Nanomechanical topological insulators with an auxiliary orbital degree of freedom

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.