Weak ${\mathbb{Z}}_2$ Supertopology

Abstract

Crystal symmetries can enforce all bands of a material to be topological, a property that is commonly referred to as ``supertopology". Here, we determine the symmetry-enforced ${\mathbb{Z}}_2$ supertopologies of non-magnetic centrosymmetric materials with weak and strong spin-orbit coupling (SOC). For weak (i.e., negligible) SOC, crystal symmetries can enforce Dirac nodal lines protected by a $\pi$-Berry phase, while for strong SOC, crystal symmetries can give rise to nontrival weak ${\mathbb{Z}}_2$ topologies in 2D subplanes of the 3D Brillouin zone. We catalogue all centrosymmetric space groups whose symmetries enforce these ${\mathbb{Z}}_2$ supertopologies. Suitable material realizations are identified and experimental signatures of the supertopologies, such as quantum spin Hall states, are being discussed.

12 pages, 10 figures, 3 tables

References in corpus (44)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Topological Insulators
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Classification of topological quantum matter with symmetries
• Topological invariants of time-reversal-invariant band structures
• Quantized Electric Multipole Insulators
• High-throughput electronic band structure calculations: challenges and tools
• Higher-Order Topological Insulators
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Reflection symmetric second-order topological insulators and superconductors
• Dirac Line Nodes in Inversion Symmetric Crystals
• Topological nodal line semimetals
• Antiferromagnetic topological insulators
• Inversion Symmetric Topological Insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Experimental discovery of a topological Weyl semimetal state in TaP
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Quantized Response and Topology of Insulators with Inversion Symmetry
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Topological Materials Discovery from Crystal Symmetry
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Topological correspondence between magnetic space group representations
• Filling-enforced Magnetic Dirac Semimetals in Two Dimensions
• Spinless hourglass nodal-line semimetals
• Weyl Josephson Circuits
• Global band topology of simple and double Dirac-point (semi-)metals
• Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Kramers Nodal Line Metals
• Bulk metals with helical surface states
• Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes
• Symmetry enforced line nodes in unconventional superconductors
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines
• Cooper-pair transistor as a minimal topological quantum circuit
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model