The possibility of obtaining robust edge state of light by mimicking the topological properties of solid state system, have brought a profound impact on optical sciences. With the advent of high-brilliance, accelerator-driven light sources such as storage rings or X-ray lasers, it has become attractive to extend the concept of optical topological manipulation to the X-ray regime. In this paper, we theoretically proposed and experimentally demonstrated the topological edge state at the interface of two photonic crystals having different band-gap topological characteristics for X-ray. Remarkably, this topologically protected edge state is immune to the weak disorder in form of the thickness disorder and strong disorder in form of the positional disorder of layers in the structure, as long as the zero-average-effective-mass condition is satisfied. Our investigation therefore brings the topological characteristics to the X-ray regime, provides new theoretical tools to study X-ray optics and may pave way to exploit some important potential applications, such as the high efficiency band filter in X-ray band.
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