The Bloch band theory and Brillouin zone(BZ)that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics,ranging from condensed matter to topological physics.Recent theoretica...The Bloch band theory and Brillouin zone(BZ)that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics,ranging from condensed matter to topological physics.Recent theoretical breakthrough revealed that,under the projective symmetry algebra enforced by artificial gauge fields,the usual two-dimensional(2D)BZ(orientable Brillouin two-torus)can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct manifold topology.However,the physical consequence of artificial gauge fields on the more general three-dimensional(3D)BZ(orientable Brillouin three-torus)was so far missing.Here,we theoretically discovered and experimentally observed that the fundamental domain and topology of the usual 3D BZ can be reduced to a non-orientable Brillouin Klein space or an orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields.We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures.Moreover,we experimentally demonstrate a novel stacked weak Klein bottle insulator featuring a nonzero Z2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist,radically distinct from all previous 3D topological insulators.Our discovery not only fundamentally modifies the fundamental domain and topology of 3D BZ,but also opens the door towards a wealth of previously overlooked momentum-space multidimensional manifold topologies and novel gaugesymmetry-enriched topological physics and robust acoustic wave manipulations beyond the existing paradigms.展开更多
基金funding from the National Natural Science Foundation of China(62375118,6231101016,and 12104211)Shenzhen Science and Technology Innovation Commission(20220815111105001)+8 种基金SUSTech(Y01236148 and Y01236248)Zhengyou Liu acknowledges funding from the National Key R&D Program of China(2022YFA1404900 and 2018YFA0305800)the National Natural Science Foundation of China(11890701)the National Natural Science Foundation of China(12304484)Basic and Applied Basic Research Foundation of Guangdong Province(2414050002552)Shenzhen Science and Technology Innovation Commission(202308073000209)Perry Ping Shum acknowledges the National Natural Science Foundation of China(62220106006)Shenzhen Science and Technology Program(SGDX20211123114001001)Kexin Xiang acknowledges the Special Funds for the Cultivation of Guangdong College Students’Scientific and Technological Innovation(pdjh2023c21002).
文摘The Bloch band theory and Brillouin zone(BZ)that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics,ranging from condensed matter to topological physics.Recent theoretical breakthrough revealed that,under the projective symmetry algebra enforced by artificial gauge fields,the usual two-dimensional(2D)BZ(orientable Brillouin two-torus)can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct manifold topology.However,the physical consequence of artificial gauge fields on the more general three-dimensional(3D)BZ(orientable Brillouin three-torus)was so far missing.Here,we theoretically discovered and experimentally observed that the fundamental domain and topology of the usual 3D BZ can be reduced to a non-orientable Brillouin Klein space or an orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields.We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures.Moreover,we experimentally demonstrate a novel stacked weak Klein bottle insulator featuring a nonzero Z2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist,radically distinct from all previous 3D topological insulators.Our discovery not only fundamentally modifies the fundamental domain and topology of 3D BZ,but also opens the door towards a wealth of previously overlooked momentum-space multidimensional manifold topologies and novel gaugesymmetry-enriched topological physics and robust acoustic wave manipulations beyond the existing paradigms.
