Investigating topological valley disclinations using multiple scattering and null-field theories

Surprisingly, topological metamaterials became a frontier topic in wave physics. What began as a curiosity driven undertaking in condensed matter physics, evolved in serious possibilities to provide topologically resilient guiding of light, sound and vibrations. Topological defects, in the form of disclinations, dislocations, vortices, etc., have capitalized on man-made structures to demonstrate their wave-confining capabilities. In this report, we discuss topological edge and disclination states in valley Hall sonic lattices. A prime meta-constituent is the three-legged rod or tripod as its mere rotation enables spatial symmetry breaking. For the most part, this complicated unit is numerically treated with commercially available finite element solvers. Here, we derive the structure factor for plane wave expansions and a null-field method in combination with a multiple scattering theory to study both valley edge and disclination states. We showcase how this method enables rapid evaluation of both spatial and spectral properties related to valley topological sound wave physics. Topological metamaterials are becoming increasingly interesting for their wave-confining capabilities, providing topologically robust guiding of light, sound and vibrations. Here, topological edge and disclination states in valley Hall sonic lattices are investigated via a non-commercial analytical approach combining the null-field method with multiple scattering techniques.