Classification of time-reversal-invariant crystals with gauge structures

Abstract

A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain largely unexplored. Despite recent advances in artificial crystals, whose intrinsic gauge structures necessarily require a projective description, a unified theory is yet to be established. Here, we establish such a unified theory by exhaustively classifying and representing all 458 projective symmetry algebras of time-reversal-invariant crystals from 17 wallpaper groups in two dimensions-189 of which are algebraically non-equivalent. We discover three physical signatures resulting from projective symmetry algebras, including the shift of high-symmetry momenta, an enforced nontrivial Zak phase, and a spinless eight-fold nodal point. Our work offers a theoretical foundation for the field of artificial crystals and opens the door to a wealth of topological states and phenomena beyond the existing paradigms.

arXiv comment62 pages, 11 pages for main text + 51 pages for supplementary information

References in corpus (21)

• Anyons in an exactly solved model and beyond
• Topological Photonics
• Topological Photonics
• Artificial gauge potentials for neutral atoms
• Topological Acoustics
• Topolectrical circuit realization of topological corner modes
• Quantum Orders and Symmetric Spin Liquids
• Topological Bands for Ultracold Atoms
• Topological acoustics
• Topological phonon modes and their role in dynamic instability of microtubules
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Observation of an acoustic octupole topological insulator
• 4D spinless topological insulator in a periodic electric circuit
• Projective symmetry group classification of chiral spin liquids
• Projectively enriched symmetry and topology in acoustic crystals
• Acoustic Möbius insulators from projective symmetry
• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Switching spinless and spinful topological phases with projective $PT$ symmetry
• Brillouin Klein Bottle From Artificial Gauge Fields

Cited by in corpus (17)

• Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• Klein-bottle quadrupole insulators and Dirac semimetals
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Non-Abelian Braiding of Topological Edge Bands
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model
• Projective Spacetime Symmetry of Spacetime Crystals
• Brillouin Platycosms and Topological Phases
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Floquet Möbius topological insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials
• Negative exchange interaction in Si quantum dot arrays via valley-phase induced ${\mathbb{Z}}_2$ gauge field