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1. Particle-hole symmetry and the reentrant integer quantum Hall Wigner solid

   https://doi.org/10.1038/s42005-021-00709-x  

   Shingla, Vidhi ; Myers, Sean A. ; Pfeiffer, Loren N. ; Baldwin, Kirk W. ; Csáthy, Gábor A. ( December 2021 , Communications Physics)

   Abstract The interplay of strong Coulomb interactions and of topology is currently under intense scrutiny in various condensed matter and atomic systems. One example of this interplay is the phase competition of fractional quantum Hall states and the Wigner solid in the two-dimensional electron gas. Here we report a Wigner solid at ν  = 1.79 and its melting due to fractional correlations occurring at ν  = 9/5. This Wigner solid, that we call the reentrant integer quantum Hall Wigner solid, develops in a range of Landau level filling factors that is related by particle-hole symmetry to the so called reentrant Wigner solid. We thus find that the Wigner solid in the GaAs/AlGaAs system straddles the partial filling factor 1/5 not only at the lowest filling factors, but also near ν  = 9/5. Our results highlight the particle-hole symmetry as a fundamental symmetry of the extended family of Wigner solids and paint a complex picture of the competition of the Wigner solid with fractional quantum Hall states. 

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2. Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

   https://doi.org/10.1038/s41467-023-40784-y  

   Deng, Peng ; Zhang, Peng ; Eckberg, Christopher ; Chong, Su Kong ; Yin, Gen ; Emmanouilidou, Eve ; Che, Xiaoyu ; Ni, Ni ; Wang, Kang L. ( September 2023 , Nature Communications)

   In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.

    

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3. Anomalous high-field magnetotransport in CaFeAsF due to the quantum Hall effect

   https://doi.org/10.1038/s41535-022-00470-6  

   Terashima, Taichi ; Hirose, Hishiro T. ; Kikugawa, Naoki ; Uji, Shinya ; Graf, David ; Morinari, Takao ; Wang, Teng ; Mu, Gang ( June 2022 , npj Quantum Materials)

   CaFeAsF is an iron-based superconductor parent compound whose Fermi surface is quasi-two dimensional, composed of Dirac-electron and Schrödinger-hole cylinders elongated along thecaxis. We measured the longitudinal and Hall resistivities in CaFeAsF with the electrical current in theabplane in magnetic fields up to 45 T applied along thecaxis and obtained the corresponding conductivities via tensor inversion. We found that both the longitudinal and Hall conductivities approached zero above ~40 T as the temperature was lowered to 0.4 K. Our analysis indicates that the Landau-level filling factor isν = 2 for both electrons and holes at these high field strengths, resulting in a total filling factorν = ν_hole − ν_electron = 0. We therefore argue that theν = 0 quantum Hall state emerges under these conditions.

    

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4. 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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5. Edge reconstruction and emergent neutral modes in integer and fractional quantum Hall phases

   https://doi.org/10.1063/10.0010207  

   Khanna, Udit ; Goldstein, Moshe ; Gefen, Yuval ( May 2022 , Low Temperature Physics)

   This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the ν = 2/5 phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counter-propagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particle-like phases at ν = 1, 1/3, and 2/5 as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorder-induced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases and could explain the absence of anyonic interference in electronic Mach-Zehnder setups.

    

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