Linear Band Crossings Research Articles

Dirac crossings and band inversion in hexagonal superconductors emerging by chemical substitution: SrAlGe, BaAlGe, SrGaGe and BaGaGe

In this work, we used DFT calculations to compare the electronic structure of four hexagonal superconducting materials. Two of them are SrAlGe and BaAlGe, and the other two are given by substituting Al for Ga, resulting in SrGaGe and BaGaGe. The band structure, the density of states, and the Fermi surface were obtained for each compound with and without the spin–orbit coupling effect. For the SrGaGe and BaGaGe compounds, a band unfolding calculation was performed. We found that BaGaGe exhibits a quasi-flat-band localized in a specific direction of the Brillouin zone. In addition, band inversion can be induced by replacing Al for Ga in these compounds. Furthermore, we found that linear band crossings are gaped after spin–orbit coupling is considered to SrAlGe, BaAlGe, SrGaGe, and BaGaGe. These Dirac-like band crossings point to non-trivial topological behavior.

Comprehensive study of all spinful and spinless linear band crossings in the 80 layer groups

Comprehensive study of all spinful and spinless linear band crossings in the 80 layer groups

Family behavior and Dirac bands in armchair nanoribbons with 4–8 defect lines

Bottom-up synthesis from molecular precursors is a powerful route for the creation of novel synthetic carbon-based low-dimensional materials, such as planar carbon lattices. The wealth of conceivable precursor molecules introduces a significant number of degrees-of-freedom for the design of materials with defined physical properties. In this context, a priori knowledge of the electronic, vibrational and optical properties provided by modern ab initio simulation methods can act as a valuable guide for the design of novel synthetic carbon-based building blocks. Using density functional theory, we performed simulations of the electronic properties of armchair-edged graphene nanoribbons (AGNR) with a bisecting 4–8 ring defect line. We show that the electronic structures of the defective nanoribbons of increasing width can be classified into three distinct families of semiconductors, similar to the case of pristine AGNR. In contrast to the latter, we find that every third nanoribbon is a zero-gap semiconductor with Dirac-type crossing of linear bands at the Fermi energy. By employing tight-binding models including interactions up to third-nearest neighbors, we show that the family behavior, the formation of direct and indirect band gaps and of linear band crossings in the defective nanoribbons is rooted in the electronic properties of the individual nanoribbon halves on either side of the defect lines, and can be effectively through introduction of additional ‘interhalf’ coupling terms.

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.

Exploring the Dirac nature of RbBi2

Characteristics of topological semimetals such as a nonsaturating magnetoresistance (MR), a field-induced metal to semiconducting crossover and a robust resistivity plateau are observed under a magnetic field in type-I ${\mathrm{RbBi}}_{2}$ bulk superconductor with ${T}_{\mathrm{c}}=4.15$ K. The MR exhibits a notable 3500% increase at 2 K and 9 T and the resistivity follows a power law temperature dependence, while the MR $\ensuremath{\propto}\phantom{\rule{4pt}{0ex}}{H}^{1.26}$, indicating weak carrier compensation. First principles calculations provided insights into the dynamical stability of the cubic structure at 0 K. Both hole and electron pockets are observed at the Fermi surface. The electron-phonon interaction constant indicates weak coupling strength ($<1$) that leads to a maximum predicted ${T}_{\mathrm{c}}$ of 2.852 K. Just below the Fermi level, ${\mathrm{E}}_{F}$, the electronic band structure consists of linear band crossings at the $X$ points in the Brillouin zone (BZ) corresponding to massless, symmetry-protected Dirac fermions.

Dirac Nodal Line in Hourglass Semimetal Nb3SiTe6.

Glide-mirror symmetry in nonsymmorphic crystals can foster the emergence of novel hourglass nodal loop states. Here, we present spectroscopic signatures from angle-resolved photoemission of a predicted topological hourglass semimetal phase in Nb3SiTe6. Linear band crossings are observed at the zone boundary of Nb3SiTe6, which could be the origin of the nontrivial Berry phase and are consistent with a predicted glide quantum spin Hall effect; such linear band crossings connect to form a nodal loop. Furthermore, the saddle-like Fermi surface of Nb3SiTe6 observed in our results helps unveil linear band crossings that could be missed. In situ alkali-metal doping of Nb3SiTe6 also facilitated the observation of other band crossings and parabolic bands at the zone center correlated with accidental nodal loop states. Overall, our results complete the system's band structure, help explain prior Hall measurements, and suggest the existence of a nodal loop at the zone center of Nb3SiTe6.

Fully linear band crossings at high symmetry points in layers: classification and role of spin–orbit coupling and time reversal

Symmetry imposed restrictions to the Hamiltonian are systematized and applied to all of 80 clusters of single/double ordinary/gray groups (320 groups in total), to single out linear (in all directions) band crossings and corresponding effective Hamiltonians in high-symmetry Brillouin zone points of layered materials. The resulting dispersion types are isotropic or anisotropic forms of: single cone (with double degenerate crossing point and non-degenerate branches, or four-fold degenerate crossing point with double degenerate conical branches), poppy-flower (four-fold degenerate crossing point with two pairs of non-degenerate mutually rotated conical branches), and fortune teller (with nodal lines). Further, we describe the nontrivial patterns of dispersions’ behavior in high symmetry points when symmetry is varied within a cluster. Namely, Clebsch–Gordan series of the products of spin representation with the integer ones are relevant when spin–orbit coupling is included, and clarify observed scenarios (gap closing, gap opening, cone preserving, cone splitting etc). Analogously, analysis of behavior of dispersions in transition from ordinary to gray group enlightens the role of time reversal symmetry. The results refine and expand data existing in literature, and interesting or even unexpected cases are singled out in discussion.

Evidence for strong electron correlations in a nonsymmorphic Dirac semimetal

Metallic iridium oxides (iridates) provide a fertile playground to explore new phenomena resulting from the interplay between topological protection, spin-orbit and electron-electron interactions. To date, however, few studies of the low energy electronic excitations exist due to the difficulty in synthesising crystals with sufficiently large carrier mean-free-paths. Here, we report the observation of Shubnikov-de Haas quantum oscillations in high-quality single crystals of monoclinic SrIrO3 in magnetic fields up to 35 T. Analysis of the oscillations reveals a Fermi surface comprising multiple small pockets with effective masses up to 4.5 times larger than the calculated band mass. Ab-initio calculations reveal robust linear band-crossings at the Brillouin zone boundary, due to its non-symmorphic symmetry, and overall we find good agreement between the angular dependence of the oscillations and the theoretical expectations. Further evidence of strong electron correlations is realized through the observation of signatures of non-Fermi liquid transport as well as a large Kadowaki-Woods ratio. These collective findings, coupled with knowledge of the evolution of the electronic state across the Ruddlesden-Popper iridate series, establishes monoclinic SrIrO3 as a topological semimetal on the boundary of the Mott metal-insulator transition.

Conservation of chirality at a junction between two Weyl semimetals

In Weyl semimetals the location of linear band crossings, the Weyl cones, is not bound to any high symmetry point of the Brillouin zone, unlike the Dirac nodes in graphene. This flexibility is advantageous for valleytronics, where information is encoded in the valleys of the band structure when intervalley scattering is weak. However, if numerous Weyl cones coexist the encoded information can decohere rapidly because of band mixing. Here, we investigate how the helical iso-spin texture of Weyl cones affects valleytronics in heterojunctions of Weyl materials, and show how the chirality of this iso-spin texture can serve to encode information.

Anomaly-induced sound absorption in Weyl semimetals

Topology of Weyl semimetals affects sound attenuation in these materials. Most notably, the existence of Berry monopoles associated with linear band crossings leads to the existence of acoustic magnetochiral dichroism: sound attenuation is different for opposite directions of sound propagation. The effect is within reach of current experimental techniques, and, importantly, is of quantum mechanical origin. This should help its detection in available compounds.

Large Fermi-Energy Shift and Suppression of Trivial Surface States in NbP Weyl Semimetal Thin Films.

Weyl semimetals, a class of 3D topological materials, exhibit a unique electronic structure featuring linear band crossings and disjoint surface states (Fermi-arcs). While first demonstrations of topologically driven phenomena have been realized in bulk crystals, efficient routes to control the electronic structure have remained largely unexplored. Here, a dramatic modification of the electronic structure in epitaxially grown NbP Weyl semimetal thin films is reported, using in situ surface engineering and chemical doping strategies that do not alter the NbP lattice structure and symmetry, retaining its topological nature. Through the preparation of a dangling-bond-free, P-terminated surface which manifests in a surface reconstruction, all the well-known trivial surface states of NbP are fully suppressed, resulting in a purely topological Fermi-arc dispersion. In addition, a substantial Fermi-energy shift from -0.2to 0.3 eVacross the Weyl points is achieved bysurfacechemical doping, unlocking access to the hitherto unexplored n-type region of the Weyl spectrum. These findings constitute a milestone toward surface-state and Fermi-level engineering of topological bands in Weyl semimetals, and, whilethere are still challenges in minimizing doping-driven disorder and grain boundary density in the films,they do represent a major advance to realize device heterostructures based on Weyl physics.

Three-dimensional borophene: A light-element topological nodal-line semimetal with direction-dependent type-II Weyl fermions

Since spin can be regarded as a dummy degree of freedom, light-element topological semimetals (TSMs) are expected to be a promising alternative for spin-orbit-coupling based TSMs, which usually contain costly and toxic heavy elements. Using first-principles calculations combined with a bottom-up assembly strategy, herein we identify an intriguing light-element TSM, termed 3D borophene, which can be obtained by stacking synthesized 2D triangular borophene along the perpendicular direction. Under the protection of mirror symmetry, the linear band crossings between $\mathrm{B}\ensuremath{-}{p}_{xz}$ and ${p}_{y}$ states in the vicinity of the Fermi energy form two Weyl nodal lines running across the Brillouin zone in the ${k}_{y}=0$ plane. When the nodal lines are projected on the (010) surface, drumheadlike surface states and open Fermi arcs are observed, which provide vital evidence for experimental identification. Remarkably, by examining the defined slope index of the crossing bands in all possible $\mathbit{k}$ paths, we find that the nodal lines of 3D borophene are composed of type-II Weyl points due to the emergence of tilted Weyl cones. Our findings not only establish a lightweight Weyl-nodal-line semimetal, but also highlight a bottom-up assembly strategy for designing desirable TSMs from synthetic 2D materials.

Near Fermi level electronic structure of Ti3SiC2 revealed by angle-resolved photoemission spectroscopy

An in-depth study of the Fermi surface and electronic structure of the ternary nanolamellar carbide ${\mathrm{Ti}}_{3}\mathrm{Si}{\mathrm{C}}_{2}$ is reported. The outputs of angle-resolved photoemission spectroscopy (ARPES) measured on single crystals and density functional theory calculations are systematically compared. The band structure is found to be dominated by Ti $d$ orbitals near the Fermi level. Band inversions near K points are responsible for the intricate shape of the ${\mathrm{Ti}}_{3}\mathrm{Si}{\mathrm{C}}_{2}$ pockets. Previous theory found that those pockets were giving opposite contributions leading to zero thermoelectric power in polycrystalline samples. Here we directly visualize them by ARPES, describe their precise shape, and examine the way they should behave regarding thermoelectric power. The presence of linear band crossings and the effect of spin-orbit coupling on the near Fermi level electronic structure are discussed, as well as potential consequences for magnetotransport and spin Hall effect.

Computational Insights Into the Electronic Structure and Magnetic Properties of Rhombohedral Type Half-Metal GdMnO3 With Multiple Dirac-Like Band Crossings.

In spintronics, half-metallic materials (HMMs) with Dirac-like cones exhibit interesting physical properties such as massless Dirac fermions and full spin polarization. We combined first-principles calculations with the quasi-harmonic Debye model, and we proposed that the rhombohedral GdMnO3 is an HMM with multiple linear band crossings. The physical properties of GdMnO3 were studied thoroughly. Moreover, the changes of multiple linear band crossings and 100% spin polarization under spin-orbit coupling as well as the electron and hole doping were also investigated. It is noted that such spin-polarized HMMs with linear band crossings are still very rare in two-dimensional and three-dimensional materials.

Quantum critical scaling of gapped phases in nodal-line semimetals

We study the effect of short range interactions in three dimensional nodal-line semimetals with linear band crossings. We analyze the Yukawa theories for gapped instabilities in the charge, spin and superconducting channels using the Wilsonian renormalization group framework, employing a large number of fermion flavors $N_{f}$ for analytical control. We obtain stable non-trivial fixed points and provide a unified description of the critical exponents for the ordering transitions in terms of the number of order parameter components $N_{b}$ systematically to order $1/N_{f}$. We show that in all cases, the dynamical exponent z = 1 in one loop, whereas $1/N_{f}$ corrections to various exponents follow from the anomalous dimension of the bosonic fields only.

Coexistence of parabolic and linear band crossings and electron-doped spin-gapless properties in rhombohedral type YbBO3

Very recently, a novel Dirac half-metal has been investigated in the perovskite-type lanthanum manganite (LaMnO3) by Ma et al. [1] and the half metallicity with 100% spin polarization is discovered. More remarkably, multiple linear Dirac crossings are observed around the Fermi energy level in the spin-up direction. Inspired by this work, another perovskite-type material YbBO3, which has been synthesized before, is investigated by first principles calculation. Results confirm the presence of half metallicity in this material with also multiple Dirac-like linear and parabolic band crossings around the Fermi level. The estimated Curie temperature is 469.4 K and the mechanic and dynamic stabilities have been verified. Besides, the elastic anisotropy is revealed with the directional dependent Young’s modulus and shear modulus, together with the acoustic wave properties. The effect of the uniform strain, electron doping and spin-orbital coupling on the electronic structures have been also accessed. In particular, nearly spin-gapless semiconducting behavior with linear or parabolic energy dispersions is obtained by electron doping. Moreover, several thermodynamic properties have been examined under temperature from 0 to 500 K and pressure from 0 to 5 GPa. In combination, we expect YbBO3 can attract more research attention and even facilitate the spintronic application.

Dirac Operators and Domain Walls

We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying “mass” term. It is well-known that when the mass function has the form of a kink, or domain wall, transitioning between strictly positive and strictly negative asymptotic mass, $\pm\kappa_\infty$, at $\pm\infty$, the Dirac operator has a simple eigenvalue of zero energy (geometric multiplicity equal to one) within a gap in the continuous spectrum, with corresponding exponentially localized zero mode. We consider the eigenvalue problem for the one-dimensional Dirac operator with mass function defined by “gluing” together $n$ domain wall--type transitions, assuming that the distance between transitions, $2 \delta$, is sufficiently large, focusing on the illustrative cases $n = 2$ and $3$. When $n = 2$ we prove that the Dirac operator has two real simple eigenvalues of opposite sign and of order $e^{- 2 |\kappa_\infty| \delta}$. The associated eigenfunctions are, up to $L^2$ error of order $e^{- 2 |\kappa_\infty| \delta}$, linear combinations of shifted copies of the single domain wall zero mode. For the case $n = 3$, we prove the Dirac operator has two nonzero simple eigenvalues as in the two domain wall case and a simple eigenvalue at energy zero. The associated eigenfunctions of these eigenvalues can again, up to small error, be expressed as linear combinations of shifted copies of the single domain wall zero mode. When $n > 3$ no new technical difficulty arises and the result is similar. Our methods are based on a Lyapunov--Schmidt reduction/Schur complement strategy, which maps the Dirac operator eigenvalue problem for eigenstates with near-zero energies to the problem of determining the kernel of an $n \times n$ matrix reduction, which depends nonlinearly on the eigenvalue parameter. The class of Dirac operators we consider controls the bifurcation of topologically protected “edge states” from Dirac points (linear band crossings) for classes of Schrödinger operators with domain wall modulated periodic potentials in one and two space dimensions. The present results may be used to construct a rich class of defect modes in periodic structures modulated by multiple domain walls.

New [formula omitted]-type half-metal MnBO3 with remarkable multiple Dirac-like band crossings: Effects of uniform strain, vacancies, spin–orbit coupling, and hole and electron doping on its electronic structures

Very recently, two R3−c Dirac half-metal materials, LaMnO3 and MnF3, were found and investigated by Du et al. via first principles. They stated that these types of materials with half-metallic band structures and multiple linear band dispersions might exhibit excellent 100% spin polarization and ultrafast electron transport. However, the application of MnF3 material in the field of spintronics is limited owing to its low Curie temperature (Tc). In this work, we proposed a new half-metal material—MnBO3. This material satisfies two demands at the same time—it is a half-metal with a high Tc, and it has multiple nearly linear band crossings. The effects of the uniform strain, vacancies, spin–orbit coupling, as well as hole and electron doping on its electronic structures have been discussed in detail. Furthermore, to better study its specific behaviors under extreme conditions, such as high temperature or pressure, we also investigated the thermodynamic properties of MnBO3 through the quasi-harmonic Debye model. Finally, its thermal stability at room temperature has been proved in this article by means of ab initio molecular dynamics (AIMD) simulations. We hope that MnBO3 can attract more attention for R3−c-type half-metallic materials with linear band crossings and a high Curie temperature in experimental and theoretical areas.

Topological massive Dirac fermions inβ-tungsten

Ultrathin films of $\ensuremath{\beta}$-tungsten $(\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W})$ is attracting extensive attentions because of its promising application in spintronics due to giant spin Hall effect and its fundamental interest in superconductivity. By means of first-principles calculations, we have elucidated its nontrivial topological nature with multiple Dirac nodal lines in the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W}$ metal when spin-orbit coupling (SOC) is ignored. The analysis of electronic structures reveal that its topology is associated with the band inversion between the ${d}_{xz}+{d}_{yz}$ and ${d}_{{z}^{2}}$ orbitals at the $M$ point in its Brillouin zone. By switching on the SOC, these Dirac nodal lines become gapped, as accompanied with the occurrence of 24 massive Dirac fermions at the energy of 87 meV below the Fermi level. Different from the exact gapless Dirac fermions with the linear band crossings, we have identified that these massive Dirac fermions all open a tiny gap of 7 meV. In addition, we have observed the topologically protected nontrivial surface arc states connecting these massive Dirac fermions. The existence of these massive Dirac fermions in the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W}$ phase would be important to understand its giant spin Hall effect according to a recent study [Nature 555, 638 (2018)] where massive Dirac fermions were identified to generate Berry-curvature-induced Hall conductivity.

Rhombohedral Lanthanum Manganite: A New Class of Dirac Half-Metal with Promising Potential in Spintronics.

Dirac half-metals have drawn great scientific interests in spintronics because of their outstanding physical properties such as the large spin polarization and massless Dirac fermions. By using first-principles calculations, we investigate the perovskite-type lanthanum manganite (LaMnO3) as a novel Dirac half-metal. Specifically, LaMnO3 displays multiple linear band crossings in the spin-up direction, while it has a large band gap (∼5 eV) in the spin-down orientation. The intriguing linear band dispersions guarantee the ultrafast electron transport and the significant band differences between spin up and down directions promise the realization of 100% spin-polarized current and the extremely low energy consumption. Such a spin-polarized Dirac material is rare among perovskite-type compounds. By adopting the mean-field theory, the estimated Curie temperature Tc is 438.4 K. Importantly, the LaMnO3 crystal has been experimentally realized 2 decades ago, which facilitates the future experimental validation. With the novel spin-polarized electronic properties and the high possibility of experimental fabrication, LaMnO3 is ideal for the spintronic application.