Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals

Abstract

Topological phases of matter are classified based on symmetries, with nonsymmorphic symmetries like glide reflections and screw rotations being of particular importance in the classification. In contrast to extensively studied glide reflections in real space, introducing space-dependent gauge transformations can lead to momentum-space glide reflection symmetries, which may even change the fundamental domain for topological classifications, e.g., from a torus to a Klein bottle. Here we discover a new class of three-dimensional (3D) higher-order topological insulators, protected by a pair of momentum-space glide reflections. It supports gapless hinge modes, as dictated by the quadrupole moment and Wannier Hamiltonians defined on a Klein bottle manifold, and we introduce two topological invariants to characterize this phase. Our predicted topological hinge modes are experimentally verified in a 3D-printed acoustic crystal, providing direct evidence for 3D higher-order Klein bottle topological insulators. Our results not only showcase the remarkable role of momentum-space glide reflections in topological classifications, but also pave the way for experimentally exploring physical effects arising from momentum-space nonsymmorphic symmetries.

37 pages, 14 figures

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• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Weyl points on non-orientable manifolds
• Brillouin Platycosms and Topological Phases
• Quantized crystalline-electromagnetic responses in insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Exceptional topology on nonorientable manifolds
• Asymmetric real topology of conduction and valence bands