  Sliding bilayers are systems that exploit the possibility of relatively
translating two monolayers along a specific direction in real space, such that
different stackings could be implemented in the process. This simple approach
allows for manipulating the electronic properties of layered materials
similarly as in twisted multilayers. In this work, the sliding of bilayers,
composed of one type of monolayer with spatial symmetry described by space
group P$\bar{3}1m$ is studied. Using a minimal tight-binding model along with
symmetry analysis, we propose two effects that arise in a specific sliding
direction. First, the sliding-induced control of the band gap magnitude, which
produces a metal-insulator transition, is demonstrated. In addition, the
potential to achieve a topological adiabatic charge pump for cyclic sliding is
discussed. For each effect, we also present material implementations using
first-principles calculations. Bilayer GaS is selected for the metal-insulator
transition and bilayer transition metal dichalcogenide ZrS$_2$ is found to
display the topological pump effect. Both realizations show good agreement with
the predictions of the model.
