Hopper-Like Growth of Higher-Order Topological Insulators

Understanding crystal growth and morphology is a fundamental issue in condensed matter physics. While crystal morphology due to the distribution and dynamics of the diffusion field has been intensively studied, how the intrinsic material properties affect crystal morphology remains unclear. In this Letter, we demonstrate that higher-order topological phases can give rise to hollowed crystal morphologies, where the corners advance faster than the central regions of the crystal, through an unconventional mechanism originating from topological electronic states. We quantitatively show this connection by analyzing both the fractal dimension $D_f$ and the fractal dimension of coastlines $D_{f,c}$. When we compare the crystals in the normal insulator and higher-order topological insulator phases with the same $D_{f}$ in the case of relatively rapid crystal growth, the former is in the dendritic shape, while the latter is in the hopper-like shape, quantified by the smaller $D_{f,c}$ in the higher-order topological phase.