Simple math acoustic11/14/2023 ![]() ![]() ![]() Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences have been presented for this intriguing topological observable in solid-state systems, owing to the huge challenges in creating controllable dislocations and conclusively identifying topological signals. Here, using a three-dimensional acoustic weak topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Top Notch (Acoustic) Theres two twin deaf kids And theyve got to make an ungodly decision They decide which one gets to leave this place, And which one. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented control over wave propagations.ĭislocations are rather ubiquitous in three-dimensional (3D) solid-state materials and their existence may significantly modulate the physical properties of the systems 1, 2. In recent years, topological matter has emerged as a major branch in broad areas of physics, from condensed matter 3, 4 to cold-atom 5. As topological line defects in real space, the dislocations are characterized by Burgers vector B and cannot be removed by local perturbations due to the conservation of B. The dislocations can be classified into two elementary types according to their orientations with respect to B: screw dislocations and edge dislocations, whose dislocation lines are parallel and perpendicular to B, respectively. In general, a dislocation line can be a combination of these two simple types, which either forms a loop or branches into a network owing to the conservation of B. solution of the wave equation with piecewise smooth coefficients, Math. ![]() In recent years, topological matter has emerged as a major branch in broad areas of physics, from condensed matter 3, 4 to cold-atom 5, 6 and classical systems 7, 8, 9, 10. Approach to Constructing Fourth Order Methods for Acoustic Wave Propagation. ![]()
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