As a novel type of fermionic state, hybrid nodal loop with the coexistence of both type-I and type- II band crossings has attracted intense research interest. However, it remains a challenge to realize hybrid nodal loop in both two-dimensional (2D) materials and in ferromagnetic (FM) materials. Here, we propose the first FM hybrid nodal loop in 2D CrN monolayer. We show that the material has a high Curie temperature (> 600 K) FM ground state, with the out-of-plane [001] magnetization. It shows a half-metallic band structure with two bands in the spin-up channel crossing each other near the Fermi level. These bands produce both type-I and type-II band crossings, which form a fully spin-polarized hybrid nodal loop. We find the nodal loop is protected by the mirror symmetry and robust against spin-orbit coupling (SOC). An effective Hamiltonian characterizing the hybrid nodal loop is established. We further find the configuration of nodal loop can be shifted under external perturbations such as strain. Most remarkably, we demonstrate that both type-I and type-II Weyl nodes can be realized from such FM hybrid nodal loop by simply shifting the magnetization from out-of-plane to in-plane. Our work provides an excellent candidate to realize FM hybrid nodal loop and Weyl fermions in 2D material, and is also promising for related topological applications with their intriguing properties.
For topological materials with coexistence of Weyl nodes and nodal rings, the surface-state configuration and connection are unique yet have never been studied and discussed before. In this paper, we predict a ferromagnetic (FM) material, Cs2MoCl6, with coexistence of Weyl and nodering fermions in its spinful FM electronic band structure, which is unusual since FM materials are very rare in nature and node-ring band crossings will usually open a gap when spin-orbit coupling (SOC) is taken into consideration. We find that the surface states of Cs2MoCl6 show different properties along different …
Based on $ab$ $initio$ calculations and low-energy effective $k{\cdot}p$ model, we propose a type of Weyl nodal point-line fermion, composed of 0D Weyl points and 1D Weyl nodal line, in ferromagnetic material Eu$_5$Bi$_3$. In the absence of spin-orbital coupling (SOC), the spin-up bands host a pair of triply degenerate points together with a unique bird-cage like node structure. In the presence of SOC with (001) magnetization, each triplet point splits into a double Weyl point and a single Weyl point accompanied by two nodal rings, forming two sets of Weyl nodal point-line fermions near the Fe…
The hourglass fermions in solid-state materials have been attracting significant interest recently. However, realistic two-dimensional (2D) materials with hourglass-shaped band structures are still very scarce. Here, through the first-principles calculations, we identify the monolayer Pb(ClO$_{2}$)$_{2}$ and Sr(ClO$_{2}$)$_{2}$ materials as the new realistic materials platform to realize 2D hourglass Weyl nodal loop. We show that these monolayer materials possess an hourglass Weyl nodal loop circling around the $Γ$ point and Weyl nodal line on the Brillouin zone (BZ) boundary in the absence of…
Weyl-Dirac nodal line phonons with type-selective surface states
Inner Mongolia University（内蒙古大学）；Research Center for Quantum Physics and Technologies, School of Physical Science and Technology, Inner Mongolia University（内蒙古大学物理科学与技术学院量子物理与技术研究中心）；Key Laboratory of Semiconductor Photovoltaic Technology and Energy Materials at Universities of Inner Mongolia Autonomous Region, Inner Mongolia University（内蒙古自治区高校半导体光伏技术与能源材料重点实验室（内蒙古大学））
Weyl nodes can be classified into zero-dimensional (0D) Weyl points (WPs), 1D Weyl nodal lines (WNL) and 2D Weyl nodal surfaces (WNS), which possess finite Chern numbers. Up to date, the largest Chern number of WPs identified in Weyl semimetals is 4, which is thought to be a maximal value for linearly crossing points in solids. On the other hand, whether the Chern numbers of nonzero-dimensional linear crossing Weyl nodal objects have one upper limit is still an open question. In this work, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show …
Recently, magnetic topological semimetals have received a lot of attention due to their potential applications in the field of spintronics. By using first-principles calculations, we propose that two ferromagnetic spinel materials of X2MnO4 (X=Li, Na) have Weyl-type nodal chains around the Fermi level. Their stabilities are validated by cohesive energies, phonon dispersions, and elastic constants. The nodal chains are composed of two types of nodal loops, which are protected by the glide operation Mz, the mirror operation M101 and their equivalent. The drumhead surface states are observed on t…
In parallel to electronic systems, the concept of topology has been extended to phonons, which has led to the birth of topological phonons. Very recently, nodal point phonons, nodal line phonons, and nodal surface phonons have been proposed, and a handful of candidate materials have been predicted in solid-state materials. In this work, based on symmetry analysis and first-principles calculations, we propose that hourglass Weyl nodal line (HWNL) phonons and Dirac nodal line (DNL) phonons coexist in the phonon dispersion of a single material, KCuS, with a $Pnma$-type structure. The HWNLs and DN…
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 operation…
Nodal line semimetals in two-dimensional (2-D) materials have attracted intense attention currently. From fundamental physics and spintronic applications points of view, high Curie temperature ferromagnetic (FM) ones with nodal lines robust against spin-orbit coupling (SOC) are significantly in desirable. Here, we propose that FM K2N monolayer is such Weyl nodal line semimetal. We show that K2N monolayer is dynamically stable, and has a FM ground magnetic state with the out-of-plane [001] magnetization. It shows two nodal lines in the low-energy band structures. Both nodal lines are robust aga…
Here, we systematically investigate the structure, phase stability, half-metallicity, and topological electronic structure for a new topological spintronic material NaV2O4. The material has a tetragonal structure with excellent dynamical and thermal stabilities. It shows a half-metallic ground state, where only the spin-up bands present near the Fermi level. These bands form a Weyl nodal line close to the Fermi level, locating in the kz = 0 plane. The nodal line is robust against SOC, under the protection of the mirror symmetry. The nodal line band structure is very clean, thus the drumhead su…
Two-dimensional (2D) materials have attracted great attention and spurred rapid development in both fundamental research and device applications. The search for exotic physical properties, such as magnetic and topological order, in 2D materials could enable the realization of novel quantum devices and is therefore at the forefront of materials science. Here, we report the discovery of two-fold degenerate Weyl nodal lines in a 2D ferromagnetic material, a single-layer gadolinium-silver compound, based on combined angle-resolved photoemission spectroscopy measurements and theoretical calculation…
Using first-principles electronic structure calculations, we show that ferromagnetic Heusler compounds Co$_2$MnX (X= Si, Ge, Sn) present non-trivial topological characteristics and belong to the category of Weyl semimetals. These materials exhibit two topologically interesting band crossings near the Fermi level. These band crossings have complex 3D geometries in the Brillouin zone and are characterized by non-trivial topology as Hopf links and chain-like nodal lines, that are protected by the perpendicular mirror planes. The spin-orbit interaction split these nodal lines into several zero-dim…
Symmetry-Protected Weyl Nodal Loops in a Triangular Altermagnet
University of Utah（犹他大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Australian Nuclear Science and Technology Organisation（澳大利亚核科学和技术组织）；The University of Sydney（悉尼大学）
Magnetic topological quantum materials have attracted great attention due to their exotic topological quantum physics induced by the interplay among crystalology, magnetism, and topology, which is of profound importance to fundamental research and technology applications. However, limited materials are experimentally available, most of whom are realized by magnetic impurity doping or heterostructural constructions. In this work, based on the first-principles calculations, we predict that double perovskite Ba2CdReO6 is an intrinsic ferromagnetic topological semi-half-metal, while the ferrimagne…
Using both an effective three-band model and {\it ab initio} calculations, we have investigated various topological features in the cubic ferromagnetic $5d^{1,2}$ systems showing large spin-orbit coupling (SOC): Ba$_2$NaOsO$_6$, Sr$_2$SrOsO$_6$, and Ba$_2$$B$ReO$_6$ ($B$= Mg, Zn). In the presence of time-reversal symmetry (${\cal T}$), spinless Dirac nodal loops linked to each other at the $W$ points appear in the mirror planes. Remarkably, breaking ${\cal T}$ leads to spinful magnetic Weyl nodal loops (MWNLs) that are robust even at large SOC and correlation strength $U$ variation due to the …
Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic ban…
We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetiza…
Despite of a rapidly expanding inventory of possible crystalline Weyl semimetals, all of them are constrained by the Nielsen-Ninomiya no-go theorem, namely, that left- and right-handed Weyl points appear in pairs. With time-reversal (T) symmetry, an even stronger version holds for the semimetals, i.e., all eight time-reversal-invariant points in the Brillouin zone (BZ) simultaneously host Weyl points or not. However, all the well-known conclusions from the no-go theorem are implicitly within the current framework of topological semimetals, and in this work, we shall go beyond it by exploring c…
Based on first-principles calculations and effective model analysis, we propose that the noncentrosymmetric superconductor YCoC$_2$ in normal state is a topological semimetal. In the absence of spin-orbit coupling (SOC), it can host two intersecting nodal rings protected by two mirror planes, respectively. One ring is composed of type-I nodes, where the two crossing bands have opposite slop sign in their dispersions. The other ring consists of both type-I and type-II nodes (the slop signs of the two bands are the same in certain direction). In the presence of SOC, the former nodal ring is gapp…
Materials containing multiple topological characteristics become more exotic when combined with noncentrosymmetric crystal structures and unusual magnetic phases such as the compensated half-metal state, which is gapped in one spin direction and conducting in the other. First principles calculations reveal these multiple topological features in the compensated half-metal Cr$_2$CoAl having neither time-reversal nor inversion symmetries. In the absence of (minor) spin-orbit coupling (SOC), there are (1) a total of twelve pairs of magnetic Weyl points, (2) three distinct sets of triple nodal poin…
Topological semimetals are three dimensional materials with symmetry-protected massless bulk excitations. As a special case, Weyl nodal-line semimetals are realized in materials either having no inversion or broken time-reversal symmetry and feature bulk nodal lines. The 111-family of materials, LaNiSi, LaPtSi and LaPtGe (all lacking inversion symmetry), belong to this class. Here, by combining muon-spin rotation and relaxation with thermodynamic measurements, we find that these materials exhibit a fully-gapped superconducting ground state, while spontaneously breaking time-reversal symmetry a…
Three dimensional materials with strong spin-orbit coupling and magnetic interactions represent an opportunity to realize a variety of rare and potentially useful topological phases. In this work, we use first principles calculations to show that the recently synthesized material Bi2MnSe4 displays a combination of band inversion and magnetic interactions, leading to several topological phases. Bi2PbSe4, also studied, also displays band inversion and is a topological insulator. In bulk form, the ferromagnetic phase of Bi2MnSe4 is either a nodal line or Weyl semimetal, depending on the direction…
Nodal-Surface and Flat-Band Driven Large Anomalous Nernst Effect in Epitaxial Ferromagnetic Weyl Metal Fe5Si3
Indian Institute of Technology Delhi（印度德里理工学院）；Indian Institute of Technology Hyderabad（印度海得拉巴理工学院）；National Institute for Materials Science（日本国立材料研究所）
By utilizing symmetry analysis and electronic structure calculations, we investigated the low-temperature orthorhombic phase of Ag$_{2}$Se in ${\cal SG}$~17. In addition to the discovery of a nodal plane at $k_{z}=π$ protected by the joint operation of time-reversal (${\cal T}$) and the 2-fold screw rotation $S_{2z}$, we found 24 Weyl points mainly residing at the $k_{y}=0$ plane with notable Fermi arc and large quasiparticle interference pattern (QPI). Due to the absence of mirror symmetry, a pair of Weyl points with opposite chirality reside at different binding energies, which makes this sy…
WloopPHI is a Python code that expands the features of WIEN2k, a full-potential all-electron density functional theory package, by the characterization of Weyl semimetals. It enables the calculation of the chirality (or "monopole charge") associated with Weyl nodes and nodal lines. The theoretical methodology for the calculation of the chirality is based on an extended Wilson loop method and a Berry phase approach. We validate the code using TaAs, which is a well-characterized Weyl semimetal, both theoretically and experimentally. Afterwards, we applied the method to the characterization of YR…
We report the identification of symmetry-enforced nodal planes (NPs) in CoSi providing the missing topological charges in an entire network of band-crossings comprising in addition multifold degeneracies and Weyl points, such that the fermion doubling theorem is satisfied. In our study we have combined measurements of Shubnikov-de Haas (SdH) oscillations in CoSi with material-specific calculations of the electronic structure and Berry curvature, as well as a general analysis of the band topology of space group (SG) 198. The observation of two nearly dispersionless SdH frequency branches provid…
By means of first-principles calculations and modeling analysis, we have predicted that the traditional 2D-graphene hosts the topological phononic Weyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum. The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 at the BZ corners \emph{K} and \emph{K}', and PW3 locating along the $Γ$-\emph{K} line), one type-II PW4 locating along the $Γ$-\emph{M} line, and one PNL surrounding the centered $Γ$ point in the $q_{x,y}$ plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout t…
We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in the space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire …
In mesoscopic physics, the application of a time-periodic drive leads to novel transport behaviour, which is absent in the static regimes. Here we consider a quantum pumping protocol, such that the quasiparticles of Weyl/multi-Weyl and nodal-line semimetals are subjected to a time-periodic rectangular potential well. The presence of an oscillating potential of frequency $ω$ creates equispaced Floquet side-bands with spacing $\hbar ω$. As a result, a Fano resonance is observed when the difference in the Fermi energy (i.e., the energy of the incident quasiparticle), and the energy of one of the …
Dissipationless transport signature of topological nodal lines
Leibniz Institute for Solid State and Materials Research (IFW Dresden)（莱布尼茨固体的和材料研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群 ct.qmat）；Laboratoire de Physique des Solides (LPS Orsay)（固体物理实验室）；CNRS, Laboratoire National des Champs Magnétiques Intenses, Université Grenoble-Alpes, Université Toulouse 3, INSA-Toulouse, EMFL（法国国家科学研究中心，强磁场国家实验室，格勒诺布尔阿尔卑斯大学，图卢兹第三大学，图卢兹国立理工学院，法兰西金属联邦）
