Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries

Abstract

The topology of the Brillouin zone, foundational in topological physics, is always assumed to be a torus. We theoretically report the construction of Brillouin real projective plane (${\mathrm{RP}}^2$) and the appearance of quadrupole insulating phase, which are enabled by momentum-space nonsymmorphic symmetries stemming from ${\mathbb{Z}}_2$ synthetic gauge fields. We show that the momentum-space nonsymmorphic symmetries quantize bulk polarization and Wannier-sector polarization nonlocally across different momenta, resulting in quantized corner charges and an isotropic binary bulk quadrupole phase diagram, where the phase transition is triggered by a bulk energy gap closing. Under open boundary conditions, the nontrivial bulk quadrupole phase manifests either trivial or nontrivial edge polarization, resulting from the violation of momentum-space nonsymmorphic symmetries under lattice termination. We present a concrete design for the ${\mathrm{RP}}^2$ quadrupole insulator based on acoustic resonator arrays and discuss its feasibility in optics, mechanics, and electrical circuits. Our results show that deforming the Brillouin manifold creates opportunities for realizing high-order band topology.

arXiv comment5 pages,5 figures

References in corpus (44)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Imaging topological edge states in silicon photonics
• Higher-Order Topological Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topolectrical circuit realization of topological corner modes
• Experimental realization of a topological crystalline insulator in SnTe
• Observation of a phononic quadrupole topological insulator
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Photonic quadrupole topological phases
• Hourglass Fermions
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Three-dimensional topological photonic crystal with a single surface Dirac cone
• Acoustic realization of quadrupole topological insulators
• Artificial gauge fields in materials and engineered systems
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Observation of an acoustic octupole topological insulator
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Demonstration of a quantized acoustic octupole topological insulator
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological non-symmorphic crystalline insulators
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Boundary-obstructed topological phases
• Synthesis and Observation of Non-Abelian Gauge Fields in Real Space
• Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals
• Projectively enriched symmetry and topology in acoustic crystals
• Acoustic Möbius insulators from projective symmetry
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Partial lattice defects in higher order topological insulators
• Brillouin Klein Bottle From Artificial Gauge Fields
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Classification of time-reversal-invariant crystals with gauge structures
• Realization of Surface-Obstructed Topological Insulators
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals

Cited by in corpus (8)

• Weyl points on non-orientable manifolds
• Quantized crystalline-electromagnetic responses in insulators
• Brillouin Platycosms and Topological Phases
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Exceptional topology on nonorientable manifolds
• Asymmetric real topology of conduction and valence bands
• Breakdown of the symmetry constraint in a Floquet topological insulator