  We investigate the layer localization control of two-dimensional states in
multilayer metal-organic frameworks (MOFs). For finite stackings of (NiC4S4)3
MOFs, the weak van der Waals coupling between adjacent layers leads to a Fermi
level dependent distribution of the electronic states in the monolayers. Such
distribution is reflected in the topological edge states of multilayer
nanoribbons. Moreover, by applying an external electric field, parallel to the
stacking direction, the spacial localization of the electronic states can be
controlled for a chosen Fermi energy. This localization behavior is studied
comparing density functional theory calculations with a kagome lattice
tight-binding model. Furthermore, for infinite stacked nanoribbons, a new
V-gutter Dirac state is found in the side surfaces, which allows anisotropic
current control by tuning the Fermi energy. Our results can be immediately
extended to other kagome MOFs with eclipsed stackings, introducing a new degree
of freedom (layer localization) to materials design.
