Nodal Surface States Research Articles

Observation of flat band, Dirac nodal lines and topological surface states in Kagome superconductor CsTi3Bi5

Kagome lattices of various transition metals are versatile platforms for achieving anomalous Hall effects, unconventional charge-density wave orders and quantum spin liquid phenomena due to the strong correlations, spin-orbit coupling and/or magnetic interactions involved in such a lattice. Here, we use laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations to investigate the electronic structure of the newly discovered kagome superconductor CsTi3Bi5, which is isostructural to the AV3Sb5 (A = K, Rb or Cs) kagome superconductor family and possesses a two-dimensional kagome network of titanium. We directly observe a striking flat band derived from the local destructive interference of Bloch wave functions within the kagome lattice. In agreement with calculations, we identify type-II and type-III Dirac nodal lines and their momentum distribution in CsTi3Bi5 from the measured electronic structures. In addition, around the Brillouin zone centre, {{mathbb{Z}}}_{2} nontrivial topological surface states are also observed due to band inversion mediated by strong spin-orbit coupling.

Spontaneous Formation of Exceptional Points at the Onset of Magnetism.

We reveal how symmetry-protected nodal points in topological semimetals may be promoted to pairs of generically stable exceptional points (EPs) by symmetry-breaking fluctuations at the onset of long-range order. This intriguing interplay between non-Hermitian (NH) topology and spontaneous symmetry breaking is exemplified by a magnetic NH Weyl phase spontaneously emerging at the surface of a strongly correlated three-dimensional topological insulator, when entering the ferromagnetic regime from a high-temperature paramagnetic phase. Here, electronic excitations with opposite spin acquire significantly different lifetimes, thus giving rise to an anti-Hermitian structure in spin that is incompatible with the chiral spin texture of the nodal surface states, and hence facilitate the spontaneous formation of EPs. We present numerical evidence of this phenomenon by solving a microscopic multiband Hubbard model nonperturbatively in the framework of dynamical mean-field theory.

Topological Nodal Surface and Quadratic Dirac Semimetal States and van Hove Singularities in ScH3 and LuH3 Superconductors.

The coexistence of non-trivial topology and superconductivity in a material may induce a novel physical phenomenon known as topological superconductivity. Topological superconductors have been the subject of intense research, yet there are severe limitations in their application due to a lack of suitable materials. Topological nodal surface semimetals with nearly flat nodal surfaces near the Fermi level can be promising materials to achieve topological superconductivity. Here, we use first-principles calculations to examine the topological electronic characteristics of two new superconductors, ScH3 and LuH3, at both ambient and high pressures. Our studies show that both ScH3 and LuH3 have van Hove singularities, which confirms their superconductivity. Interestingly, both materials host topological nodal surface states under the protection of time reversal and spatial inversion symmetries in the absence of spin-orbit coupling (SOC). These nodal surfaces are distinguished by a pair of unique drum-head-like surface states not previously observed in nodal surface semimetals. Moreover, the nodal surfaces transform into essential spin-orbit quadratic Dirac points when SOC is included. Our findings demonstrate that ScH3 and LuH3 are good candidates to investigate the exotic properties of both nodal surface semimetals (NSSMs) and quadratic Dirac semimetal states and also provide a platform to explore the coexistence of topology and superconductivity in NSSMs with promising applications in high-speed electronics and topological quantum computing.

Coincident Nodal Line and Nodal Surface Phonon States in Ternary Phosphide Compound BaLiP

With the continuous development of topological properties in condensed matter systems, the current research focus has been expanded into phononic bosonic states. Compared with the conventional electronic fermions, topological phonons exhibit very distinct features. In this study, based on density functional calculations, we have systematically investigated the topological phonons in the ternary phosphide compound BaLiP. Coincident nodal line and nodal surface states are revealed in the middle part of the phononic spectrum and they are formed by the same two phonon bands. Detailed band structure mechanism and symmetry operation formalism are provided. More importantly, evident surface states are observed from the entire nodal line and they are all well separated from the bulk state projection, very beneficial and preferable for future experimental investigation. Lastly, the mechanical properties are also examined and several important parameters are provided, which can be very useful for the practical application. Considering the multiple advantages of the topological nodal states in this material, the corresponding experimental study can be immediately inspired.

Coexistence of multifold and multidimensional topological phonons in KMgBO3

Topological interpretations of phonons facilitate a new platform for novel concepts in phonon physics. Though there are ubiquitous set of reports on topological electronic excitations, the same for phonons are extremely limited. Here, we propose a new candidate material, KMgBO 3 , which showcase the co-existence of several multifold and multidimensional topological phonon excitations, which are protected by spatial and non-spatial symmetries. This includes zero dimensional double, triple and quadratic Weyl phonon nodes, one dimensional nodal line/loop and two dimensional doubly degenerate nodal surface states. Nodal line/loop emerges from the spin- 12 phonon nodes, while the two dimensional doubly degenerate nodal surface arises from a combination of two fold screw rotational and time reversal symmetries. Application of strain breaks the C 3 rotational symmetry, which annihilates the spin-1 double Weyl nodes, but preserves other topological features. Interestingly, strain helps to create two extra single Weyl nodes, which in turn preserve the total chirality. Alloying also breaks certain symmetries, destroying most of the topological phonon features in the present case. Thus, KMgBO 3 is a promising candidate which hosts various Weyl points, large Fermi arcs with a very clean phonon spectra and tunable topological phonon excitations, and hence certainly worth for future theoretical/experimental investigation of topological phononics.

First-principles study of the structural, electronic, dynamical, and mechanical properties of Pd–Nb binary systems

We study the structural, electronic, dynamical, and mechanical properties of the whole Pd–Nb binary systems based on first-principles density functional theory calculations. Using the variable-composition evolutionary structure search algorithm, we predict five new ground-state phases (cI32-Pd15Nb, oF60-Pd13Nb2, mC24-Pd5Nb, oC16-PdNb7, and oC32-PdNb15) and nine metastable phases (oC24-Pd11Nb, mC18-Pd8Nb, hP9-Pd8Nb, mC12-Pd5Nb, tP2-PdNb, oC20-PdNb, tI10-Pd2Nb3, oC20-Pd2Nb3, and mP10-PdNb4) that have not yet been either experimentally reported or theoretically predicted. All the predicted phases are dynamically stable in the absence of soft phonon modes in calculated phonon dispersions. The elastic properties calculations show that all these compounds are also mechanically stable. We find that the Young’s modulus, bulk modulus as well as shear modulus exhibit similar convex variations with respect to the Nb concentrations, while the Poisson’s ratio shows the opposite trend. These trends are found to be highly correlated with the atomic arrangement in crystal structures and associated chemical bondings. Among all the predicted PdxNby compounds, tI8-Pd3Nb exhibits the largest elastic moduli due to its relatively close-packed structure induced near homogeneous chemical bondings. The electronic structure calculations reveal that all predicted Pd–Nb compounds are metallic with complex band structures. Interestingly, the oI6-Pd2Nb compound hosts nontrivial Dirac nodal lines around the Fermi energy and exhibits topological nodal line surface states on the (001) plane. This work provides the first complete survey on the whole Pd–Nb systems, paving the way to exploring potential candidates for Pd-based electrocatalysts.

Topological nodal surface semimetal states in Sr5X3 compounds (X=As,Sb,Bi)

Topological nodal surface semimetals are a class of materials characterized by degenerate conduction and valence bands on closed nodal surfaces in the Brillouin zone that are protected by crystalline symmetries. These materials attract considerable attention for exhibiting intriguing, topologically driven quantum phenomena that are fundamentally interesting and practically useful. Here we identify by systematic ab initio calculations and topological quantum chemistry analysis prominent topological nodal surface semimetal states in ${\mathrm{Sr}}_{5}{X}_{3}(X$ = As, Sb, Bi) compounds in hexagonal $P{6}_{3}/mcm$ (${D}_{6h}^{3}$) symmetry. These nodal surface states comprise degenerate the highest occupied band and the lowest unoccupied band that overlap in a single band at the ${k}_{z}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ plane and are protected by time-reversal and nonsymmorphic twofold screw rotation symmetry. Topological quantum chemistry theory analysis reveals a twofold band degeneracy without spin-orbit coupling at the high-symmetry and generic $\mathbit{k}$ points located at the ${k}_{z}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ plane, which is formed by the bands of (${\mathrm{A}}_{1}\ensuremath{\bigoplus}{\mathrm{B}}_{2})@6g$ band representations. Since the compounds studied here have been already experimentally synthesized, the present results have an immediate impact on the experimental detection and characterization of the theoretically predicted topological physics.

Embedded topological semimetals

Topological semimetals, such as Dirac, Weyl, or line-node semimetals, are gapless states of matter characterized by their nodal band structures and surface states. In this work, we consider layered (topologically trivial) insulating systems in $D$ dimensions that are composed of coupled multi-layers of $d$-dimensional topological semimetals. Despite being nominal bulk insulators, we show that crystal defects having co-dimension $(D-d)$ can harbor robust lower dimensional topological semimetals embedded in a trivial insulating background. As an example we show that defect-bound topological semimetals can be localized on stacking faults and partial dislocations. Finally, we propose how an embedded topological Dirac semimetal can be identified in experiment by introducing a magnetic field and resolving the relativistic massless Dirac Landau level spectrum at low energies in an otherwise gapped system.

Weyl nodal-line surface half-metal in CaFeO3

Manipulating the spin degrees of freedom of electrons affords an excellent platform for exploring novel quantum states in condensed-matter physics and material science. Based on first-principles calculations and analysis of crystal symmetries, we propose a fully spin-polarized composite semimetal state, which is combined with the one-dimensional nodal lines and two-dimensional nodal surfaces, in the half-metal material CaFeO$_3$. In the nodal line-surface states, the Baguenaudier-like nodal lines feature six rings linked together, which are protected by the three independent symmetry operations:$\mathcal{PT}$, $\mathcal{M}_{y}$, and $\mathcal{\widetilde{M}}_{z}$. Near the Fermi level, the spin-polarized nodal surface states are guaranteed by the joint operation $\mathcal{T}\mathcal{S}_{2i}$ in the $k_{i(i=x,y,z)}=\pi$ plane. Furthermore, high-quality CaFeO$_3$ harbors ultra-clean energy dispersion, which is rather robust against strong triaxial compressional strain and correlation effect. The realization of the Weyl nodal line-surface half-metal presents great potential for spintronics applications with high speed and low power consumption.

Hexagonal Zr3X (X = Al, Ga, In) Metals: High Dynamic Stability, Nodal Loop, and Perfect Nodal Surface States.

In recent years, topological semimetals/metals, including nodal point, nodal line, and nodal surface semimetals/metals, have been studied extensively because of their potential applications in spintronics and quantum computers. In this study, we predict a family of materials, Zr3X (X = Al, Ga, In), hosting the nodal loop and nodal surface states in the absence of spin–orbit coupling. Remarkably, the energy variation of the nodal loop and nodal surface states in Zr3X are very small, and these topological signatures lie very close to the Fermi level. When the effect of spin–orbit coupling is considered, the nodal loop and nodal surface states exhibit small energy gaps (<25 and 35 meV, respectively) that are suitable observables that reflect the spin-orbit coupling response of these topological signatures and can be detected in experiments. Moreover, these compounds are dynamically stable, and they consequently form potential material platforms to study nodal loop and nodal surface semimetals.

Hypothetical P63/mmc-Type CsCrCl3 Ferromagnet: Half-Metallic Property and Nodal Surface State

This work is focusing on the electronic, magnetic, half-metallic behaviors, and interesting surface state of hypothetical CsCrCl3 ferromagnet with P63/mmc space group that are investigated under the spin-polarized Generalized Gradient Approach (GGA) and spin-polarized GGA plus Hubbard U correction within the framework of the Density Functional Theory (DFT). The calculated total magnetic moment of P63/mmc CsCrCl3 is ~7.397 µB, and the mainly contribution to the total magnetism is coming from the Cr atoms. Based on obtained spin-polarized band structures, we confirmed that this hypothetical CsCrCl3 is a half-metal with 100% spin-polarization. Without spin-orbit coupling, i.e., the spin and the orbit degrees of freedom are dependents, we found that there should be a interesting nodal surface state at kz = plane due to P63/mmc type lattice structure enjoys a two-fold screw axis S2z. Our study can be seen as a strong evidence to exhibit that the protected nodal surface state can be achieved in magnetic materials.

Pure Zirconium: Type II Nodal Line and Nodal Surface States.

Type II nodal line states have novel properties, such as direction-reliant chiral anomalies and high anisotropic negative magneto-resistance. These type II nodal line states have been widely investigated. Compared to nodal line materials, there are far fewer proposed nodal surface materials, and furthermore, a very recent challenge is to find a realistic material that co-exhibits both nodal line and nodal surface states. In this manuscript, we present the study of the electronic and topological states of pure zirconium within the density functional theory. We found that pure Zr is an interesting material that rarely exhibits both the type II nodal line state (in kz = 0 plane) and nodal surface state (in kz = π plane). The nontrivial topological states are explained based on the orbital-resolved band structures. Our study shows that pure Zr can serve as a new platform to investigate the interplay between the nodal line state and the nodal surface state.

Organic-inorganic hybrid coordination polymer C3H9CdCl3N co-exhibiting superior Dirac point and nodal surface states

In this work, based on first-principles, we reported that synthesized organic-inorganic hybrid coordination polymer C3H9CdCl3N is an excellent topological material co-exhibiting superior Dirac point (DP) and nodal surface (NS) states. Importantly, C3H9CdCl3N enjoys the following advantages: (1) this material is easily synthesized and the high-quality compound has been obtained before; (2) this material features a DP state at K point near the Fermi level (EF), and the calculated Fermi velocity of this DP is 1.323 × 105 m/s; (3) this material exhibits NS in the kz = π plane, and the energy variation of the NS is very small; (4) Both of the DP and NS features are close to the EF; (5) In addition to the DP and NS states, there are no other energy bands near the EF. It is hoped that organic-inorganic hybrid coordination polymers C3H9CdCl3N can be seen as a good platform to further study the rich topological states in the near future.

Predicted remarkably topological nodal surface states in P63/m type Sr3WN3 from first-principles

In this study, a new P63/m type material Sr3WN3 with excellent topological nodal surface (NS) state, i.e., the conduction and valence bands cross on closed NSs in the Brillouin zone (BZ), was predicted via first-principle calculation. The mentioned compound has mechanical and dynamic stability based on the calculated elastic constants and the observed phonon dispersion curves. Importantly, the NS of this material features the following advantages: (1) the energy variation of the NS is very small; (2) the energy of the NS is close to the Fermi level (EF); (3) no other energy bands observed near the EF. The orbital-resolved band structures of Sr3WN3 were calculated and we found that the NS states along A-L (H-A) and L-H directions are mainly formed from the N-p and W-d orbitals, respectively. Moreover, the effect of the spin–orbit coupling on the topological property were also discussed. We should point out the Sr3WN3 can be well described as a perfect TNS semimetal due to its SOC-induced gap sizes throughout the NS are less than 10 meV.

Nearly flat nodal surface states in pseudo-one-dimensional molybdenum monochalcogenides X(MoS)3(X = K, Rb, and Cs)

The compounds X(MoS)3exhibit ideal nodal surface states in terms of nearly flat energy variation close to the Fermi energy with a large linear dispersion.

Anomalous Dirac Plasmons in 1D Topological Electrides.

The plasmon opens up the possibility to efficiently couple light and matter at subwavelength scales. In general, the plasmon frequency, intensity, and damping are dependent on the carrier density. These dependencies, however, are disadvantageous for stable functionalities of plasmons and render fundamentally a weak intensity at low frequency, especially for the Dirac plasmon (DP) widely studied in graphene. Here we demonstrate a new type of DP, emerging from a Dirac nodal-surface state, which can simultaneously exhibit a density-independent frequency, intensity, and damping. Remarkably, we predict the realization of anomalous DP (ADP) in 1D topological electrides, such as Ba_{3}CrN_{3} and Sr_{3}CrN_{3}, by first-principles calculations. The ADPs in both systems have a density-independent frequency and high intensity, and their frequency can be tuned from terahertz to midinfrared by changing the excitation direction. Furthermore, the intrinsic weak electron-phonon coupling of anionic electrons in electrides affords an added advantage of low-phonon-assisted damping and hence a long lifetime of the ADPs. Our Letter paves the way to developing novel plasmonic and optoelectronic devices by combining topological physics with electride materials.