Spatiotemporal Chaos in the Interface Growth of Topological Insulators

We demonstrate that topological insulators exhibit an intrinsic interfacial instability that amplifies small interface fluctuations, resulting in chaotic behavior during interface growth. This mechanism is fundamentally different from conventional interfacial instabilities in crystal growth that are driven by external non-uniformities such as surface diffusion, and instead arises from intrinsic electronic properties of topological materials. We find that the boundary states of topological insulators have a pronounced impact on the surface stiffness, which quantifies how strongly a surface resists changes in its shape or orientation. While trivial insulators possess positive stiffness that smooths out surface roughness, topological insulators exhibit negative stiffness that amplifies small shape fluctuations. We derive an effective equation of the interface growth with this negative stiffness and demonstrate that the interface dynamics is governed by the Kuramoto--Sivashinsky equation, a prototypical nonlinear equation exhibiting spatiotemporal chaos.