Spinless hourglass nodal-line semimetals

Abstract

Nodal-line semimetals, one of the topological semimetals, have degeneracy along nodal lines where the band gap is closed. In many cases, the nodal lines appear accidentally, and in such cases it is impossible to determine whether the nodal lines appear or not, only from the crystal symmetry and the electron filling. In this paper, for spinless systems, we show that in specific space groups at $4N+2$ fillings ($8N+4$ fillings including the spin degree of freedom), presence of the nodal lines is required regardless of the details of the systems. Here, the spinless systems refer to crystals where the spin-orbit coupling is negligible and the spin degree of freedom can be omitted because of the SU(2) spin degeneracy. In this case the shape of the band structure around these nodal lines is like an hourglass, and we call this a spinless hourglass nodal-line semimetal. We construct a model Hamiltonian as an example and we show that it is always in the spinless hourglass nodal-line semimetal phase even when the model parameters are changed without changing the symmetries of the system. We also establish a list of all the centrosymmetric space groups, under which spinless systems always have hourglass nodal lines, and illustrate where the nodal lines are located. We propose that Al${}_3$FeSi${}_2$, whose space-group symmetry is Pbcn (No. 60), is one of the nodal-line semimetals arising from this mechanism.

14 pages, 9 figures

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Crystalline Insulators
• Topological quantum chemistry
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Tunable Line Node Semimetals
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• Universal phase transition and band structures for spinless nodal-line and Weyl semimetals

Cited by in corpus (36)

• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Observation of Dirac-like energy band and ring-torus Fermi surface associated with the nodal line in topological insulator CaAgAs
• Observation of non-Abelian nodal links in photonics
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Topological carbon materials: a new perspective
• Nodal Line Spin-gapless Semimetals and High-quality Candidate Materials
• Topological band crossings in hexagonal materials
• Hourglass-like Nodal Net Semimetal in Ag2BiO3
• Topological Hourglass Dirac Semimetal in the Nonpolar Phase of Ag${}_2$BiO${}_3$
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Degenerate topological line surface phonons in quasi-1D double helix crystal SnIP
• Exhaustive List of Topological Hourglass Band Crossings in 230 Space Groups
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Double Dirac Nodal Line Semimetal with Torus Surface State
• Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines
• Multiple band-crossings and Fermi surface topology: role of double nonsymmorphic symmetries in MnP-type crystal structures
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Spectroscopic Evidence for Dirac Nodal Surfaces and Nodal Rings in Superconductor NaAlSi
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Spin-orbit enabled unconventional Stoner magnetism
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• $n$-Hourglass Weyl fermions in nonsymmorphic materials
• Linking structures of doubly charged nodal surfaces in centrosymmetric superconductors
• Designing single and degenerate flat bands in the kagome lattice with long-range hopping
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Two-dimensional chiral stacking orders in quasi-one-dimensional charge density waves
• Topological bound states for quantum charges
• Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr${}_8$CoGa${}_3$ Family
• Unveiling the Chiral States in Multi-Weyl Semimetals through Magneto-Optical Spectroscopy
• Nodal-line semimetals and their variance
• Less is more: Vacancy-engineered nodal-line semimetals
• Two-dimensional hourglass Weyl nodal loop in monolayer Pb(ClO${}_2$)${}_2$ and Sr(ClO${}_2$)${}_2$
• Eightfold Degenerate Dirac Nodal Line in Collinear Antiferromagnet Mn${}_5$Si${}_3$
• Realisation of Symmetry Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic $\alpha$-Bismuthene
• Weak ${\mathbb{Z}}_2$ Supertopology
• Essentially degenerate hidden nodal lines in two-dimensional magnetic layer groups