  Quantum materials that host a flat band, such as pseudospin-1 lattices and
magic-angle twisted bilayer graphene, can exhibit drastically new physical
phenomena including unconventional superconductivity, orbital ferromagnetism,
and Chern insulating behaviors. We report a surprising class of electronic
in-gap edge states in pseudospin-1 materials without the conventional need of
band-inversion topological phase transitions or introducing magnetism via an
external magnetic type of interactions. In particular, we find that, in
two-dimensional gapped (insulating) Dirac systems of massive spin-1
quasiparticles, in-gap edge modes can emerge through only an {\em electrostatic
potential} applied to a finite domain. Associated with these unconventional
edge modes are spontaneous formation of pronounced domain-wall spin textures,
which exhibit the feature of out-of-plane spin-angular momentum locking on both
sides of the domain boundary and are quite robust against boundary deformations
and impurities despite a lack of an explicit topological origin. The in-gap
modes are formally three-component evanescent wave solutions, akin to the
Jackiw-Rebbi type of bound states. Such modes belong to a distinct class due to
the following physical reasons: three-component spinor wave function, unusual
boundary conditions, and a shifted flat band induced by the external scalar
potential. Not only is the finding of fundamental importance, but it also paves
the way for generating highly controllable in-gap edge states with emergent
spin textures using the traditional semiconductor gate technology. Results are
validated using analytic calculations of a continuum Dirac-Weyl model and
tight-binding simulations of realistic materials through characterizations of
local density of state spectra and resonant tunneling conductance.
