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In several models of beyond Standard Model physics (BSM) discrete symmetriesplay an important role. For instance, in order to avoid flavor changing neutralcurrents (FCNC), a discrete $Z_2$ symmetry is imposed onTwo-Higgs-Doublet-Models (2HDM). This can lead to the formation of domain walls(DW) as the $Z_2$ symmetry gets spontaneously broken during electroweaksymmetry breaking (EWSB) in the early universe. Due to this simultaneousspontaneous breaking of both the discrete symmetry and the electroweaksymmetry, the vacuum manifold has the structure of two disconnected 3-spheresand the formed domain walls can exhibit several special properties in contrastto standard domain walls. We focus on some of these properties such as CP andelectric charge violating vacua localized inside the domain walls. The breakingof $U(1)_{em}$ inside the wall leads to the known phenomenon of"clash-of-symmetries" mechanism, meaning that the symmetry group inside thewall is smaller than the symmetry group far from the wall. We also discuss thescattering of top quarks off such types of domain walls and show, for example,that they can be reflected or transmitted off the wall as a bottom quark.

SM fermion scattering off electric charge and CP-violating domain walls in the 2HDM