  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.
