Topological nodal-line semimetals in ferromagnetic rare-earth-metal monohalides
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The topological nodal-line semimetals (TNLSs) found so far are extremely limited to nonmagnetic materials and most of them are spinless. Here, the authors find from first-principles calculations and an effective model analysis that the single-layer rare-earth monohalides La$X$ and single-layer Gd$X$ (where $X$ is Cl or Br) are ideal 2D Weyl semimetals and large-gap 2D quantum anomalous Hall insulators (QAHIs), respectively. Moreover, 3D La$X$ and 3D Gd$X$ are TNLSs and 3D weak QAHIs, respectively. The nodal lines in 3D La$X$ are robust against strong spin-orbit coupling, providing a novel platform toward exploring the exotic properties in nodal-line fermions.Keywords:
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We use first principles calculations to study the electronic properties of rock salt rare earth monopnictides La$X$ ($X=$N, P, As, Sb, Bi). A new type of topological band crossing termed `linked nodal rings' is found in LaN when the small spin-orbital coupling (SOC) on nitrogen orbitals is neglected. Turning on SOC gaps the nodal rings at all but two points, which remain gapless due to $C_4$-symmetry and leads to a 3D Dirac semimetal. Interestingly, unlike LaN, compounds with other elements in the pnictogen group are found to be topological insulators (TIs), as a result of band reordering due to the increased lattice constant as well as the enhanced SOC on the pnictogen atom. These TI compounds exhibit multi-valley surface Dirac cones at three $\bar{M}$-points on the $(111)$-surface.
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Topological Dirac semimetals with accidental band touching between conduction and valence bands protected by time reversal and inversion symmetry are at the frontier of modern condensed matter research. Theoretically one can get Weyl and/or nodal-line semimetals by breaking either one of them. Most of the discovered topological semimetals are nonmagnetic i.e respect time reversal symmetry. Here we report the experimental observation of a topological nodal-line semi metallic state in GdSbTe using angle-resolved photoemission spectroscopy. Our systematic study reveals the detailed electronic structure of the paramagnetic state of GdSbTe. We observe the presence of multiple Fermi surface pockets including a diamond-shape, an elliptical shape, and small circular pockets around the zone center and high symmetry M and X points of the Brillouin zone (BZ), respectively. Furthermore, we observe the presence of a Dirac-like state at the X point of the BZ. Interestingly, our experimental data shows a robust Dirac like state both below and above the magnetic transition temperature (T_N ~ 13 K). Having relatively higher transition temperature, GdSbTe provides an archetype platform to study the interaction between magnetism and topological states of matter.
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Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds $A{X}_{2}$ $(A=\text{Ca}$, Sr, Ba; $X=\text{Si}$, Ge, Sn). Taking ${\mathrm{BaSn}}_{2}$ as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snakelike nodal loop in three-dimensional momentum space. Drumheadlike surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated double-drumhead-like surface states appear on the (010) surface. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with ${\mathbb{Z}}_{2}$ topological invariants (1;001). Since spin-orbit coupling effects are weak in light elements, the nodal-line semimetal phase is expected to be achievable in some alkaline-earth germanides and silicides.
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Topological semimetals (TSMs) including Weyl semimetals and nodal-line semimetals are expected to open the next frontier of condensed matter and materials science. Although the first inversion breaking Weyl semimetal was recently discovered in TaAs, its magnetic counterparts, i.e., the time-reversal breaking Weyl and nodal line semimetals, remain elusive. They are predicted to exhibit exotic properties distinct from the inversion breaking TSMs including TaAs. In this paper, we identify the magnetic topological semimetal state in the ferromagnetic half-metal compounds Co$_2$TiX (X=Si, Ge, or Sn) with Curie temperatures higher than 350 K. Our first-principles band structure calculations show that, in the absence of spin-orbit coupling, Co$_2$TiX features three topological nodal lines. The inclusion of spin-orbit coupling gives rise to Weyl nodes, whose momentum space locations can be controlled as a function of the magnetization direction. Our results not only open the door for the experimental realization of topological semimetal states in magnetic materials at room temperatures, but also suggest potential applications such as unusual anomalous Hall effects in engineered monolayers of the Co$_2$TiX compounds at high temperatures.
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Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional (3D) Weyl semimetals, 3D Dirac semimetals, and 3D node-line semimetals (NLSs). In particular, several compounds (e.g., certain 3D graphene networks, CuPdN, CaP) were discovered to be 3D NLSs, in which the conduction and valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional (2D) Dirac semimetal (e.g., graphene), 2D topological semimetals are much less investigated. Here we propose a new concept of a 2D NLS and suggest that this state could be realized in a new mixed lattice (named as HK lattice) composed by Kagome and honeycomb lattices. It is found that AB (A is a group-IIB cation and B is a group-VA anion) compounds (such as HgAs) with the HK lattice are 2D NLSs due to the band inversion between the cation Hg-s orbital and the anion As- orbital with respect to the mirror symmetry. Since the band inversion occurs between two bands with the same parity, this peculiar 2D NLS could be used as transparent conductors. In the presence of buckling or spin-orbit coupling, the 2D NLS state may turn into a 2D Dirac semimetal state or a 2D topological crystalline insulating state. Since the band gap opening due to buckling or spin-orbit coupling is small, HgAs with the HK lattice can still be regarded as a 2D NLS at room temperature. Our work suggests a new route to design topological materials without involving states with opposite parities.
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Magnetic topological semimetals have brought new insights into topological aspects because they nicely combine the band topology with intrinsic magnetic order. Comparing with ferromagnetic topological semimetals, antiferromagnetic (AFM) ones are even more special since they can break the time-reversal symmetry but show no net magnetic moment, and are highly expected for applications of topological AFM spintronics. Here, we report ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ compound is an ideal AFM Weyl nodal line semimetal. It shows time-reversal breaking Weyl nodal lines in both the spin-up and spin-down channels. Each nodal line arises from the band in one single spin channel, thus is spin-polarized. The nodal lines locate quite near the Fermi level and do not coexist with other extraneous bands. The drumhead surface state of the nodal line can be clearly identified. The nodal lines are protected by the glide mirror symmetry and are robust against spin-orbit coupling. We also show that ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can transform into an AFM Weyl semimetal under an in-plane external magnetic field. Our results suggest ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can serve as an excellent platform to investigate AFM topological semimetals with attractive features.
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Using first--principles density functional calculations, we systematically investigate electronic structures and topological properties of InNbX2 (X=S, Se). In the absence of spin--orbit coupling (SOC), both compounds show nodal lines protected by mirror symmetry. Including SOC, the Dirac rings in InNbS2 split into two Weyl rings. This unique property is distinguished from other dicovered nodal line materials which normally requires the absence of SOC. On the other hand, SOC breaks the nodal lines in InNbSe2 and the compound becomes a type II Weyl semimetal with 12 Weyl points in the Brillouin Zone. Using a supercell slab calculation we study the dispersion of Fermi arcs surface states in InNbSe2, we also utilize a coherent potential approximation to probe their tolernace to the surface disorder effects. The quasi two--dimensionality and the absence of toxic elements makes these two compounds an ideal experimental platform for investigating novel properties of topological semimetals.
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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.
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In topological semimetals the Dirac points can form zero-dimensional and one-dimensional manifolds, as predicted for Dirac/Weyl semimetals and topological nodal line semimetals, respectively. Here, based on first-principles calculations, we predict a topological nodal line semimetal phase in the two-dimensional compounds ${X}_{2}Y$ ($X$ = Ca, Sr, and Ba; $Y$ = As, Sb, and Bi) in the absence of spin-orbit coupling (SOC) with a band inversion at the M point. A nontrivial ${\mathbb{Z}}_{2}$ invariant of ${\mathbb{Z}}_{2}=1$ remains although a tiny gap appears at the nodal line when SOC is included. The mirror symmetry as well as the electrostatic interaction, which can be engineered via strain, are responsible for the nontrivial phase. In addition, the nontrivial phase is further explicitly confirmed via the existence of exotic edge states without and with SOC.
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Antiferromagnetic β-Fe2PO5 is a new topological semimetal with coexisting rich fermionic states, and with the potential to be applied in topological antiferromagnetic spintronics.
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