Spatiotemporal chaos in the interface growth of topological insulators

Understanding interfacial growth between a solid and its surrounding environment is a fundamental problem in condensed matter physics. In this talk, we demonstrate that topological insulators exhibit a morphological instability during interface growth. 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. Whereas trivial insulators possess positive stiffness that smooths out surface roughness, topological insulators exhibit negative stiffness that amplifies small shape fluctuations. As a consequence of this negative stiffness, the interfacial growth of topological insulators is governed by the Kuramoto–Sivashinsky equation, a prototypical nonlinear equation exhibiting spatiotemporal chaos. Our results reveal that a fundamental interfacial instability is intrinsically embedded in topological insulators, providing unconventional insights into the crystal morphology.