  We investigate the consequences of applying electric fields perpendicularly
to thin films of topological semimetals. In particular, we consider Weyl and
Dirac semimetals in a configuration such that their surface Fermi arcs lie on
opposite edges of the films. We develop an analytical approach based on
perturbation theory and a single-surface approximation and we compare our
analytical results with numerical calculations. The effect of the electric
field on the dispersion is twofold: it shifts the dispersion relation and
renormalizes the Fermi velocity, which would, in turn, have direct effects on
quantum transport measurements. Additionally, it modifies the spatial decay
properties of surface states which will impact the connection of the Fermi arcs
in opposite sides of a narrow thin film.
