  Symmetry and topology play key roles in the identification of phases of
matter and their properties. Both concepts are central to understanding quantum
Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously
broken spin or pseudospin symmetry whose wavefunctions also have topological
properties. Domain walls between distinct broken symmetry QHFM phases are
predicted to host gapless one-dimensional (1D) modes that emerge due to a
topological change of the underlying electronic wavefunctions at such
interfaces. Although a variety of QHFMs have been identified in different
materials, probing interacting electronic modes at these domain walls has not
yet been accomplished. Here we use a scanning tunneling microscope (STM) to
directly visualize the spontaneous formation of boundary modes, within a
sign-changing topological gap, at domain walls between different
valley-polarized quantum Hall phases on the surface of bismuth. By changing the
valley occupation and the corresponding number of modes at the domain wall, we
can realize different regimes where the valley-polarized channels are either
metallic or develop a spectroscopic gap. This behavior is a consequence of
Coulomb interactions constrained by the symmetry-breaking valley flavor, which
determines whether electrons in the topological modes can backscatter, making
these channels a unique class of interacting Luttinger liquids.
