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Register a new userEmergence of Topological Nodal Lines and Type II Weyl Nodes in Strong Spin--Orbit Coupling System InNbX2(X=S,Se)
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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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The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners K and K, analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal Fe$_3$Sn$_2$, without spin-orbit coupling we identify two energetically split helical nodal lines winding along $z$ in the vicinity of K and K resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. The effect of spin-orbit coupling is found to resemble that of a Kane-Mele term, where the nodal lines can either be fully gapped to quasi-two-dimensional massive Dirac fermions, or remain gapless at discrete Weyl points depending on the ferromagnetic moment orientation. Aside from numerically establishing Fe$_3$Sn$_2$ as a model Dirac kagome metal, our results provide insights into materials design of topological phases from the lattice point of view, where paradigmatic low dimensional lattice models often find realizations in crystalline materials with three-dimensional stacking.
NbP is one member of a new class of nodal loop semimetals characterized by the cooperative effects of spin-orbit coupling (SOC) and a lack of inversion center. Here transport and spectroscopic properties of NbP are evaluated using density functional theory methods. SOC together with the lack of inversion symmetry splits degeneracies, giving rise to Russian doll nested Fermi surfaces containing 4*10$^{-4}$ electron (hole) carriers/f.u. Due to the modest SOC strength in Nb, the Fermi surfaces map out the Weyl nodal loops. Calculated structure around T$^*$~100 K in transport properties reproduces well the observed transport behavior only when SOC is included, attesting to the precision of the (delicate) calculations and the stoichiometry of the samples. Low energy collective electron-hole excitations (plasmons) in the 20-60 meV range result from the nodal loop splitting.
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 combination of mirror symmetry and broken ${cal T}$. Additionally, there are two types of magnetic Weyl points with chiral charges $|chi|=1, 2$ along the $C_{4v}$ symmetry line, and another type-II MWNL encircling the zone center, that are dependent on $U$. Furthermore, the ferromagnetic Ba$_2$ZnReO$_6$ is an ideal half semimetal with MWNLs and magnetic Weyl nodes at the Fermi level without the interference of topologically trivial bulk states. These systems give rise to a remarkably large anomalous Hall conductivity $sigma_{xy}$ of up to 1160 ($Omega$cm)$^{-1}$. Our findings may apply widely for $t_{2g}$ systems with cubic (or slightly distorted) fcc-like structures.
The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the k space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the c axis, and magnetic field rotating in the ab plane. The extremal orbits identified through the field orientation dependence of the QOs interlock with the nodal line, leading to a nonzero Berry phase. Most importantly, the Berry phase shows a significant dependence on the magnetic field orientation, which we argue to be due to the finite spin-orbit coupling gap. Our results demonstrate the importance of the spin-orbit coupling and the nodal-line dispersion in understanding the quantum transport of NLSMs.
Spin-orbit coupling (SOC) is essential in understanding the properties of 5d transition metal compounds, whose SOC value is large and almost comparable to other key parameters. Over the past few years, there have been numerous studies on the SOC-driven effects of the electronic bands, magnetism, and spin-orbit entanglement for those materials with a large SOC. However, it is less studied and remains an unsolved problem in how the SOC affects the lattice dynamics. We, therefore, measured the phonon spectra of 5d pyrochlore Cd2Os2O7 over the full Brillouin zone to address the question by using inelastic x-ray scattering (IXS). Our main finding is a visible mode-dependence in the phonon spectra, measured across the metal-insulator transition at 227 K. We examined the SOC strength dependence of the lattice dynamics and its spin-phonon (SP) coupling, with first-principle calculations. Our experimental data taken at 100 K are in good agreement with the theoretical results obtained with the optimized U = 2.0 eV with SOC. By scaling the SOC strength and the U value in the DFT calculations, we demonstrate that SOC is more relevant than U to explaining the observed mode-dependent phonon energy shifts with temperature. Furthermore, the temperature dependence of the phonon energy can be effectively described by scaling SOC. Our work provides clear evidence of SOC producing a non-negligible and essential effect on the lattice dynamics of Cd2Os2O7 and its SP coupling.
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