Most topological insulators discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped TI phases and the gapless TSMs. Recently, we have proposed a new family of TSMs in time-reversal invariant {\it spinless} systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a $\mathbb{Z}_{4}$ = 2 topological crystalline insulator (TCI), by including substantial SOC. We demonstrate that in three space groups ({\it i.e.} $Pbam$ (No.55), $P4/mbm$ (No.127) and $P4_2/mbc$ (No.135)), the TCI supports a fourfold Dirac fermion on the (001) surface protected by two glide symmetries, which originates from the intertwined drumhead surface states of the CICE NLs. The higher order topology is further demonstrated by the emergence of one-dimensional helical hinge states, indicating a new higher order topological insulator protected by a glide symmetry.
In recent years, the exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in seeking for new topological phases and material realization. In this work, we propose a new family of TSMs which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE) at half-filling. Meanwhile, the CICE at half-filling guarantees the presence of a second pair of CICE beyond half-filling. Both CICEs are linked at four-fold degenerate points (FDPs) at zone boundaries. In addition, we…
Using ab initio calculations based on density-functional theory and effective model analysis, we propose that the trigonal YH3(Space Group: P-3c1) at ambient pressure is a node-line semimetal when spin-orbit coupling (SOC) is ignored. This trigonal YH3 has very clean electronic structure near Fermi level and its nodal lines locate very closely to the Fermi energy, which makes it a perfect system for model analysis. Symmetry analysis shows that the nodal ring in this compound is protected by the glide-plane symmetry, where the band inversion of |Y+,dxz> and |H1-,s> orbits at Gamma point is resp…
We elaborate that single-layer graphene with periodic vacancies can have a band structure containing nodal lines or nodal loops, opening the possibility of graphene-based electronic or spintronic devices with novel functionalities. The principle is that by removing carbon atoms such that the lattice becomes nonsymmorphic, every two sublattices in the unit cell will map to each other under glide plane operation. This mapping yields degenerate eigenvalues for the glide plane operation, which guarantees that the energy bands must stick together pairwise at a boundary of the Brillouin zone. Moving…
Previously known three-dimensional Dirac semimetals (DSs) occur in two types -- topological DSs and nonsymmorphic DSs. Here we present a novel three-dimensional DS that exhibits both features of the topological and nonsymmorphic DSs. We introduce a minimal tight-binding model for the space group 100 that describes a layered crystal made of two-dimensional planes in the $p4g$ wallpaper group. Using this model, we demonstrate that double glide-mirrors allow a noncentrosymmetric three-dimensional DS that hosts both symmetry-enforced Dirac points at time-reversal invariant momenta and twofold-dege…
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…
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…
Based on first-principles calculations and effective model analysis, we propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can host a three-dimensional nodal chain semimetal state. Distinguished from the previous material IrF4 [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal chain here is protected by mirror reflection symmetries of a simple space group, while in IrF4 the nonsymmorphic space group with a glide plane is a necessity. Moreover, in the presence of SOC, the nodal chain in WC type HfC evolves into Weyl points. In the Brillouin zone, a total of 30 pairs o…
Spin-gapless semimetals (SGSMs), which generate 100\% spin polarization, are viewed as promising semi-half-metals in spintronics with high speed and low consumption. We propose and characterize a new $\mathbb{Z_{\mathrm{2}}}$ class of topological nodal line (TNL) in SGSMs. The proposed TNLSGSMs are protected by space-time inversion symmetry or glide mirror symmetry with two-dimensional (2D) fully spin-polarized nearly flat surface states. Based on first-principles calculations and effective model analysis, a series of high-quality materials with $\textit{R}\overline{3}\textit{c}$ and $\textit{…
A well-established result in condensed matter physics states that materials crystallizing in symmetry groups containing glide reflection symmetries possess nodal lines on the energy bands. These nodal lines are topologically protected and appear on the fixed planes of the reflection in reciprocal space. In the presence of inversion symmetry, the energy bands are degenerate and the nodal lines on the fixed plane may hybridize or may cross. In the former case, the crossing is avoided, thus producing lines on reciprocal space where the energy gap is small, and in the latter, the nodal lines will …
We reveal a class of three-dimensional $d$-orbital topological materials in the antifluorite Cu$_2$S family. Derived from the unique properties of low-energy $t_{2g}$ states, their phases are solely determined by the sign of spin-orbit coupling (SOC): topological insulator for negative SOC, whereas topological semimetal for positive SOC; both having Dirac-cone surface states but with contrasting helicities. With broken inversion symmetry, the semimetal becomes one with a nodal box consisting of butterfly-shaped nodal lines that are robust against SOC. Further breaking the tetrahedral symmetry …
The materials with spin-polarized electronic states have attracted a huge amount of interest due to their potential applications in spintronics. Based on first-principles calculations, we study the electronic characteristics of a series of AB2X4 chalcogeniden spinel structures and propose two promising candidates, VZn2O4 and VCd2S4, are spin-polarized semimetal materials. Both of them have ferromagnetic ground states. Their bands near the Fermi level are completely spin-polarized and form two types of nodal rings in the spin-up channel, and the large gaps in the spin-down channel prevent the s…
Nodal-loop semimetals are materials in which the conduction and valence bands cross on a one-dimensional loop in the reciprocal space. For the nodal-loop character to manifest in physical properties, it is desired that the loop is close to the Fermi level, relatively flat in energy, simple in its shape, and not coexisting with other extraneous bands. Here, based on the first-principles calculations, we show that the monoclinic CuTeO$_3$ is a realistic nodal-loop semimetal that satisfies all these requirements. The material features only a single nodal loop around the Fermi level, protected by …
We study three-dimensional nodal line semimetals (NLSMs) with magnetic ordering and strong spin-orbit interaction. Two distinct classes of magnetic NLSMs are proposed. The first class is band-inversion NLSM where the accidental line node is induced by band inversion and locally protected by glide mirror plane and the combined time-reversal and inversion symmetries. This can be viewed as a trivial stacking of the two-dimensional antiferromagnetic Dirac semimetals. The second class is essential NLSM where the nodal features are filling-enforced by specific magnetic symmetry group. We further pro…
As emerging topological nodal-line semimetals, the family of ZrSiX (X = O, S, Se, Te) has attracted broad interests in condensed matter physics due to their future applications in spintonics. Here, we apply a scanning tunneling microscopy (STM) to study the structural symmetry and electronic topology of ZrSiSe. The glide mirror symmetry is verified by quantifying the lattice structure of the ZrSe bilayer based on bias selective topographies. The quasiparticle interference analysis is used to identify the band structure of ZrSiSe. The nodal line is experimentally determined at $\sim$ 250 meV ab…
We propose a class of topological metals, which we dub \emph{Hund nodal line semimetals}, arising from the strong Coulomb interaction encoded in the Hund's coupling between itinerant electrons and localized spins. We here consider a particular twisted spin configuration, which is realized in the double exchange model which describes the manganite oxides. The resulting effective tetragonal lattice of electrons with hoppings tied to the local spin features an antiunitary \emph{non-symmorphic} symmetry that in turn, together with another non-symmorphic but unitary, glide mirror symmetry, protects…
We have performed angle-resolved photoemission spectroscopy of layered ternary telluride Ta3SiTe6 which is predicted to host nodal lines associated with nonsymmorphic crystal symmetry. We found that the energy bands in the valence-band region show Dirac-like dispersions which present a band degeneracy at the R point of the bulk orthorhombic Brillouin zone. This band degeneracy extends one-dimensionally along the whole SR high-symmetry line, forming the nodal lines protected by the glide mirror symmetry of the crystal. We also observed a small band splitting near EF which supports the existence…
The study of topology protected electronic properties is a fascinating topic in present day condensed matter physics research. New topological materials are frequently being proposed and explored through various experimental techniques. Ta$_{3}$SiTe$_{6}$ is a newly predicted topological semimetal with fourfold degenerate nodal-line crossing in absence of spin-orbit coupling (SOC) and an hourglass Dirac loop, when SOC is included. Recent angle-resolved photoemission spectroscopy study in this material, has also confirmed Dirac like dispersions and two nodal-lines near the Fermi energy, protect…
Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point---a four-fold-degenerate band-crossing point with cubic dispersion in a plane and a linear dispersion in the third direction---can be stabilized through the presence of a nonsymmorphic glide mirror symmetry in the space group of the crystal. Notably, the cubic Dirac point in our case appears on a threefold axis, even though it has been believed previously that such a point can only appear on a sixfold axi…
We investigate the topological nodal structure of three-dimensional (3D) ZrTe$_5$ driven by Zeeman splitting as a function of the direction of external magnetic (B) field by using a Wannier-function-based tight-binding (WFTB) model obtained from first-principles calculations. It is known that small external stimuli can drive 3D ZrTe$_5$ into different topological phases including Dirac semimetal. In order to emphasize the effect of Zeeman splitting, we consider 3D ZrTe$_5$ in a strong TI phase with a small band gap. With Zeeman splitting greater than the band gap, the WFTB model suggests that …
We instigate the angle-dependent magnetoresistance (AMR) of the layered nodal-line Dirac semimetal ZrSiS for the in-plane and out-of-plane current directions. This material has recently revealed an intriguing butterfly-shaped in-plane AMR that is not well understood. Our measurements of the polar out-of-plane AMR show a surprisingly different response with a pronounced cusp-like feature. The maximum of the cusp-like anisotropy is reached when the magnetic field is oriented in the $a$-$b$ plane. Moreover, the AMR for the azimuthal out-of-plane current direction exhibits a very strong four-fold …
Magnetically tunable symmetry-enforced nodal lines producing huge anomalous Hall conductivity in altermagnetic $α$-MnTe
International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所磁顶国际研究中心）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；New Technologies-Research Center, University of West Bohemia in Pilsen（比尔森西波希米亚大学新技术研究中心）；Photon Science Division, Paul Scherrer Institut（保罗谢尔研究所光子科学部）；Institute of Semiconductor and Solid State Physics, Johannes Kepler University of Linz（林茨约翰内斯开普勒大学半导体与固体物理研究所）；Solaris National Synchrotron Radiation Centre（索拉里斯国家同步辐射中心）
Nonsymmorphic symmetries like screws and glides produce electron band touchings, obstructing the formation of a band insulator and leading, instead, to metals or nodal semimetals even when the number of electrons in the unit cell is an even integer. Here, we calculate the electron fillings compatible with being a band insulator for all 230 space groups, for noninteracting electrons with time-reversal symmetry. Our bounds are tight - that is, we can rigorously eliminate band insulators at any forbidden filling and produce explicit models for all allowed fillings - and stronger than those recent…
Degenerate points/lines in the bulk band structures of crystals have become a staple of the growing number of topological materials. The bulk-boundary correspondence provides a relation between bulk topology and surface states. While line degeneracies of bulk excitations have been extensively characterized, line degeneracies of surface states are not well understood. We show that SnIP, a quasi-one-dimensional van der Waals material with a double helix crystal structure, exhibits topological nodal rings/lines in both the bulk phonon modes and their corresponding surface states. Using a combinat…
A recent experiment reported two new non-centrosymmetric superconductors NbIr$_{2}$B$_{2}$ and TaIr$_{2}$B$_{2}$ with respective superconducting transition temperatures of 7.2 K and 5.2 K and further suggested their superconductivity to be unconventional [K. Górnicka \textit{et al}., Adv. Funct. Mater. 2007960 (2020)]. Here, based on first-principles calculations and symmetry analysis, we propose that $T$Ir$_{2}$B$_{2}$ ($T$=Nb, Ta) are topological Weyl metals in the normal state. In the absence of spin-orbit coupling (SOC), we find that NbIr$_{2}$B$_{2}$ has 12 Weyl points, and TaIr$_{2}$B$_{…
It was recently shown that nonsymmorphic space group symmetries can protect novel surface states with hourglass-like dispersions. In this paper, we show that such dispersions can also appear in the bulk of three-dimensional (3D) systems which respect nonsymmorphic symmetries. Specifically, we construct 3D lattice models featuring hourglass-like dispersions in the bulk, which are protected by nonsymmorphic and time-reversal symmetries. We call such systems hourglass semimetals, as they have point or line nodes associated with hourglass-like dispersions. Hourglass nodal lines appear in glide-inv…
Discovery of an Antiferromagnetic Topological Nodal-line Kondo Semimetal
Beijing Normal University（北京师范大学）；Zhejiang University（浙江大学）；Donostia International Physics Center (DIPC)（多诺斯蒂亚国际物理中心）；University of Oxford（牛津大学）；Diamond Light Source（钻石光源）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Nanjing University（南京大学）；ShanghaiTech University（上海科技大学）；Tsinghua University（清华大学）；MAX IV Laboratory, Lund University（隆德大学MAX IV实验室）；Stanford Synchrotron Radiation Light Source, SLAC National Accelerator Laboratory（斯坦福同步辐射光源，SLAC国家加速器实验室）；Swiss Light Source, Paul Scherrer Institute（瑞士光源，保罗谢尔研究所）；Tokyo Institute of Technology（东京工业大学）；Princeton University（普林斯顿大学）
In some Dirac systems with time-reversal (T) and glide (G) symmetries, multihelicoid surface states (MHSSs) appear, as discussed in various systems such as electronic and photonic ones. However, the topological nature and the conditions for the appearance of the MHSSs have not been understood. Here we show that MHSSs result from bulk-surface correspondence for the $Z_2$ monopole charge Q, which cannot be defined as a local quantity associated with the Dirac point, unlike the Z monopole charge characterizing Weyl points. The previously known formula of Q turns out to be non-gauge-invariant and …
In this work, we construct a generalized Kane model with a new coupling term between itinerant electron spins and local magnetic moments of anti-ferromagnetic ordering in order to describe the low energy effective physics in a large family of anti-ferromagnetic half-Heusler materials. Topological properties of this generalized Kane model is studied and a large variety of topological phases, including Dirac semimetal phase, Weyl semimetal phase, nodal line semimetal phase, type-B triple point semimetal phase, topological mirror (or glide) insulating phase and anti-ferromagnetic topological insu…
