Engineering parafermions in helical Luttinger liquids

Yuli B. Lyanda-Geller; Vadim Ponomarenko; Ying Wang; Leonid P. Rokhinson

doi:10.1117/12.2595632

1 August 2021 Engineering parafermions in helical Luttinger liquids

Yuli B. Lyanda-Geller, Vadim Ponomarenko, Ying Wang, Leonid P. Rokhinson

Proceedings Volume 11805, Spintronics XIV; 1180515 (2021) https://doi.org/10.1117/12.2595632
Event: SPIE Nanoscience + Engineering, 2021, San Diego, California, United States

Abstract

Parafermions or Fibonacci anyons leading to universal quantum computing, require strongly interacting systems. A leading contender is the fractional quantum Hall effect, where helical channels can arise from counter- propagating chiral modes. These modes have been considered weakly interacting. However, experiments on transport in helical channels in the fractional quantum Hall effect at a 2/3 filling shows current passing through helical channels on the boundary between polarized and unpolarized quantum Hall liquids nine-fold smaller than expected. This current can increase three-fold when nuclei near the boundary are spin polarized. We develop a microscopic theory of strongly interacting helical states and show that emerging helical Luttinger liquid manifests itself as unequally populated charge, spin and neutral modes in polarized and unpolarized fractional quantum Hall liquids. We show that at strong coupling counter-propagating modes of opposite spin polarization emerge at the sample edges, providing a viable path for generating proximity topological superconductivity and parafermions. Current, calculated in strongly interacting picture is in agreement with the experimental data.

Conference Presentation

Citation Download Citation

Yuli B. Lyanda-Geller, Vadim Ponomarenko, Ying Wang, and Leonid P. Rokhinson "Engineering parafermions in helical Luttinger liquids", Proc. SPIE 11805, Spintronics XIV, 1180515 (1 August 2021); https://doi.org/10.1117/12.2595632

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