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Owing to the natural compatibility with current semiconductor industry, silicon allotropes with diverse structural and electronic properties provide promising platforms for the next-generation Si-based devices. After screening 230 all-silicon crystals in the zeolite frameworks by first-principles calculations, we disclose two structurally stable Si allotropes (AHT-Si24 and VFI-Si36) containing open channels as topological node-line semimetals with Dirac nodal points forming a nodal loop in the kz=0 plane of Brillouin zone. Interestingly, their nodal loops protected by inversion and time-reversal symmetries are robust against SU(2) symmetry breaking due to very weak spin-orbit coupling of Si. When the nodal lines are projected onto the (001) surface, flat surface bands can be observed because of the nontrivial topology of the bulk band structures. Our discoveries extend the topological physics to the three-dimensional Si materials, highlighting the possibility to realize low-cost, nontoxic and semiconductor-compatible Si-based electronics with topological quantum states.
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We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this Review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials and (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals and other topological phases and (v) we discuss the possible physical effects accessible to experimental probes in these materials.
The realization of Dirac and Weyl physics in solids has made topological materials one of the main focuses of condensed matter physics. Recently, the topic of topological nodal line semimetals, materials in which Dirac or Weyl-like crossings along special lines in momentum space create either a closed ring or line of degeneracies, rather than discrete points, has become a hot topic in topological quantum matter. Here we review the experimentally confirmed and theoretically predicted topological nodal line semimetals, focusing in particular on the symmetry protection mechanisms of the nodal lines in various materials. Three different mechanisms: a combination of inversion and time-reversal symmetry, mirror reflection symmetry, and non-symmorphic symmetry, and their robustness under the effect of spin orbit coupling are discussed. We also present a new Weyl nodal line material, the Te-square net compound KCu$_2$EuTe$_4$, which has several Weyl nodal lines including one extremely close to the Fermi level ($<$30 meV below E$_F$). Finally, we discuss potential experimental signatures for observing exotic properties of nodal line physics.
We show a holographic model of a strongly coupled topological nodal line semimetal (NLSM) and find that the NLSM phase could go through a quantum phase transition to a topologically trivial state. The dual fermion spectral function shows that there are multiple Fermi surfaces each of which is a closed nodal loop in the NLSM phase. The topological structure in the bulk is induced by the IR interplay between the dual mass operator and the operator that deforms the topology of the Fermi surface. We propose a practical framework for building various strongly coupled topological semimetals in holography, which indicates that at strong coupling topologically nontrivial semimetal states generally exist.
Based on the first-principles study, we report a new set of topological semimetals (TiS, TiSe, TiTe, HfS, HfSe, HfTe and ZrS) which show the co-existence of a nodal-ring and triply-degenerate points. The two-fold degenerate one-dimensional nodal ring structure in the bulk Brillouin zone exhibits the characteristic drumhead surface states. In addition to this, a peculiar band crossing along the $k_z$ direction takes place consisting of a point-crossing with three-fold band degeneracy. These triply-degenerate points give rise to nexus fermions as quasiparticles having no analogous elementary particle of the standard model. In this article, we simulate angle-resolved photoemission spectroscopy to obtain the exotic topological surface states and the characteristic Fermi arcs, and explain the evolution and separation of triple-points with the magnitude of spin-orbit coupling. This intermediate linearly dispersive degeneracy between Weyl and Dirac points may offer prospective candidates for quantum transport applications.
The optical properties of YbMnSb2 have been measured in a broad frequency range from room temperature down to 7 K. With decreasing temperature, a flat region develops in the optical conductivity spectra at about 300cm-1, which can not be described by the well-known Drude-Lorentz model. A frequency-independent component has to be introduced to model the measured optical conductivity. Our first-principles calculations show that YbMnSb2 possesses a Dirac nodal line near the Fermi level. A comparison between the measured optical properties and calculated electronic band structures suggests that the frequency-independent optical conductivity component arises from interband transitions near the Dirac nodal line, thus demonstrating that YbMnSb2 is a Dirac nodal line semimetal.
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