  Topological insulators are materials that conduct on the surface and insulate
in their interior due to non-trivial topological order. The edge states on the
interface between topological (non-trivial) and conventional (trivial)
insulators are topologically protected from scattering due to structural
defects and disorders. Recently, it was shown that photonic crystals can serve
as a platform for realizing a scatter-free propagation of light waves. In
conventional photonic crystals, imperfections, structural disorders, and
surface roughness lead to significant losses. The breakthrough in overcoming
these problems is likely to come from the synergy of the topological photonic
crystals and silicon-based photonics technology that enables high integration
density, lossless propagation, and immunity to fabrication imperfections. For
many applications, reconfigurability and capability to control the propagation
of these non-trivial photonic edge states is essential. One way to facilitate
such dynamic control is to use liquid crystals, which allow to modify the
refractive index with external electric field. Here, we demonstrate dynamic
control of topological edge states by modifying the refractive index of a
liquid crystal background medium. Background index is changed depending on the
orientation of a liquid crystal, while preserving the topological order of the
system. This results in a change of the spectral position of the photonic
bandgap and the topologically protected edge states. The proposed concept might
be implemented using conventional semiconductor technology, and can be used for
robust energy transport in integrated photonic devices, all-optical circuity,
and optical communication systems.
