From triple-point materials to multiband nodal links
Patrick M. Lenggenhager, Xiaoxiong Liu, Stepan S. Tsirkin, Titus Neupert, Tomáš Bzdušek
备注：
4 pages (3 figures, 1 table) + 12 pages of Supplemental Material (13 figures, 3 tables) + references; updated with peer-reviewed version and new title; fixed broken figure and errors in Table I
We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Focusing specifically on $\mathcal{P}\mathcal{T}$-symmetric crystalline solids with negligible spin-orbit coupling, we find that such triple points can be stabilized by little groups containing a three-, four- or six-fold rotation axis, and we develop a classification of all possible triple points as type A vs. type B according to the absence vs. presence of attached nodal-line arcs. Furthermore, by employing the recently discovered non-Abelian band topology, we argue that a rotation-symmetry-breaking strain transforms type-A triple points into multiband nodal links. Although multiband nodal-line compositions were previously theoretically conceived and related to topological monopole charges, a practical condensed-matter platform for their manipulation and inspection has hitherto been missing. By reviewing the known triple-point materials with weak spin-orbit coupling, and by performing first-principles calculations to predict new ones, we identify suitable candidates for the realization of multiband nodal links in applied strain. In particular, we report that an ideal compound to study this phenomenon is Li$_2$NaN, in which the conversion of triple points to multiband nodal links facilitates largely tunable density of states and optical conductivity with doping and strain, respectively.
Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce at a single eigenenergy. For spinless particles, the stability of a triple nodal point requires two ingredients: rotation symmetry of order three, four or six; combined with mirror or space-time-inversion symmetry. However, despite ample studies of their classification, robust boundary signatures of triple nodal points have until now remained elusive. In this work, we first show that pairs of triple nodal points in semimetals and metals can be characterized by Stiefel-Whitney …
We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines in the momentum space by a crossing of three bands transforming according to a 1D and a 2D irreducible corepresentation (ICR) of the little co-group. The result is a complete classification of such TPs in all magnetic space groups, including the non-symmorphic ones, according to several characteristics of the nodal-line structure at a…
Coexistence of topological elements in a topological metal/semimetal (TM) has gradually attracted attentions. However, the non-topological factors always mess up the Fermi surface and cover interesting topological properties. Here, we find that Ba3Si4 is a "clean" TM in which coexists nodal-chain network, intersecting nodal rings (INRs) and triple points, in the absence of spin-orbit coupling (SOC). Moreover, the nodal rings in the topological phase exhibit diverse types: from type-I, type-II to type-III rings according to band dispersions. All the topological elements are generated by crossin…
Symmetry-protected topological semimetals are at the focus of solid-state research due to their unconventional properties, for example, regarding transport. By investigating local two-band Bloch Hamiltonians in the spin-1/2 basis for the 122 magnetic point groups, we classify twofold-degenerate band touchings such as Weyl points, robust nodal lines on axes and in mirror planes, and fragile nodal lines. We find that all magnetic point groups that lack the product of inversion and time-reversal symmetries can give rise to topologically nontrivial band touchings. Hence, such nodes are the rule ra…
Phonon mode splitting and phonon anomaly in multiband electron systems
Institut für Physik, Universität Augsburg（奥格斯堡大学物理研究所）；Physics Department, New York City College of Technology, The City University of New York（纽约市立大学纽约城市技术学院物理系）
Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated. The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermi…
Acoustic phonon in a crystalline solid is a well-known and ubiquitous example of elementary excitation with a triple degeneracy in the band structure. Because of the Nambu-Goldstone theorem, this triple degeneracy is always present in the phonon band structure. Here, we show that the triple degeneracy of acoustic phonons can be characterized by a topological charge $\mathfrak{q}$ that is a property of three-band systems with $\mathcal{PT}$ symmetry, where $\mathcal{P}$ and $\mathcal{T}$ are the inversion and the time-reversal symmetries, respectively. We therefore call triple points with nontr…
We study the electronic structure and topological properties of monolayer and ABC-stacked multilayer of graphyne-$N$, which are a family of planar carbon sheets consisting of $sp$ and $sp_2$-bonding. By using the density-functional theory and the effective continuum model, we find a striking even-odd effect in the dependence of the band structure on $N$ (the number of carbon-carbon triple bonds between neighboring benzene rings). Specifically, even-$N$ graphyne monolayer has doubly-degenerate conduction and valence bands near the Fermi energy, and in its ABC multilayer, the band inversion of t…
Fermi surface and topology of multiband superconductor BeAu
Leibniz Institute for Solid State and Materials Research (IFW) Dresden（德累斯顿莱布尼茨固体与材料研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群 ct.qmat）；Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics（布达佩斯技术与经济大学物理学院理论物理系）；Regroupement Québécois sur les Matériaux de Pointe (RQMP)（魁北克尖端材料研究组）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Département de Physique et Institut Quantique, Université de Sherbrooke（舍布鲁克大学物理系与量子研究所）；Institute of Theoretical Physics, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
Quasiparticle excitations of free electrons in condensed-matter physics, characterized by the dimensionality of the band crossing, can find their elementary-particle analogs in high-energy physics, such as Majorana, Weyl, and Dirac fermions. While crystalline symmetry allows more quasiparticle excitations and exotic fermions to emerge. Using symmetry analysis and {\it ab-initio} calculations, we propose that the 3D honeycomb crystal NaCu$_3$Te$_2$ hosts triply degenerate nodal points (TDNPs) which are perfectly separated from the bulk states. We find a tunable phase transition between TDNPs an…
Recently, Ising superconductors which possess in-plane upper critical fields much larger than the Pauli limit field are under intense experimental study. Many monolayer or few layer transition metal dichalcogenides are shown to be Ising superconductors. In this work, we show that in a wide range of experimentally accessible regimes where the in-plane magnetic field is higher than the Pauli limit field but lower than $H_{c2}$, a 2H-structure monolayer NbSe$_2$ or simiarly TaS$_2$ becomes a nodal topological superconductor. The bulk nodal points appear on the $Γ- M$ lines of the Brillouin zone w…
Triple points and nexus points are two interesting topological phases, which have been reported in some three-dimensional (3D) materials. Here, we propose that triple points, nexus points and related phases, such as topological tangle nodal lines, can be obtained by alternatively stacking two types of monolayers. Two conditions for the stacking monolayers are required: the first condition is that they have a three-fold (C3) rotation symmetry and three mirror planes along the C3 axis; the second condition is that one of the monolayers should be insulating while the other one should be metallic …
