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Discrete degrees of freedom, such as spin and orbital, can provide intriguing strategies to manipulate electrons, photons, and phonons. With a spin degree of freedom, topological insulators have stimulated intense interests in condensed-matter physics, optics, acoustics, and mechanics. However, orbital as another fundamental attribute in crystals has seldom been investigated in topological insulators. Here, we invent a new type of topological insulators with an auxiliary orbital degree of freedom on a nanomechanical platform. We experimentally realized nanomechanical topological insulators where the orbital can arbitrarily be manipulated by the crystal. Harnessing this unique feature, we demonstrated adiabatic transition between distinct topological edge states, which is a crucial functionality for complicated systems that involve distinct topological edge channels. Beyond the one-dimensional edge states, we further constructed zero-dimensional Dirac-vortex states. Our results have unveiled unprecedented strategies to manipulate topological phase transitions and to study topological phases of matter on an integrated platform.
We theoretically propose a gigantic orbital Edelstein effect in topological insulators and interpret the results in terms of topological surface currents. We numerically calculate the orbital Edelstein effect for a model of a three-dimensional Chern
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of non-linearity.
Robustness against disorder and defects is a pivotal advantage of topological systems, manifested by absence of electronic backscattering in the quantum Hall and spin-Hall effects, and unidirectional waveguiding in their classical analogs. Two-dimens
Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the change of th
The Su-Schrieffer-Heeger (SSH) model on a two-dimensional square lattice has been considered as a significant platform for studying topological multipole insulators. However, due to the highly-degenerate bulk energy bands protected by $ C_{4v} $ and