In this work, we introduce a new class of chiral altermagnetic magnetoelectrics in structurally chiral, nonpolar altermagnetic systems and identify the experimentally well-characterized three-dimensional metal-organic framework K[Co(HCOO) 3 ] as a promising material platform. K[Co(HCOO) 3 ] exhibits chirality-locked g-wave altermagnetic spin splitting together with dual-mode switchable electric polarization controlled by Néel-vector reorientation and structural chirality. Specifically, Néel-vector reorientation generates a finite electric polarization and reverses its sign, whereas chirality switching between left- and right-handed enantiomers produces an additional sign reversal. The associated electronic and optical responses provide effective readout channels for these switchable states. Our results establish chiral altermagnetic magnetoelectrics as a promising route to chirality- and Néel-vector-controlled nonvolatile multifunctional spintronics.

All-d Heusler alloys are promising candidates for advanced spintronic and magnetoelastic applications, yet many lack the intrinsic large anomalous Hall conductivity (AHC) and magnetostriction required for practical device integration. In this work, we systematically investigate the topological transport and magnetostrictive = Sc, Ti, V; and R = Re, Os, Ir, Pt) using first-principles calculations. We demonstrate that the fractional substitution of 5d transition metals serves as a highly effective strategy to tune the electronic structure via strong spin-orbit coupling (SOC). Our calculations identify eight materials exhibiting giant AHC values exceeding 1000 S/cm, with Co2Mn0.75Os0.25Sc and Co2Mn0.75Re0.25V approaching 1500 S/cm. Detailed symmetry and electronic structure analyses reveal that this massive AHC originates from the SOC-induced gap opening of Weyl nodal lines near the Fermi level, which generates an extended distribution of large Berry curvature. Furthermore, the introduction of strong SOC significantly enhances the magnetocrystalline anisotropy energy, transforming alloys with initially negligible magnetostriction into high-performance magnetoelastic materials. Notably, Co2Fe0.75Os0.25Ti and Co2FeSc0.75Ir0.25 exhibit giant magnetostriction coefficients of 752 and 609 ppm, respectively. Our findings establish heavy-element substitution as a robust, dual-purpose approach for the design and realization of multifunctional topological magnetic materials.

Unlike electron systems, the phonon system has its own advantages (such as no limitations regarding Fermi energy and the effect of spin-orbit coupling) and, therefore, can be viewed as a unique platform to predict spinless nodal-line states. Nodal-line phonons can be divided into open and closed nodal-line phonons from a mathematical point of view. In this work, using first-principle calculations, we select Ba(AgS)2 and Ca(ZnP)2, with the space group P3m$P\overline{3}m$1, as examples of realistic materials to investigate the difference between the open and closed nodal-line phonons. Two phonon band-crossing points (PBCPs) along the K-Gamma and H-A paths are present in their phonon spectra, and they correspond to closed nodal lines in Ba(AgS)2 and open nodal lines in Ca(ZnP)2, respectively. The difference between these two types nodal-line phonons is explained through symmetry analysis. All the nodal-line phonons are topologically nontrivial, with the prominent phonon surface states well separated from the bulk states, favorable for experimental detection. This work offers a deep understanding of the open and closed nodal-line phonons. It also proposes ideal candidates with multiple open and closed nodal-line phonons for follow-up experimental confirmation.

In recent years, 2D second-order topological insulators (SOTIs) have garnered considerable interest because of their unique properties. However, only the FeSe monolayer with four corner states (two occupied and two unoccupied states) near the Fermi level has been reported to be a candidate for 2D intrinsic antiferromagnetic SOTIs in theory. The limited amount of antiferromagnetic SOTIs has hindered future research, and corner states should be at the Fermi level in order to manifest interesting physics. Herein, we propose NiRuCl6 as a candidate for 2D antiferromagnetic SOTIs with corner states strictly at the Fermi level. Without spin–orbit coupling (SOC), NiRuCl6 is an antiferromagnetic half-metal with a compensating magnetic moment and decoupled spin bands. In the spin-up channel, NiRuCl6 hosts a nontrivial gap of 1.11 eV, where zero-dimensional corner states appear. In the spin-down channels, NiRuCl6 hosts metallically behaved bands, where a spin-polarized quadratic Weyl point emerges. With SOC, two spin bands are coupled, and NiRuCl6 becomes an antiferromagnetic SOTI with three degenerate corner states at the Fermi level inside the SOC-induced gap with a value of 0.11 eV. Remarkably, the corner states in NiRuCl6 are resistant to changes in SOC strength and magnetization orientation. We also reveal that the phononic second-order topology and corner vibrational modes appear in the phonon dispersion curves of NiRuCl6. The presented results improve the general understanding of antiferromagnetic SOTIs and contribute to the prediction of materials with ideal corner states at the Fermi level, thereby advancing the field of topological antiferromagnetic spintronics.

The discovery of topological quantum states in two-dimensional (2D) systems is one of the most promising advancements in condensed matter physics. Linear Weyl point (LWP) phonons have been theoretically investigated in some 2D materials. Especially, Jin, Wang, and Xu [Nano Lett. 2018, 18, 12, 7755-7760] proposed in 2018 that the candidates with threefold rotational symmetry at the corners of the hexagonal Brillouin zone can host LWP phonons with a quantized valley Berry phase. However, all the candidates with hexagonal lattices may not host LWP phonons at $K$ ($K'$) high-symmetry points (HSPs). Hence, a more accurate recipe for LWP phonons in 2D is highly required. This work provides an exhaustive list of valley LWP phonons at HSPs in 2D by searching the entire 80 layer groups (LGs). We found that the valley LWP phonons can be obtained at HSPs in 11 of the 80 LGs. Guided by the symmetry analysis, we also contributed to realizing the ideal 2D material with valley LWP phonons. We identified the existence of the valley LWP phonons in eleven 2D material candidates with 11 LGs. This work offers a method to search for valley LWPs in 2D phononic systems and proposes 2D material candidates to obtain the valley LWP phonons.

When the spin-orbit coupling (SOC) is absent, almost all the proposed half-metals with the twofold degenerate nodal points at the K (or K') in two-dimensional (2D) materials are misclassified as "Dirac half-metals" owing to the way graphene was utilized in the earliest studies. Actually, each band crossing point at K or K' is described by a 2D Weyl Hamiltonian with definite chirality; hence, it must be a Weyl point. To the best of our knowledge, there have been no reports of a genuine (i.e., fourfold degenerate) Dirac point half-metal in 2D yet. In this Letter, we proposed for the first time that the 2D d0-type ferromagnet Mg4N4 is a genuine Dirac half-metal with a fourfold degenerate Dirac point at the S high-symmetry point, intrinsic magnetism, high Curie temperature, 100% spin-polarization, robustness to the SOC and uniaxial and biaxial strains, and 100% spin-polarized edge states. The work can be seen as a starting point for future predictions of intrinsically magnetic materials with genuine Dirac points, which will aid the frontier of topo-spintronics researchers.

The conceptual framework of topological states has recently been extended to bosonic systems, particularly phononic systems. In this work, we chose the recently experimentally prepared two-dimensional (2D) Kekule-order graphene as a target to propose the coexistence of gapless and gapped topological phonon states in its phonon curves. This is the first work to investigate rich gapped and gapless topological phonon states in experimentally feasible 2D materials. For the gapped topological phonons, 2D Kekule-order graphene hosts phononic real Chern insulator states, i.e., second-order topological states, and corner vibrational modes inside frequency gaps at 27.96 and 37.065THz. For the gapless topological phonons, 2D Kekule-order graphene hosts a phononic Weyl pair [comprising two linear Weyl points (LWPs)] and a phononic Weyl complex [comprising one quadratic nodal point (QNP) and two LWPs] around 7.54 and 47.3THz (39.2THz), respectively. Moreover, the difference between the phononic Weyl pair and the phononic Weyl complex was investigated in detail. Our study not only promotes 2D Kekule-order graphene as a concrete material platform for exploring the intriguing physics of phononic second-order topology but also proposes the coexistence of different categories of Weyl phonons, i.e., a Weyl complex that comprises two LWPs and one QNP, in two dimensions. Our work paves the way for new advancements in topological phononics comprising gapless and gapped topological phonons.

2D second-order topological insulators (SOTIs) have sparked significant interest, but currently, the proposed realistic 2D materials for SOTIs are limited to nonmagnetic systems. In this study, for the first time, a single layer of chalcogenide CrSiTe3-an experimentally realized transition metal trichalcogenide is proposed with a layer structure-as a 2D ferromagnetic (FM) SOTI. Based on first-principles calculations, this study confirms that the CrSiTe3 monolayer exhibits a nontrivial gapped bulk state in the spin-up channel and a trivial gapped bulk state in the spin-down channel. Based on the higher-order bulk-boundary correspondence, it demonstrates that the CrSiTe3 monolayer exhibits topologically protected corner states with a quantized fractional charge (e3$\frac{e}{3}$) in the spin-up channel. Notably, unlike previous nonmagnetic examples, the topological corner states of the CrSiTe3 monolayer are spin-polarized and pinned at the corners of the sample in real space. Furthermore, the CrSiTe3 monolayer retains SOTI features when the spin-orbit coupling (SOC) is considered, as evidenced by the corner charge and corner states distribution. Finally, by applying biaxial strain and hole doping, this study transforms the magnetic insulating bulk states into spin-gapless semiconducting and half-metallic bulk states, respectively. Importantly, the topological corner states persist in the spin-up channel under these conditions.

The discovery of topological quantum states in two-dimensional (2D) systems is one of the most promising advancements in condensed matter physics. Linear Weyl point (LWP) phonons have been theoretically investigated in some 2D materials. Especially, Jin, Wang, and Xu [Nano Lett. 18, 7755 (2018)] proposed in 2018 that the candidates with threefold rotational symmetry at the corners of the hexagonal Brillouin zone can host LWP phonons with a quantized valley Berry phase. Note that all the candidates with hexagonal lattices may not host LWP phonons at K (K') high-symmetry points (HSPs). Hence a strategy for narrowing the search range for LWP phonons in 2D is highly required. This work provides an exhaustive list of valley LWP phonons at HSPs in 2D by searching the entire 80 layer groups (LGs). We found that the valley LWP phonons can be obtained at HSPs in 11 of the 80 LGs. Guided by the symmetry analysis, we also contributed to realizing the ideal 2D material with valley LWP phonons. We identified the existence of the valley LWP phonons in 11 2D material candidates with 11 LGs. This work offers a method to search for valley LWPs in 2D phononic systems and proposes 2D material candidates to obtain the valley LWP phonons.

Recently, Wang et al. [Phys. Rev. B, 106, 195129 (2022)] challenged a widely held belief in the field of Weyl physics, demonstrating that single-pair-Weyl-points (SP-WPs) can exist in nonmagnetic spinless systems, contrary to previous assumptions that they could only exist in magnetic systems. Wang et al. observed that the SP-WPs with opposite and even chiral charges (i.e., |C| = 2 or 4) could also exist in nonmagnetic spinless systems. In this Letter, we present a novel finding in which SP-WPs have a partner, namely a charged nodal surface, in nonmagnetic spinless systems. In contrast to previous observations, we show that the SP-WPs can have uneven chiral charges (i.e., |C| = 1). We identify 6 (out of 230) space groups (SGs) that contain such SP-WPs by searching the encyclopedia of emergent particles in three-dimensional crystals. Our finds were confirmed through the phonon spectra of two specific materials Zr3O (with SG 182) and NaPH2NO3 (with SG 173). This discovery broadens the range of materials that can host SP-WPs and applies to other nonmagnetic spinless crystals.

The realization of multi-Weyl systems with the minimum nonzero number of Weyl points and the maximum charge number remains challenging in topology physics. In this work, based on first-principles calculations, we propose that BeH2 is thermodynamically, mechanically, and dynamically stable in a cubic crystal structure with the P23 space group. Importantly, this is the first work to report the appearance of single-pair multi-Weyl point phonons with the maximum charge number in P23-type BeH2. Furthermore, the number and charge of the Weyl points and the phononic surface modes can be tuned by applying 1% and 2% uniaxial strains along the [100] and [111] directions, respectively. Finally, we report that clean charge-two single-pair triple-point phonons appear in P23-type BeH2 and investigate the related chiral phonon transition under the uniaxial strains.

When spin-orbit coupling (SOC) is absent, all proposed half-metals with twofold degenerate nodal points at the K (or K') point in 2D materials are classified as "Dirac half-metals" owing to the way graphene is utilized in the earliest studies. Actually, each band crossing point at the K or K' point is described by a 2D Weyl Hamiltonian with definite chirality; hence, it should be a Weyl point. To the best of its knowledge, there have not yet been any reports of a genuine (i.e., fourfold degenerate) 2D Dirac point half-metal. In this work, using first-principles calculations, it proposes for the first time that the 2D d0 -type ferromagnet Mg4 N4 is a genuine 2D Dirac half-metal candidate with a fourfold degenerate Dirac point at the S high-symmetry point, intrinsic magnetism, a high Curie temperature, 100% spin polarization, topology robust under the SOC and uniaxial and biaxial strains, and spin-polarized edge states. This work can serve as a starting point for future predictions of intrinsically magnetic materials with genuine 2D Dirac points, which will aid the frontier of topo-spintronics research in 2D systems.

Nowadays, it is recognized that semiconductors are prospective candidates for promising thermoelectric materials and the gapless topological phonon modes can result in a high phonon scattering rate. Therefore it is necessary to identify the topological phonons in semiconductors, which will aid future research aimed at gaining a better understanding of the thermoelectric properties of semiconductors. Using first-principles calculations and symmetry analysis, we propose a series of semiconductors as excellent candidates for the presence of exotic topological phonons. Remarkably, almost all the types of topological phonons, including various cases of Weyl/Dirac/triple point phonons, sextuple point phonons, nodal line phonons with different shapes and degenerates, and one-, two-, and three-nodal surface phonons can be observed in the phonon curves of these proposed semiconductors, revealing the ubiquitous existence of topological phonon modes in semiconductors. Moreover, the diverse types of topological phonons induce rich types of phononic surface modes in the surface orientations of semiconductors, which is advantageous to surface physics research.

Second-order topological phases (SOTPs) in two-dimensional (2D) magnetic and phononic systems are rarely reported. In this Letter, using first-principles calculations, we propose that the NiZrCl6 monolayer with space group P312 (No. 149) is a 2D ferromagnetic material with rich SOTPs: (i) magnetic SOTPs can be found in the band structures of both spin channels in NiZrCl6. NiZrCl6 hosts topologically protected corner states that have a quantized fractional charge (e/3) and are spin-polarized and pinned at the corners of the sample in real space. The SOTP nature in the NiZrCl6 monolayer is resistant to the spin–orbit coupling effect. (ii) Phononic SOTPs can be found in the phonon curves of NiZrCl6. The corner vibrational modes appear inside the frequency gap around 7.98 THz of the NiZrCl6 monolayer, and the secondary topological index can verify the nontrivial phase. The proposed 2D NiZrCl6 material can be a starting point for exploring higher-order topological phases in 2D magnetic and phononic systems.

Topological quantum catalysts are developing rapidly due to the emergence of exotic quantum materials and their corresponding catalytic performance. Although tens of thousands of topological semimetals have been developed, their low topological surface density of states (DOSs) remains a hindrance to the development of high-performance catalysts for electrochemical hydrogen evolution reactions (HERs). In this work, we investigate the potential of double dual-nodal line (DDNL) semimetals, which exhibit large surface DOSs and fair-low Gibbs free energies, as ideal topological quantum catalysts (TQCs) for HER. Using the NaAlGe compound as a representative example, we demonstrate that its DDNLs and high surface DOSs around the Fermi level provide advantages for achieving exceptionally high catalytic activity in the electrochemical HER process. Through a comparison of catalytic performance under different (electron and hole) doping and uniaxial strain conditions, we establish a linear correlation between the Gibbs free energy (AGH*) and the projected surface DOSs on the (001) semi-infinite surface of the DDNL semimetal NaAlGe, specifically for the hydrogen evolution process. Our work introduces an alternative category of high-performance TQCs free of noble metals and contributes to a better understanding of the relationship between catalytic performance for HER and surface DOSs in DDNL semimetals.

AbstractUnlike electron systems, the phonon system has its own advantages (such as no limitations regarding Fermi energy and the effect of spin‐orbit coupling) and, therefore, can be viewed as a unique platform to predict spinless nodal‐line states. Nodal‐line phonons can be divided into open and closed nodal‐line phonons from a mathematical point of view. In this work, using first‐principle calculations, we select Ba(AgS)2 and Ca(ZnP)2, with the space group 1, as examples of realistic materials to investigate the difference between the open and closed nodal‐line phonons. Two phonon band‐crossing points (PBCPs) along the K–Γ and H–A paths are present in their phonon spectra, and they correspond to closed nodal lines in Ba(AgS)2 and open nodal lines in Ca(ZnP)2, respectively. The difference between these two types nodal‐line phonons is explained through symmetry analysis. All the nodal‐line phonons are topologically nontrivial, with the prominent phonon surface states well separated from the bulk states, favorable for experimental detection. This work offers a deep understanding of the open and closed nodal‐line phonons. It also proposes ideal candidates with multiple open and closed nodal‐line phonons for follow‐up experimental confirmation.

Heusler alloys, a class of easily prepared, highly ordered intermetallic compounds, were first reported in 1903. Since then, Heusler alloys have presented various physical phenomena in modern condensed-matter physics. Among Heusler alloys, Heusler-based fully compensated ferrimagnetic half-metals (FCF-HMs) are, particularly, relevant because they host fully spin polarization and have no net magnetic moment, making them have no stray field and less affected by external magnetic fields. Based on first-principles calculations and a tight-binding Hamiltonian model, we provide new insight into inverse-Heusler-based (IHB) FCF-HMs and reveal that they exhibit spin-polarized Weyl and quadratic nodal lines as well as spin-polarized drumheadlike surface states. This paper presents the electron-filling-based design rule and material candidates for IHB FCF-HMs and suggests that IHB FCF-HMs are promising candidates for follow-up investigations in the field of topological spintronics. Subsequent experimental confirmation of the topological states in IHB FCF-HMs is imminent.

This year, researchers have been on the lookout for real materials with one-nodal, two-nodal (two-NS), and three-nodal surface phonons. However, materials with two-NS phonons have been scarce until recently. This paper contributes to the understanding of the symmetry conditions of two-NS phonons. Two-NS phonons have NS states that are localized on two of three k(i) = +/-pi (i = x, y, z) planes in the three-dimensional Brillouin zone). They are dominated by twofold screw symmetry and time-reversal symmetry. This paper also contributes the prediction of a series of materials with two-NS states in their phonon dispersions. First, by screening all 230 space groups (SGs), we discovered 19 SG candidates (with Nos. 18, 55-60, 90, 94, 113, 114, 127-130, and 135-138) that have two-NS phonons. Second, based on first-principles calculations, we proposed 19 realistic material candidates hosting two-NS phonons: P2(1)2(1)2-type ZnTeMoO6 (with SG No. 18), Pbma-type Cs2Te2 (with SG No. 55), Pccn-type Sr2SnO4 (with SG No. 56), Pbon-type CaAlPd (with SG No. 57), Pnnm-type PtO2 (with SG No. 58), Pmmn-type KLi2As (with SG No. 59), Pbcn-type CV2 (with SG No. 60), P42(1)2-type BaVCu4P4O17 (with SG No. 90), P4(2)2(1)2-type Na5Fe3F14 (with SG No. 94), P (4) over bar2(1)m-type BaS3 (with SG No. 113), P (4) over bar2(1)c-type Na4SnS4 (with SG No. 114), P4/mbm-type ReO3 (with SG No. 127), P4/mnc-type Sr4Li2Si4N8O (with SG No. 128), P4/nmm-type BaHfN2 (with SG No. 129), P4/ncc-type Bi2CuO4 (with SG No. 130), P4(2)/mbc-type YB2C (with SG No. 135), P4(2)/mnm-type MgF2 (with SG No. 136), P4(2)/nmc-type YB4Rh4 (with SG No. 137), and P4(2)/non-type LiClO2 (with SG No. 138). Third, we discovered 622 (out of 10 037) materials with two-NS phonons by checking the phonon database at Kyoto University. Our present paper provides a better understanding of the two-NS states in phonon systems (or even other bosonic systems) and suggests a huge number of material candidates with two-NS phonons.

Topological states with quadratic dispersion and multiple-fold band degeneracy have not only fundamentally updated our knowledge of the phases of matter but also become a major cutting-edge research direction in condensed matter physics. Note that the sixfold band degeneracy corresponds to the maximum degeneracy in phononic systems. Remarkably, in this work, based on first-principles calculations, we proposed an authentic material, Ta3Sn, which hosts phononic nodal points with both quadratic dispersion and maximum band degeneracy, i.e., quadratic contact triple point, quadratic contact Dirac point and sixfold-degenerate point. Furthermore, the corresponding symmetry analysis with the help of the k ?? p model further deepens the understanding of the relative physics. Evident arc-shaped surface states, originating from the projected phononic nodal points, can strongly benefit the experimental detection. It is hoped that the rich types of phonon points with quadratic dispersion and multiple-fold band degeneracy as well as the surface states can be confirmed in experiments soon.