I will present recent work on ferromagnetic quantum Hall states that form on (111) surfaces of elemental Bismuth in high magnetic fields. This unusual states of matter combine the topological features of quantum Hall states with orientational symmetry breaking characteristic of nematic order. Recent scanning tunneling microscopy measurements have directly visualized the spontaneous formation of boundary modes between distinct nematic domains and investigated their electronic structure . I will demonstrate that these boundary modes belong to a new class of `symmetry-protected’ Luttinger liquid that arise from the interplay of symmetry-breaking with quantum Hall physics, and that they provide a concrete realization of `anomaly inflow’ . The analysis reveals strikingly different behavior of domain wall transport at quantum Hall filling factor $\nu=1,2$, in striking agreement with the STM results. I will explore implications of these ideas for the global phase diagram of quantum Hall valley nematics .
1. M.T. Randeria, K. Agarwal, B. E. Feldman, H. Ding , Huiwen Ji3 , R. J. Cava , S. L. Sondhi , S. A. Parameswaran, A. Yazdani, under review
2. K. Agarwal, M.T. Randeria, A. Yazdani, S.L. Sondhi, S.A. Parameswaran, arXiv:1807.10293
3. S.A. Parameswaran and B.E. Feldman, arXiv:1809.09616
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