Exhaustive List of Topological Hourglass Band Crossings in 230 Space Groups

Abstract

Topological semimetals with band crossings (BCs) near the Fermi level have attracted intense research activities in the past several years. Among various BCs, those enforced by an hourglass-like connectivity pattern, which are just located at the vertex in the neck of an hourglass and thus called hourglass BCs (HBCs), show interesting topological properties and are intimately related with the space group symmetry. Through checking compatibility relations in the Brillouin zone (BZ), we list all possible HBCs for all 230 space groups by identifying positions of HBCs as well as the compatibility relations related with the HBCs.The HBCs can be coexisting with conventional topological BCs such as Dirac andWeyl fermions and based on our exhaustive list, the dimensionality and degeneracy of the HBCs can be quickly identified. It is also found that the HBCs can be classified into two categories: one contains essential HBCs which are guaranteed to exist, while the HBCs in the other category may be tuned to disappear. Our results can help in efficiently predicting hourglass semimetals combined with first-principles calculations as well as studying transitions among various topological crystalline phases.

main text: 9 pages; supplementary material: 66 pages, including tables listing all hourglass band crossings

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Multiple types of topological fermions in transition metal silicides
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer $X_3$SiTe${}_6$ ($X=$ Ta, Nb)
• Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• Dual topological nodal line and nonsymmorphic Dirac semimetal in three dimensions

Cited by in corpus (11)

• Symmorphic and nonsymmorphic symmetries jointly-protected hourglass phonons
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Symmetry-enforced Band Nodes in 230 Space Groups
• Magnetic hourglass fermions: from exhaustive symmetry conditions to high-throughput materials predictions
• Fully-gapped superconductivity and topological aspects of the noncentrosymmetric TaReSi superconductor
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Hilbert band complexes and their applications
• Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation
• Two-dimensional hourglass Weyl nodal loop in monolayer Pb(ClO${}_2$)${}_2$ and Sr(ClO${}_2$)${}_2$