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Register a new userTopological Dirac Nodal-net Fermions in AlB$_2$-type TiB$_2$ and ZrB$_2$
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Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in AlB$_2$-type TiB$_2$ and ZrB$_2$ when spin-orbit coupling (SOC) is ignored. Taking TiB$_2$ as an example, there are several topological excitations in this nodal-net structure including triple point, nexus, and nodal link, which are protected by coexistence of spatial-inversion symmetry and time reversal symmetry. This nodal-net state is remarkably different from that of IrF$_4$, which requires sublattice chiral symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points are identified as having emerged on the B-terminated and Ti-terminated (001) surfaces of TiB$_2$ respectively, which are analogous to those of monolayer and bilayer graphene.
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The effect of electron correlation (EC) on the electronic structure in MgB$_2$, AlB$_2$ and ZrB$_2$, is studied by examining the partial density of states (PDOS) of B-2$psigma$ and $ppi$ orbitals using the polarization dependence of x-ray emission and absorption spectra. The discrepancies between observed and calculated PDOSs cannot be attributed to EC effects. The present results suggest that the EC effect is less than the experimental error ($sim$ 0.2 eV), which indirectly supports a scenario that electron-phonon interaction plays an essential role in the occurrence of superconductivity.
Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) we study the electronic structure of layered BaZnBi$_2$. Our experimental results show no evidence of Dirac states in BaZnBi$_2$ originated either from the bulk or the surface. The calculated band structure without spin-orbit interaction shows several linear dispersive band crossing points throughout the Brillouin zone. However, as soon as the spin-orbit interaction is turned on, the band crossing points are significantly gapped out. The experimental observations are in good agreement with our DFT calculations. These observations suggest that the Dirac fermions in BaZnBi$_2$ are trivial and massive. We also observe experimentally that the electronic structure of BaZnBi$_2$ comprises of several linear dispersive bands in the vicinity of Fermi level dispersing to a wider range of binding energy.
Monolayer AlB$_2$ is composed of two atomic layers: honeycomb borophene and triangular aluminum. In contrast with the bulk phase, monolayer AlB$_2$ is predicted to be a superconductor with a high critical temperature. Here, we demonstrate that monolayer AlB$_2$ can be synthesized on Al(111) via molecular beam epitaxy. Our theoretical calculations revealed that the monolayer AlB$_2$ hosts several Dirac cones along the $Gamma$--M and $Gamma$--K directions; these Dirac cones are protected by crystal symmetries and are thus resistant to external perturbations. The extraordinary electronic structure of the monolayer AlB$_2$ was confirmed via angle-resolved photoemission spectroscopy measurements. These results are likely to stimulate further research interest to explore the exotic properties arising from the interplay of Dirac fermions and superconductivity in two-dimensional materials.
Using polarized optical and magneto-optical spectroscopy, we have demonstrated universal aspects of electrodynamics associated with Dirac nodal-lines. We investigated anisotropic electrodynamics of NbAs$_2$ where the spin-orbit interaction triggers energy gaps along the nodal-lines, which manifest as sharp steps in the optical conductivity spectra. We show experimentally and theoretically that shifted 2D Dirac nodal-lines feature linear scaling $sigma_1 (omega)simomega$, similar to 3D nodal-points. Massive Dirac nature of the nodal-lines are confirmed by magneto-optical data, which may also be indicative of theoretically predicted surface states. Optical data also offer a natural explanation for the giant magneto-resistance in NbAs$_2$.
Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. These fermions with linear dispersions near the Dirac or Weyl points obey Lorentz invariance, and the chiral anomaly leads to novel quantum phenomena such as negative magnetoresistance. The Lorentz invariance is, however, not necessarily respected in condensed matter physics, and thus Lorentz-violating type-II Dirac fermions with strongly tilted cones can be realized in topological semimetals. Here, we report the first experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe$_2$ single crystal. Angle-resolved photoemission spectroscopy (ARPES) measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the $Gamma$-A direction under the symmetry protection, confirming PtTe$_2$ as a type-II Dirac semimetal. The realization of type-II Dirac fermions opens a new door for exotic physical properties distinguished from type-I Dirac fermions in condensed matter materials.
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