  We report on the experimental realization of Pb1-xSnxTe pentagonal nanowires
(NWs) with [110] orientation using molecular beam epitaxy techniques. Using
first-principles calculations, we investigate the structural stability in NWs
of SnTe and PbTe in three different structural phases: cubic, pentagonal with
[001] orientation and pentagonal with [110] orientation. Within a semiclassical
approach, we show that the interplay between ionic and covalent bonds favors
the formation of pentagonal NWs. Additionally, we find that this pentagonal
structure is more likely to occur in tellurides than in selenides. The
disclination and twin boundary cause the electronic states originating from the
NW core region to generate a conducting band connecting the valence and
conduction bands, creating a symmetry-enforced metallic phase. The metallic
core band has opposite slopes in the cases of Sn and Te twin boundary, while
the bands from the shell are insulating. We finally study the electronic and
topological properties of pentagonal NWs unveiling their potential as a new
platform for higher-order topology and fractional charge. These pentagonal NWs
represent a unique case of intrinsic core-shell one-dimensional nanostructures
with distinct structural, electronic and topological properties between the
core and the shell region.
