Movable but not removable band degeneracies in a symmorphic crystal

Abstract

Crossings of energy bands in solids that are not pinned at symmetry points in the Brillouin zone and yet cannot be removed by perturbations are thought to be conditioned on the presence of a nonsymmorphic symmetry. In this Letter we show that such band crossings can actually appear also in a symmorphic crystal. A study of a class of tight-binding multiband one-dimensional lattice models of spinful electrons reveals that chiral, time-reversal and site-mirror symmetries are suffcient to produce such movable but not removable band degeneracies.

arXiv comment11 pages (Paper plus Supplemental Material); 6 figures (4 in the Paper, 2 in the Supplemental Material); new Introduction, added references, revised text

References in corpus (25)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Dirac semimetal in three dimensions
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological nodal line semimetals with and without spin-orbital coupling
• Dirac Semimetals in Two Dimensions
• Nodal-chain metals
• Hourglass Fermions
• Double Dirac Semimetals in Three Dimensions
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Spin-Orbit Semimetals in the Layer Groups
• Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
• Filling-enforced Magnetic Dirac Semimetals in Two Dimensions
• Triple point fermions in a minimal symmorphic model
• Antiferromagnetic Dirac Semimetals in Two Dimensions
• Topological band crossings in hexagonal materials
• Symmetry protected line nodes in non-symmorphic magnetic space groups: Applications to UCoGe and UPd${}_2$Al${}_3$
• Symmetry enforced line nodes in unconventional superconductors
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Nodal lines and nodal loops in non-symmorphic odd-parity superconductors
• Topological Gapless Phases in Non-Symmorphic Antiferromagnets
• Synthesizing Majorana zero-energy modes in a periodically gated quantum wire
• Nodal S-wave Superconductivity in Antiferromagnetic Semimetals

Cited by in corpus (7)

• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines
• Multicriticality in a one-dimensional topological band insulator
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Scaling behavior in a multicritical one-dimensional topological insulator
• Symmetry-enforced nodal lines in the band structures of vacancy-engineered graphene