Analysis of optical transition rules in buckled and puckered bismuthene monolayers based on electron-photon dipole vectors

When a material absorbs incident light, electrons can undergo an optical transition between valence and conduction bands depending on the frequency and polarization of light. In atomic-layered materials such as bismuthene, even a small change in its geometrical structure, e.g. from the buckled to puckered lattices, completely alters its electronic properties and, accordingly, its possible optical transitions. Since the strength and selection rule of optical transitions can be understood by analyzing the electron-photon dipole vectors, we calculate dipole vectors as a function of electronic wave vector between two quantum states in buckled and puckered bismuthene monolayers. We find that each of the bismuthene structures has its own, unique dipole vectors, implying a certain geometrical dependence of the dipole vectors. These materials are expected as a potential candidate for optoelectronics applications. Furthermore, one would consider applying various light polarization in these materials when the optical transition rules are well understood.