Novel topological nodal lines and exotic drum-head-like surface states in synthesized CsCl-type binary alloy TiOs

Nontrivial Topological Properties and Synthesis of Sn2CoS with L21 Structure

We synthesize Sn₂CoS in experiment and study its topological properties in theory. By first-principles calculations, we study the band structure and surface state of Sn₂CoS with L2₁ structure. It is found that the material has type-II nodal line in the Brillouin zone and clear drumhead-like surface state when the spin-orbit coupling is not considered. In the case of spin-orbit coupling, the nodal line will open gap, leaving the Dirac points. To check the stability of the material in nature, we synthesize Sn₂CoS nanowires with L2₁ structure in an anodic aluminum oxide (AAO) template directly by the electrochemical deposition (ECD) method with direct current (DC). Additionally, the diameter of the typical Sn₂CoS nanowires is about 70 nm, with a length of about 70 μm. The Sn₂CoS nanowires are single crystals with an axis direction of [100], and the lattice constant determined by XRD and TEM is 6.0 Å. Overall, our work provides realistic material to study the nodal line and Dirac fermions.

An ideal Weyl nodal ring with a large drumhead surface state in the orthorhombic compound TiS2

Topological metals or semimetals have attracted great research attention and interest in condensed matter physics and chemistry due to their exotic properties. Different from the conventional topological insulators, topological metals or semimetals are characterized by distinct topological surface states, such as a Fermi arc or a drumhead surface state, which are often used in experiments to verify the corresponding topological properties. However, the current study in this field is strongly limited in the experimental characterization because of the extreme lack of perfect material candidates with a clean band structure and clear surface states. In this work, based on theoretical calculations, we propose a new topological semimetal TiS₂, which has an orthorhombic structure and exhibits excellent stability. Calculated electronic band structures reveal that there is a single Weyl nodal ring in the k_y = 0 plane. A detailed symmetry analysis is provided and the corresponding surface state is calculated, which exhibits both a large energy variation of 1.5 eV and wide space distribution without and with the spin orbit coupling effect. Besides, the surface states are well separated from the bulk state. These ideal features together make TiS₂ a promising nodal line semimetal for experimental investigation. In combination with the other two isostructural compounds TiSe₂ and TiTe₂ with similar properties, their further experimental synthesis and characterization can be highly expected and the corresponding study for the topological nodal line state can thus be greatly facilitated.

Obvious Surface States Connecting to the Projected Triple Points in NaCl's Phonon Dispersion

With the development of computer technology and theoretical chemistry, the speed and accuracy of first-principles calculations have significantly improved. Using first-principles calculations to predict new topological materials is a hot research topic in theoretical and computational chemistry. In this work, we focus on a well-known material, sodium chloride (NaCl), and propose that the triple point (TP), quadratic contact triple point (QCTP), linear and quadratic nodal lines can be found in the phonon dispersion of NaCl with Fm3¯ m type structure. More importantly, we propose that the clear surface states connected to the projected TP and QCTP are visible on the (001) surface. It is hoped that further experimental investigation and verification for these properties as mentioned above.

Computational Simulation of the Electronic State Transition in the Ternary Hexagonal Compound BaAgBi

Topological properties in metals or semimetals have sparked tremendous scientific interest in quantum chemistry because of their exotic surface state behavior. The current research focus is still on discovering ideal topological metal material candidates. We propose a ternary compound with a hexagonal crystal structure, BaAgBi, which was discovered to exhibit two Weyl nodal ring states around the Fermi energy level without the spin-orbit coupling (SOC) effect using theoretical calculations. When the SOC effect is considered, the topological phases transform into two Dirac nodal line states, and their locations also shift from the Weyl nodal rings. The surface states of both the Weyl nodal ring and Dirac nodal lines were calculated on the (001) surface projection using a tight-binding Hamiltonian, and clear drumhead states were observed, with large spatial distribution areas and wide energy variation ranges. These topological features in BaAgBi can be very beneficial for experimental detection, inspiring further experimental investigation.

Various Nodal Lines in P63/mmc-type TiTe Topological Metal and its (001) Surface State

Searching for existing topological materials is a hot topic in quantum and computational chemistry. This study uncovers P6₃/mmc type TiTe compound—an existing material—is a newly discovered topological metal that hosts the various type of nodal line states. Different nodal line states normally exhibit different properties; they may have their individual applications. We report that TiTe hosts I, II, and hybrid type nodal line (NL) states at its ground state without chemical doping and strain engineering effects. Specifically, two type I NLs, two hybrid-type NLs, and one Γ—centered type II NL can be found in the k_z = 0 plane. Moreover, the spin-orbit coupling induced gaps for these NLs are very small and within acceptable limits. The surface states of the TiTe (001) plane were determined to provide strong evidence for the appearance of the three types of NLs in TiTe. We also provide a reference for the data of the dynamic and mechanical properties of TiTe. We expect that the proposed NL states in TiTe can be obtained in future experiments.

First-principle investigation of all types of topological nodal lines in a realistic P63/mmc type titanium selenide

Topological nodal line (TNL) materials with one-dimensional band-crossing points (BCPs) exhibit interesting electronic characteristics and have special applications in electronic devices. Normally, based on the slopes of the crossing bands, the BCPs can be divided into two types, i.e., type I and type II nodal points. Based on the combination of the different types of nodal points, the nodal lines (NLs) can be divided into three categories: (i) type I NL, type II NL, and hybrid NL, these being formed by type I nodal points, type II nodal points, and type I and II nodal points, respectively. Compared with the large number of predicted type I NL materials, there are less type II and hybrid NL materials. In this study, it is predicted that P6₃/mmc type TiSe metal is a topological material which exhibits all types of NL states. Furthermore, the dynamic stability as well as the effect of spin-orbit coupling on the topological signatures are examined. Also, the nontrivial surface states are shown to provide evidence for the occurrence of the NL states. This novel material can be seen as a good platform to use for further investigations on the three types of NLs and diverse fermions.

Stabilization and electronic topological transition of hydrogen-rich metal Li5MoH11 under high pressures from first-principles predictions

Regarded as doped binary hydrides, ternary hydrides have recently become the subject of investigation since they are deemed to be metallic under pressure and possibly potentially high-temperature superconductors. Herein, the candidate structure of Li₅MoH₁₁ is predicted by exploiting the evolutionary searching. Its high-pressure phase adopts a hexagonal structure with P6₃/mcm space group. We used first-principles calculations including the zero-point energy to investigate the structures up to 200 GPa and found that the P6₃cm structure transforms into the P6₃/mcm structure at 48 GPa. Phonon calculations confirm that the P6₃/mcm structure is dynamically stable. Its stability is mainly attributed to the isostructural second-order phase transition. Our calculations reveal the electronic topological transition displaying an isostructural second-order phase transition at 160 GPa as well as the topology of its Fermi surfaces. We used the projected crystal orbital Hamilton population (pCOHP) to examine the nature of the chemical bonding and demonstrated that the results obtained from the pCOHP calculation are associated with the electronic band structure and electronic localized function.

Nodal ring spin gapless semiconductor: New member of spintronic materials

INTRODUCTION

Spin gapless semiconductors (SGSs) and nodal ring states (NRSs) have aroused great scientific interest in recent years due to their unique electronic properties and high application potential in the field of spintronics and magnetoelectronics.

OBJECTIVES

Since their advent, all SGSs and NRSs have been predicted in independent materials. In this work, we proposed a novel type of material, nodal ring spin gapless semiconductor (NRSGS), which combines both states of the SGSs and NRSs.

METHODS

The synthesized material Mg2VO4 has been detailed with band structure analysis based on first principle calculations.

RESULTS

Obtained results revealed that there are gapless crossings in the spin-up direction, which are from multiple topological nodal rings located exactly at the Fermi energy level. Mg2VO4 combines the advantages inherited from both NRSs and SGSs in terms of the innumerable gapless points along multiple nodal rings with all linear dispersions and direct contacts. In addition, Mg2VO4 also shows strong robustness against both the spin orbit coupling effect and strain conditions.

CONCLUSION

For the first time, we propose the concept of an NRSGS, and the first such material candidate Mg2VO4 can immediately advance corresponding experimental measurements and even facilitate real applications.

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.

Realization of Opened and Closed Nodal Lines and Four- and Three-fold Degenerate Nodal Points in XPt (X = Sc, Y, La) Intermetallic Compound: A Computational Modeling Study

Realizing rich topological elements in topological materials has attracted increasing attention in the fields of chemistry, physics, and materials science. Topological semimetals/metals are classified into three main types: nodal-point, nodal-line, and nodal-surface types with zero-, one-, and two-dimensional topological elements, respectively. This study reports that XPt (X = Sc, Y, La) intermetallic compounds are topological metals with opened and closed nodal lines, and triply degenerate nodal points (TNPs) when the spin-orbit coupling (SOC) is ignored. Based on the calculated phonon dispersions, one can find that ScPt and YPt are dynamically stable whereas LaPt is not. When SOC is added, the one-dimensional nodal line and zero-dimensional TNPs disappear. Interestingly, a new zero-dimensional topological element, that is, Dirac points with 4-fold degenerate isolated band crossings with linear band dispersion appear. The proposed materials can be considered a good platform to realize zero- and one-dimensional topological elements in a single compound and to study the relationship between zero- and one-dimensional topological elements.

Perfect Topological Metal CrB2: A One-Dimensional (1D) Nodal Line, a Zero-Dimensional (0D) Triply Degenerate Point, and a Large Linear Energy Range

Topological materials with band-crossing points exhibit interesting electronic characteristics and have special applications in electronic devices. However, to further facilitate the experimental detection of the signatures of these band crossings, topological materials with a large linear energy range around the band-crossing points need to be found, which is challenging. Here, via first-principle approaches, we report that the previously prepared P6/mmm-type CrB₂ material is a topological metal with one pair of 1D band-crossing points, that is, nodal lines, in the k_z= 0 plane, and one pair of 0D band-crossing points, that is, triple points, along the A–Γ–A’ paths. Remarkably, around these band-crossing points, a large linear energy range (larger than 1 eV) was found and the value was much larger than that found in previously studied materials with a similar linear crossing. The pair of nodal lines showed obvious surface states, which show promise for experimental detection. The effect of the spin–orbit coupling on the band-crossing points was examined and the gaps induced by spin–orbit coupling were found to be up to 69 meV. This material was shown to be phase stable in theory and was synthesized in experiments, and is therefore a potential material for use in investigating nodal lines and triple points.

Insight into the Topological Nodal Line Metal YB2 with Large Linear Energy Range: A First-Principles Study

The presence of one-dimensional (1D) nodal lines, which are formed by band crossing points along a line in the momentum space of materials, is accompanied by several interesting features. However, in order to facilitate experimental detection of the band crossing point signatures, the materials must possess a large linear energy range around the band crossing points. In this work, we focused on a topological metal, YB2, with phase stability and a P6/mmm space group, and studied the phonon dispersion, electronic structure, and topological nodal line signatures via first principles. The computed results show that YB2 is a metallic material with one pair of closed nodal lines in the kz = 0 plane. Importantly, around the band crossing points, a large linear energy range in excess of 2 eV was observed, which was rarely reported in previous reports that focus on linear-crossing materials. Furthermore, YB2 has the following advantages: (1) An absence of a virtual frequency for phonon dispersion, (2) an obvious nontrivial surface state around the band crossing point, and (3) small spin-orbit coupling-induced gaps for the band crossing points.

The Tetragonal Monoxide of Platinum: A New Platform for Investigating Nodal-Line and Nodal-Point Semimetallic Behavior

The search for new topological materials that are realistic to synthesize has attracted increasing attention. In this study, we systematically investigated the electronic, mechanical, and topological semimetallic properties, as well as the interesting surface states, of the tetragonal monoxide of platinum, which is realistic to synthesize, via a first-principles approach. Our calculated results indicate that PtO is a novel topological semimetal with double nodal lines in the k z = 0 plane and a pair of triple topological nodal points along the A'-M-A directions. Obvious surface states, including Fermi arc and drum-head-like surfaces, could be found around nodal points and nodal lines. The dynamic and mechanical stabilities of P4 2 /mmc-type PtO were examined in detail via calculation of the phonon dispersion and determination of elastic constants, respectively. Some other mechanical properties, including the bulk modulus, Young's modulus, shear modulus, Poisson's ratio, and Pugh's index, were considered in this study. P4 2 /mmc-type PtO provides a good research platform for investigation of novel behaviors that combine mechanical properties and rich topological elements.

Coexistence of type-I and critical-type nodal line states in intermetallic compounds ScM (M = Cu, Ag, Au)

In recent years, topological semimetals such as Weyl, Dirac, and nodal-line semimetals have been a hot topic in the field of condensed matter physics. Depending on the orientation of band crossing in momentum space, topological semimetals and metals can be identified as type-I or type-II. Here, we report the coexistence of two new types of topological metal phase in the ScM (M = Cu, Ag, Au) intermetallic compounds (IMCs): (1) multi-nodal-lines semimetals (above Fermi energy), (2) critical-type nodal-lines (lower than Fermi energy). The first case has already been investigated. So, in this paper, we focus on the second case. We find that these IMCs can be an existing topological metal lower than Fermi energy, which are characterized with type-I (for ScCu and ScAu) and critical-type (for ScAg) nodal-lines in the bulk and drumhead liked surface states in the absence of the spin-orbit coupling (SOC). It has also been shown that when SOC is included, these compounds are converted into topological metal materials.

Ternary compound HfCuP: An excellent Weyl semimetal with the coexistence of type-I and type-II Weyl nodes

In most Weyl semimetal (WSMs), the Weyl nodes with opposite chiralities usually have the same type of band dispersions (either type-I or type-II), whereas realistic candidate materials hosting different types of Weyl nodes have not been identified to date. Here we report for the first time that, a ternary compound HfCuP, is an excellent WSM with the coexistence of type-I and type-II Weyl nodes. Our results show that, HfCuP totally contains six pairs of type-I and six pairs of type-II Weyl nodes in the Brillouin zone, all locating at the H-K path. These Weyl nodes situate slightly below the Fermi level, and do not coexist with other extraneous bands. The nontrivial band structure in HfCuP produces clear Fermi arc surface states in the (1 0 0) surface projection. Moreover, we find the Weyl nodes in HfCuP can be effectively tuned by strain engineering. These characteristics make HfCuP a potential candidate material to investigate the novel properties of type-I and type-II Weyl fermions, as well as the potential entanglements between them.

Strain tuning of closed topological nodal lines and opposite pockets in quasi-two-dimensional α-phase FeSi2

Following topological nodal point semimetals, topological nodal line semimetals with one dimensional (1D) topological elements have recently aroused great interest worldwide in the fields of quantum chemistry and condensed matter physics. In this study, by means of first-principles, we predict that quasi-two-dimensional (2D) α-FeSi2 with a P4/mmm space group is a topological nodal line semimetal with two nodal lines close to the Fermi level, in the kz = 0 and kz = π planes. Usually, topological nodal line semimetals can be classified into type I, type II, and hybrid-type categories, each type with different physical properties. Importantly, for the first time, we find that type I, type II, and hybrid-type nodal lines can be realized in a realistic material, i.e., quasi-2D α-FeSi2, by strain switching. The realization of tunable nodal line types occurs because quasi-2D α-FeSi2 has special opposite-pocket-behaving bands around the Fermi level. The results presented herein reflect that α-FeSi2 is a valuable candidate for spintronics application by utilization of type I, type II, and hybrid-type topological nodal line semimetals in a single material tuned by mechanical strain.

Pnma metal hydride system LiBH: a superior topological semimetal with the coexistence of twofold and quadruple degenerate topological nodal lines

To date, a handful of topological semimetals (TMs) with multiple types of topological nodal line (TNL) states have been theoretically predicted in novel materials. However, their TNLs are often affected by many factors, such as spin-orbit coupling (SOC) effect, strain, and the extraneous bands near the band crossing points, and therefore, the TNL states cannot be easily verified by experiments. Here, by using first-principles calculations, we report that the Pnma LiBH is a potential TM with twofold and quadruple degenerate topological nodal lines. These TNLs situate very close to the Fermi level, and do not coexist with other extraneous bands. More importantly, the TNLs of this material are very robust to the effect of SOC, uniform strain, and biaxial strain. The nontrivial band structure in LiBH produces drum-head-like surface states in the (001) surface projection. Our result reveals that LiBH material is an excellent candidate to study the multiple kinds of TNLs.

Rich novel zero-dimensional (0D), 1D, and 2D topological elements predicted in the P63/m type ternary boride HfIr3B4

Topological semimetals, including topological nodal point semimetals (TNPSs), topological nodal line state semimetals (TNLSs), and topological nodal surface semimetals (TNSSs), featuring zero-dimensional (0D), one-dimensional (1D), and two-dimensional (2D) topological elements (TEs), respectively, have attracted widespread attention in recent years. In this work, based on first-principles calculations, we propose for the first time that three different (0D, 1D, and 2D) TEs are simultaneously present in a synthetic compound, HfIr₃B₄, with a P6₃/m type structure. In detail, HfIr₃B₄ hosts a Dirac point (DP) state at the K point, a TNL state in the k_z = 0 plane, and a 2D TNS state in the k_z = π plane, respectively. All sorts of topological elements, 0D, 1D, and 2D TEs, coexisting in the P6₃/m type HfIr₃B₄, provide an ideal platform to study the rich fermionic states and their related physical properties in this type of compound. In addition, because the 0D, 1D, and 2D TEs of HfIr₃B₄ are equally distributed in different energy ranges relative to the Fermi level, an approach is proposed to utilize individual TEs to build on-demand devices.

Rich topological nodal line bulk states together with drum-head-like surface states in NaAlGe with anti-PbFCl type structure

The band topology in condensed matter has attracted widespread attention in recent years. Due to the band inversion, topological nodal line semimetals (TNLSs) have band crossing points (BCPs) around the Fermi level, forming a nodal line. In this work, by means of first-principles, we observe that the synthesized NaAlGe intermetallic compound with anti-PbFCl type structure is a TNLS with four NLs in the k_z = 0 and k_z = π planes. All these NLs in NaAlGe exist around the Fermi level, and what is more, these NLs do not overlap with other bands. The exotic drum-head-like surface states can be clearly observed, and therefore, the surface characteristics of NaAlGe may more easily be detected by experiments. Biaxial strain has been explored for this system, and our results show that rich TNL states can be induced. Furthermore, the spin-orbit coupling effect has little effect on the band structure of NaAlGe. It is hoped that this unique band structure can soon be examined by experimental work and that its novel topological elements can be fully explored for electronic devices.