New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic

2015/01/22 by Chen Fang, Liang Fu · 12 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Geometry #Graphene research and applications #Homogeneous space #Mathematics #Phase transition #Physics #Quantum #Quantum mechanics #Quantum phase transition #Quantum phases #Symmetry protected topological order #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.91.161105

published as Phys. Rev. B 91, 161105 (2015) · 4 pages plus supplementary materials

arxiv created 2015/01/22 · openalex publication_date 2015/04/15 · arxiv updated 2015/04/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We theoretically predict two new classes of three-dimensional topological crystalline insulators (TCIs), which have an odd number of unpinned surface Dirac cones protected by crystal symmetries. The first class is protected by a single nonsymmorphic glide plane symmetry; the second class is protected by a composition of a twofold rotation and time-reversal symmetry (a magnetic group symmetry). Both classes of TCIs are characterized by a quantized \ensuremathπ-Berry phase associated with surface states and a Z₂ topological invariant associated with the bulk bands. In the presence of disorder, these TCI surface states are protected against localization by the average crystal symmetries, and exhibit critical conductivity in the universality class of the quantum Hall plateau transition. These new TCIs exist in time-reversal-breaking systems with or without spin-orbital coupling, and their material realizations are discussed.

Citations

• Half quantum spin Hall effect on the surface of weak topological insulators
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors
• Topological Crystalline Insulators
• Topological Insulators

Cited by

• Generic phase diagram for Weyl superconductivity in mirror-symmetric superconductors
• Nonsymmorphic Topological Phases of Non-Hermitian Systems
• Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe
• Nodal Brillouin-zone boundary from folding a Chern insulator
• Gapless Criterion for Crystals from Effective Axion Field
• Piezoelectricity and topological quantum phase transitions in two-dimensional spin-orbit coupled crystals with time-reversal symmetry
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry
• Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle
• Classification of accidental band crossings and emergent semimetals in two-dimensional noncentrosymmetric systems
• Topological invariants of a filling-enforced quantum band insulator
• Topological nonsymmorphic ribbons out of symmorphic bulk
• Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd3As2

Related

• Topological Crystalline Insulators
• The space group classification of topological band insulators
• Isotropic 3D topological phases with broken time reversal symmetry
• Hybrid symmetry class topological insulators
• Classification of topological insulators and superconductors in three spatial dimensions