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1. Transport in helical Luttinger liquids in the fractional quantum Hall regime

   https://doi.org/10.1038/s41467-021-25631-2  

   Wang, Ying ; Ponomarenko, Vadim ; Wan, Zhong ; West, Kenneth W. ; Baldwin, Kirk W. ; Pfeiffer, Loren N. ; Lyanda-Geller, Yuli ; Rokhinson, Leonid P. ( September 2021 , Nature Communications)

   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 excitations^1–3. 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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2. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

   https://doi.org/10.1038/s41598-022-22812-x  

   Wijewardena, U. Kushan ; Nanayakkara, Tharanga R. ; Kriisa, Annika ; Reichl, Christian ; Wegscheider, Werner ; Mani, Ramesh G. ( November 2022 , Scientific Reports)

   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,$$g \mu _B B$$$g{\mu }_{B}B$, 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$$\nu$$$\nu$for the$$R_{xx}$$$R_{\mathrm{xx}}$minimum, e.g., from$$\nu = 11/7$$$\nu =11/7$to$$\nu = 8/5$$$\nu =8/5$, and a corresponding change in the$$R_{xy}$$$R_{\mathrm{xy}}$, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$$R_{\mathrm{xy}}/R_K={(11/7)}^{-1}$to$$R_{xy}/R_{K} = (8/5)^{-1}$$$R_{\mathrm{xy}}/R_K={(8/5)}^{-1}$, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$$\nu =4/3$and$$\nu = 7/5$$$\nu =7/5$resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$$R_{\mathrm{xy}}$at the$$R_{xx}$$$R_{\mathrm{xx}}$minima- the latter occurring for$$\nu = 4/3, 7/5$$$\nu =4/3,7/5$and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$$\nu$and$$R_{xy}$$$R_{\mathrm{xy}}$, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

    

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3. Observation of backscattering induced by magnetism in a topological edge state

   https://doi.org/10.1073/pnas.2005071117  

   Jäck, Berthold ; Xie, Yonglong ; Andrei Bernevig, B. ; Yazdani, Ali ( June 2020 , Proceedings of the National Academy of Sciences)

   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.

    

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4. Quantifying the effect of interactions in quantum many-body systems

   https://doi.org/10.21468/SciPostPhysLectNotes.4  

   Pachos, Jiannis ; Papic, Zlatko ( November 2022 , SciPost Physics Lecture Notes)

   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. 

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5. Fractionalized conductivity and emergent self-duality near topological phase transitions

   https://doi.org/10.1038/s41467-021-25707-z  

   Wang, Yan-Cheng ; Cheng, Meng ; Witczak-Krempa, William ; Meng, Zi Yang ( December 2021 , Nature Communications)

   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. 

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