Morphological evolution induced by topological phases in crystal growth

Crystal shapes play a crucial role in determining the properties of crystals. Since crystal morphology is governed by the growth process, understanding crystal growth is a fundamental issue in condensed matter physics. Topological phases of matter support gapless boundary states that affect the surface energies. This raises the question of whether the topological phases exhibit an exotic crystal growth driven by these topological boundary states. In this work, we reveal an orientation selection of crystal growth induced by a specific topological phase that hosts corner states. In this orientation selection, the corner of crystals grows preferentially compared to the edges. Furthermore, we show that two distinct types of fractal dimensions can distinguish the crystal shapes with the topological phases from those with trivial phases.