Topological interfacial states at phase boundaries in two-dimensional ferroelectric bismuth

Using machine learning potential, we explore different types of domain walls in the recently unveiled single-element ferroelectric, the bismuth monolayer [Gou et al., Nature (London) 617, 67 (2023)]. Remarkably, our investigation reveals that the charged domain-wall configuration exhibits lower energy compared to the uncharged domain-wall structure. Using the machine learning Hamiltonian, we directly calculate the band structures for large domain-wall systems and demonstrate that the experimentally discovered tail-to-tail domain wall preserves topological interfacial states, which arise from the change in the ${Z}_{2}$ topological number between the ferroelectric and paraelectric phases. Our study suggests that domain walls in two-dimensional bismuth hold potential as a promising platform for the development of ferroelectric domain-wall devices.