Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes—that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3,4,5,6,7,8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires. QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.
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The data that support the findings of this study are available from the corresponding author on reasonable request.
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The experiments in this project were primarily supported by the Gordon and Betty Moore Foundation as part of the EPiQS initiative (GBMF4530) (B.E.F., H.D., A.Y.) and DOE-BES grant DE-FG02-07ER46419 (M.T.R., A.Y.). Other financial support for the experimental effort came from NSF-DMR-1608848 (A.Y.), NSF-MRSEC programs through the Princeton Center for Complex Materials DMR-142054 (A.Y., R.J.C.) and a Dicke fellowship (B.E.F.). A.Y. acknowledges the hospitality of The Aspen Center for Physics supported under NSF grant PHY-1607611. K.A. acknowledges support from DOE-BES grant no. DE-SC0002140 and from a private bequest to Princeton University by the UK foundation. S.A.P. acknowledges support from NSF DMR-1455366 during the early stages of this project. We acknowledge discussions with S. Kivelson and E. Fradkin.
Nature thanks Brian LeRoy and the other anonymous reviewer(s) for their contribution to the peer review of this work.