This thesis demonstrates that these solitons could be interpreted as collective
phononic excitations of specific phonon modes. This finding allowed us to construct
atomistic models of the topological solitons systematically. Concerning a band in-
version and the system’s resultant topological features, we demonstrated a highly
nonlinear phonon-phonon coupling, which is mediated by coupled electronic and lat-
tice degrees of freedom. Understanding the dynamics of soliton-soliton interactions
turned out to be dependent on electron-phonon coupling. While the previously con-
ductedresearchtantalizinglydemonstratedthattheexactphononsinvolvedcouldbe
optically controlled in a deterministic and directed regime of nuclear motion with
speed at the quantum limit, algebraic operations may be carried out using these
single excitations with topological protection.