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Register a new userCo-existence of Weyl Fermion and Massless Triply Degenerate Nodal Points
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By using first-principles calculations, we propose that WC-type ZrTe is a new type of topological semimetal (TSM). It has six pairs of chiral Weyl nodes in its first Brillouin zone, but it is distinguished from other existing TSMs by having additional two paris of massless fermions with triply degenerate nodal points as proposed in the isostructural compounds TaN and NbN. The mirror symmetry, three-fold rotational symmetry and time-reversal symmetry require all of the Weyl nodes to have the same velocity vectors and locate at the same energy level. The Fermi arcs on different surfaces are shown, which may be measured by future experiments. It demonstrates that the material universe can support more intriguing particles simultaneously.
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Using first-principles calculation and symmetry analysis, we propose that theta-TaN is a topological semimetal having a new type of point nodes, i.e., triply degenerate nodal points. Each node is a band crossing between degenerate and non-degenerate bands along the high-symmetry line in the Brillouin zone, and is protected by crystalline symmetries. Such new type of nodes will always generate singular touching points between different Fermi surfaces and 3D spin texture around them. Breaking the crystalline symmetry by external magnetic field or strain leads to various of topological phases. By studying the Landau levels under a small field along $c$-axis, we demonstrate that the system has a new quantum anomaly that we call helical anomaly.
As a new type of fermions without counterpart in high energy physics, triply degenerate fermions show exotic physical properties, which are represented by triply degenerate nodal points in topological semimetals. Here, based on the space group theory analysis, we propose a practical guidance for seeking a topological semimetal with triply degenerate nodal points located at a symmetric axis, which is applicable to both symmorphic and nonsymmorphic crystals. By using this guidance in combination with the first-principles electronic structure calculations, we predict a class of triply degenerate topological semimetals RERh$_{6}$Ge$_{4}$ (RE=Y, La, Lu). In these compounds, the triply degenerate nodal points are located at the $Gamma$-A axis and not far from the Fermi level. Especially, LaRh$_{6}$Ge$_{4}$ has a pair of triply degenerate nodal points located very closely to the Fermi level. Considering the fact that the single crystals of RERh$_{6}$Ge$_{4}$ have been synthesized experimentally, the RERh$_{6}$Ge$_{4}$ class of compounds will be an appropriate platform for studying exotic physical properties of triply degenerate topological semimetals.
According to a widely-held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue. Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision. Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states. We further find that Weyl points in systems symmetric under a $pi$-rotation composed with time-reversal are characterized by an additional integer charge that we call helicity. A pair of Weyl points with opposite chirality can annihilate only if their helicities also cancel out. We base our predictions on topological crystalline invariants derived from relative homotopy theory, and we test our predictions on simple tight-binding models. The outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.
We study the possibility of triply-degenerate points (TPs) that can be stabilized in spinless crystalline systems. Based on an exhaustive search over all 230 space groups, we find that the spinless TPs can exist at both high-symmetry points and high-symmetry paths, and they may have either linear or quadratic dispersions. For TPs located at high-symmetry points, they all share a common minimal set of symmetries, which is the point group $T$. The TP protected solely by the $T$ group is chiral and has a Chern number of $pm2$. By incorporating additional symmetries, this TP can evolve into chiral pseudospin-1 point, linear TP without chirality, or quadratic contact TP. For accidental TPs residing on a high-symmetry path, they are not chiral but can have either linear or quadratic dispersions in the plane normal to the path. We further construct effective $kcdot p$ models and minimal lattice models for characterizing these TPs. Distinguished phenomena for the chiral TPs are discussed, including the extensive surface Fermi arcs and the chiral Landau bands.
The existence and topological classification of lower-dimensional Fermi surfaces is often tied to the crystal symmetries of the underlying lattice systems. Artificially engineered lattices, such as heterostructures and other superlattices, provide promising avenues to realize desired crystal symmetries that protect lower-dimensional Fermi surface, such as nodal lines. In this work, we investigate a Weyl semimetal subjected to spatially periodic onsite potential, giving rise to several phases, including a nodal-line semimetal phase. In contrast to proposals that purely focus on lattice symmetries, the emergence of the nodal line in this setup does not require small spin-orbit coupling, but rather relies on its presence. We show that the stability of the nodal line is understood from reflection symmetry and a combination of a fractional lattice translation and charge-conjugation symmetry. Depending on the choice of parameters, this model exhibits drumhead surface states that are exponentially localized at the surface, or weakly localized surface states that decay into the bulk at all energies.
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