned effects, the theory evaluated here predicts a metal-semiconductor transition in the tBLG system when augmenting the interlayer Coulomb interaction parameter.

Dimensional Crossover and Topological Phase Transition in Dirac Semimetal Na3Bi Films

Three-dimensional (3D) topological Dirac semimetal, when thinned down to 2D few layers, is expected to possess gapped Dirac nodes via quantum confinement effect and concomitantly display the intriguing quantum spin Hall (QSH) insulator phase. However, the 3D-to-2D crossover and the associated topological phase transition, which is valuable for understanding the topological quantum phases, remain unexplored. Here, we synthesize high-quality Na3Bi thin films with √3 × √3 reconstruction on graphene and systematically characterize their thickness-dependent electronic and topological properties by scanning tunneling microscopy/spectroscopy in combination with first-principles calculations. We demonstrate that Dirac gaps emerge in Na3Bi films, providing spectroscopic evidence of dimensional crossover from a 3D semimetal to a 2D topological insulator. Importantly, the Dirac gaps are revealed to be of sizable magnitudes on three and four monolayers (72 and 65 meV, respectively) with topologically nontrivial edge states. Moreover, the Fermi energy of a Na3Bi film can be tuned via a certain growth process, thus offering a viable way for achieving charge neutrality in transport. The feasibility of controlling Dirac gap opening and charge neutrality enables realizing intrinsic high-temperature QSH effect in Na3Bi films and achieving potential applications in topological devices.

Prediction of threefold fermions in a nearly ideal Dirac semimetal BaAgAs

Materials with triply-degenerate nodal points in their low-energy electronic spectrum produce crystalline-symmetry-enforced three-fold fermions, which conceptually lie between the two-fold Weyl and four-fold Dirac fermions. Here we show how a silver-based Dirac semimetal BaAgAs realizes three-fold fermions through our first-principles calculations combined with a low-energy effective $\mathbf{k.p}$ model Hamiltonian analysis. BaAgAs is shown to harbor triply-degenerate nodal points, which lie on its $C_{3}$ rotation axis, and are protected by the $C_{6v}$($C_2\otimes C_{3v}$) point-group symmetry in the absence of spin-orbit coupling (SOC) effects. When the SOC is turned on, BaAgAs transitions into a nearly-ideal Dirac semimetal state with a pair of Dirac nodes lying on the $C_{3}$ rotation axis. We show that breaking inversion symmetry in the BaAgAs$_{1-x}$P$_x$ alloy yields a clean and tunable three-fold fermion semimetal. Systematic relaxation of other symmetries in BaAgAs generates a series of other topological phases. BaAgAs materials thus provide an ideal platform for exploring tunable topological properties associated with a variety of different fermionic excitations.

Surface states of strained thin films of the Dirac semimetal Cd3As2

We report on the growth and transport properties of strained thin films of the three-dimensional Dirac semimetal ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$. Epitaxial heterostructures, consisting of (112)-oriented ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ films, are grown on nearly lattice matched $({\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{In}}_{x})\mathrm{Sb}$ buffer layers on (111) GaAs substrates by molecular beam epitaxy. The epitaxial coherency strain breaks the fourfold rotational symmetry, which protects the bulk Dirac nodes in ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$. All strained films exhibit the quantum Hall effect with most carriers residing in the two-dimensional states, irrespective of the sign of the biaxial stress. The Hall mobility monotonically increases as the biaxial stress is changed from compressive towards tensile. Furthermore, pronounced anisotropy is seen in the transport properties. The results show that the quantum Hall effect, which is quite similar to that of unstrained (112)-oriented films, is independent of the presence of bulk Dirac nodes. Its appearance is consistent with the topological surface states that are a characteristic of the topological ${\mathbb{Z}}_{2}$ invariant.