Transport in helical Luttinger liquids in the fractional quantum Hall regime
Abstract

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations1–3. Here we investigate transport properties of hDWs in theν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

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Publication Date:
NSF-PAR ID:
10307243
Journal Name:
Nature Communications
Volume:
12
Issue:
1
ISSN:
2041-1723
Publisher:
Nature Publishing Group
National Science Foundation
##### More Like this
1. ; ; (Ed.)
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.
2. Abstract

The bond-disordered Kitaev model attracts much attention due to the experimental relevance inα-RuCl3andA3LiIr2O6(A= H, D, Ag, etc.). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions. The quantization of the thermal Hall conductivityκxy/Tdisappears by a quantum Hall transition induced by a small disorder, andκxy/Tshows a rapid crossover into a state with a negligible Hall current. We call this immobile liquid state Anderson–Kitaev spin liquid (AKSL). Especially, the critical disorder strengthδJc1~ 0.05 in the unit of the Kitaev interaction would have many implications for the stability of Kitaev spin liquids.

3. Turning on superconductivity in a topologically nontrivial insulator may provide a route to search for non-Abelian topological states. However, existing demonstrations of superconductor-insulator switches have involved only topologically trivial systems. Here we report reversible, in situ electrostatic on-off switching of superconductivity in the recently established quantum spin Hall insulator monolayer tungsten ditelluride (WTe2). Fabricated into a van der Waals field-effect transistor, the monolayer’s ground state can be continuously gate-tuned from the topological insulating to the superconducting state, with critical temperaturesTcup to ~1 kelvin. Our results establish monolayer WTe2as a material platform for engineering nanodevices that combine superconducting and topological phases of matter.

4. Abstract

Physical systems with non-trivial topological order find direct applications in metrology (Klitzinget al1980Phys.Rev. Lett.45494–7) and promise future applications in quantum computing (Freedman 2001Found. Comput. Math.1183–204; Kitaev 2003Ann. Phys.3032–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981Phys. Rev.B235632–33). At magnetic fields beyond the reach of current condensed matter experiment, around$104$T, this conductance remains precisely quantized with values based on the topological order (Thoulesset al1982Phys. Rev. Lett.49405–8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003New J. Phys.556; Miyakeet al2013Phys. Rev. Lett.111185302; Aidelsburgeret al2013Phys. Rev. Lett.111185301; Celiet al2014Phys. Rev. Lett.112043001; Stuhlet al2015Science3491514; Manciniet al2015Science3491510; Anet al2017Sci. Adv.3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of$5%$, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.

5. Abstract

Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.