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

Two-dimensional quantum Hall systems offer a versatile platform to explore the interplay between topology and symmetry breaking facilitated by Coulomb interactions. Spontaneous valley ordering of bismuth surface states in a large magnetic field gives rise to the emergence of a nematic phase. We can directly visualize the rotational symmetry breaking of this nematic phase using a scanning tunneling microscope (STM) [1]. We further use an STM to image the formation of topological boundary modes in between nematic quantum Hall domains. By changing the valley flavor and number of modes at the domain wall, we realize strikingly different regimes where these boundary modes are either metallic or insulating. This behavior is a consequence of Coulomb interactions constrained by the valley flavor, making these channels a new class of interacting symmetry-protected Luttinger liquids [2,3].

[1] B. E. Feldman, et al., Science 354, 316 (2016)
[2] M. T. Randeria, et al., Nature 566, 363 (2019)
[3] K. A. Agarwal, et al., Phys. Rev. B. 100 , 165103 (2019)