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Symmetry and topology play key roles in the identification of phases ofmatter and their properties. Both concepts are central to understanding quantumHall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneouslybroken spin or pseudospin symmetry whose wavefunctions also have topologicalproperties. Domain walls between distinct broken symmetry QHFM phases arepredicted to host gapless one-dimensional (1D) modes that emerge due to atopological change of the underlying electronic wavefunctions at suchinterfaces. Although a variety of QHFMs have been identified in differentmaterials, probing interacting electronic modes at these domain walls has notyet been accomplished. Here we use a scanning tunneling microscope (STM) todirectly visualize the spontaneous formation of boundary modes, within asign-changing topological gap, at domain walls between differentvalley-polarized quantum Hall phases on the surface of bismuth. By changing thevalley occupation and the corresponding number of modes at the domain wall, wecan realize different regimes where the valley-polarized channels are eithermetallic or develop a spectroscopic gap. This behavior is a consequence ofCoulomb interactions constrained by the symmetry-breaking valley flavor, whichdetermines whether electrons in the topological modes can backscatter, makingthese channels a unique class of interacting Luttinger liquids.

Interacting multi-channel topological boundary modes in a quantum Hall valley system