Quantum Hall Valley & Nematic Domain-Wall Transport

Anchor paper: M.T. Randeria, K. Agarwal, B.E. Feldman, H. Ding, H. Ji, R.J. Cava, S.L. Sondhi, et al., "Interacting multi-channel topological boundary modes in a quantum Hall valley system," Nature 566, 363-367 (2019). [arXiv:1902.02790]

Background

The Bi(111) surface hosts quantum Hall ferromagnets: Coulomb exchange spontaneously breaks the six-fold valley degeneracy of its hole pockets, producing nematic domains each polarized into a different subset of valleys. Theory predicted domain walls between such domains must host gapless, topologically protected 1D modes, with channel count and valley flavor set by the filling factor on each side. Open question: could these boundary modes be directly imaged and shown to behave as genuinely interacting multi-channel Luttinger liquids, with Coulomb interactions (constrained by valley flavor) controlling whether channels backscatter off each other?

New results

Using STM on Bi(111), the authors directly imaged spontaneous boundary-mode formation within a sign-changing topological gap at domain walls between differently valley-polarized quantum Hall phases — a sharp, atomically resolved low-conductance line marking the wall. Tuning the magnetic field (changing filling factor, e.g. ν̃=2 vs ν̃=1) showed the boundary could host either a pair of valley-distinct counter-propagating modes that stay gapless and metallic, or same-valley channels that develop a spectroscopic gap — direct evidence that valley-flavor-constrained Coulomb interactions control inter-channel backscattering, establishing these walls as a new class of interacting multi-channel Luttinger liquids.

Fig. 2 — STM differential-conductance map of a quantum Hall nematic domain wall on Bi(111), showing anisotropic Landau orbits of opposite orientation on either side of a sharp low-conductance boundary.

Related work in this direction

• K. Agarwal, M.T. Randeria, A. Yazdani, S.L. Sondhi, S.A. Parameswaran, "Topology- and symmetry-protected domain wall conduction in quantum Hall nematics," PRB 100, 165103 (2019) — the companion theory paper formalizing when these domain-wall Luttinger liquids stay gapless vs. gap out.
• K. Agarwal, "Quantum Hall valley ferromagnets as a platform for topologically protected quantum memory," PRB 107, 125163 (2023, solo) — proposes exploiting these protected channels for quantum memory.
• S. Vijayakrishnan, ... K. Agarwal, et al., "Anomalous electronic transport in high-mobility Corbino rings," Nature Communications 14, 3906 (2023).

See also Majorana Zero Modes — a different mechanism (particle-hole-symmetric Bogoliubov modes vs. valley-flavor Luttinger liquids) converging on the same broad question of robust, topologically/symmetry-protected 1D boundary transport.