From triple-point materials to multiband nodal links

Abstract

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.

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

References in corpus (12)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Topological nodal line semimetals
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• High performance Wannier interpolation of Berry curvature and related quantities: WannierBerri code
• Three-dimensional Pentagon Carbon with a genesis of emergent fermions
• Band-Contact Lines in Electron Energy Spectrum of Graphite
• From Type-II Triply Degenerate Nodal Points and Three-Band Nodal Rings to Type-II Dirac Points in Centrosymmetric Zirconium Oxide
• Prediction of Ideal Topological Semimetals with Triply Degenerate Points in NaCu${}_3$Te${}_2$ Family
• On the topological character of three-dimensional Nexus triple point degeneracies

Cited by in corpus (20)

• Topological Non-Hermitian skin effect
• Observation of non-Abelian topological semimetals and their phase transitions
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Topological acoustic triple point
• Four-band non-Abelian topological insulator and its experimental realization
• Experimental observation of non-Abelian earring nodal links in phononic crystals
• Non-Abelian charged nodal links in dielectric photonic crystal
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Multiple magnetism controlled topological states in EuAgAs
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Photonic nodal lines with quadrupole Berry curvature distribution
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Punctured-Chern topological invariants for semi-metallic bandstructures
• Morse theory study on the evolution of nodal lines in $\mathcal{P}\mathcal{T}$-symmetric nodal-line semimetals
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Quantum oscillation in Hopf-link semimetals
• Triply-degenerate point in three-dimensional spinless systems