skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.


Title: 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.  more » « less
Award ID(s):
1836758
NSF-PAR ID:
10322134
Author(s) / Creator(s):
; ; ;
Editor(s):
Drouhin, Henri-Jean M.; Wegrowe, Jean-Eric; Razeghi, Manijeh
Date Published:
Journal Name:
SPIE Nanoscience + Engineering
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. 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.

     
    more » « less
  2. Abstract

    Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting,$$g \mu _B B$$gμBB, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in$$\nu$$νfor the$$R_{xx}$$Rxxminimum, e.g., from$$\nu = 11/7$$ν=11/7to$$\nu = 8/5$$ν=8/5, and a corresponding change in the$$R_{xy}$$Rxy, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$Rxy/RK=(11/7)-1to$$R_{xy}/R_{K} = (8/5)^{-1}$$Rxy/RK=(8/5)-1, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$ν=4/3and$$\nu = 7/5$$ν=7/5resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$Rxyat the$$R_{xx}$$Rxxminima- the latter occurring for$$\nu = 4/3, 7/5$$ν=4/3,7/5and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$νand$$R_{xy}$$Rxy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

     
    more » « less
  3. The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer’s pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

     
    more » « less
  4. Free fermion systems enjoy a privileged place in physics. With theirsimple structure they can explain a variety of effects, ranging frominsulating and metallic behaviours to superconductivity and the integerquantum Hall effect. Interactions, e.g. in the form of Coulombrepulsion, can dramatically alter this picture by giving rise toemerging physics that may not resemble free fermions. Examples of suchphenomena include high-temperature superconductivity, fractional quantumHall effect, Kondo effect and quantum spin liquids. The non-perturbativebehaviour of such systems remains a major obstacle to their theoreticalunderstanding that could unlock further technological applications.Here, we present a pedagogical review of “interaction distance"[Nat. Commun. 8, 14926 (2017)] – a systematicmethod that quantifies the effect interactions can have on the energyspectrum and on the quantum correlations of generic many-body systems.In particular, the interaction distance is a diagnostic tool thatidentifies the emergent physics of interacting systems. We illustratethis method on the simple example of a two-site Fermi-Hubbard model. 
    more » « less
  5. 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. 
    more » « less