The van der Waals layered ferroelectric CuInP2βS6β has been found to
exhibit a variety of intriguing properties arising from the fact that the Cu
ions are unusually mobile in this system. While the polarization switching
mechanism is usually understood to arise from Cu ion motion within the
monolayers, a second switching path involving Cu motion across the van der
Waals gaps has been suggested. In this work, we perform zero-temperature
first-principles calculations on such switching paths, focusing on two types
that preserve the periodicity of the primitive unit cell: ``cooperative" paths
preserving the system's glide mirror symmetry, and ``sequential" paths in which
the two Cu ions in the unit cell move independently of each other. We find that
CuInP2βS6β features a rich and varied energy landscape, and that sequential
paths are clearly favored energetically both for cross-gap and through-layer
paths. Importantly, these segments can be assembled to comprise a globally
insulating cycle with the out-of-plane polarization evolving by a quantum as
the Cu ions shift to neighboring layers. In this sense, we argue that
CuInP2βS6β embodies the physics of a quantized adiabatic charge pump