Engineering parafermions in helical Luttinger liquids
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 counterpropagating 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.
Authors:
; ; ;
Editors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10322134
Journal Name:
SPIE Nanoscience + Engineering
3. Abstract The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.