Multidimensional topological strings by curved potentials: Simultaneous realization of a mobility edge and topological protection

By considering a cigar-shaped trapping potential elongated in proper curvilinear coordinate, we discover new form of wave localization that arises from the interplay geometry and topological protection. The is undulated its shape such local curvature introduces geometrical potential. varying along trap axis encodes Harper modulation. maps our system one-dimensional Andre-Aubry-Harper grating. We show mobility edge exists topologically protected states arise. These are extremely robust against disorder string. results may be relevant to phenomena Bose-Einstein condensates, optical fibers waveguides, laser devices.