  Domain walls are a type of topological defects that can arise in the early
universe after the spontaneous breaking of a discrete symmetry. They can form
in several beyond the Standard Model theories with an extended Higgs sector
such as the Next to-Two-Higgs-Doublet model (N2HDM). In this work, we discuss
the domain wall solution related to the singlet scalar of the N2HDM and
demonstrate the possibility of restoring the electroweak symmetry inside and in
the vicinity of the domain wall. Such symmetry restoration can have profound
implications on early universe cosmology as the weak sphaleron rate inside the
domain wall would, in principle, be unsuppressed compared to the rate outside
the wall. We also discuss the possibility of generating CP-violating vacua
localized in the vicinity of the domain wall. Our work is a first step towards
the realization of electroweak baryogenesis mediated by domain walls in the
N2HDM.
