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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. Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

   https://doi.org/10.1103/PhysRevX.15.011045  

   Waters, Dacen; Okounkova, Anna; Su, Ruiheng; Zhou, Boran; Yao, Jiang; Watanabe, Kenji; Taniguchi, Takashi; Xu, Xiaodong; Zhang, Ya-Hui; Folk, Joshua; et al (February 2025, Physical Review X)

   The advent of moiré platforms for engineered quantum matter has led to discoveries of integer and fractional quantum anomalous Hall effects, with predictions for correlation-driven topological states based on electron crystallization. Here, we report an array of trivial and topological insulators formed in a moiré lattice of rhomobohedral pentalayer graphene (R5G). At a doping of one electron per moiré unit cell ( $\nu =1$), we see a correlated insulator with a Chern number that can be tuned between $C=0$and $+1$by an electric displacement field. This is accompanied by a series of additional Chern insulators with $C=+1$originating from fractional fillings of the moiré lattice— $\nu =1/4$, $1/3$, and $2/3$—associated with the formation of moiré-driven topological electronic crystals. At $\nu =2/3$the system exhibits an integer quantum anomalous Hall effect at zero magnetic field, but further develops hints of an incipient $C=2/3$fractional Chern insulator in a modest field. Our results establish moiré R5G as a fertile platform for studying the competition and potential intertwining of integer and fractional Chern insulators. Published by the American Physical Society2025 

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3. 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)

   Abstract 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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4. Direct observation of a magnetic-field-induced Wigner crystal

   https://doi.org/10.1038/s41586-024-07212-7  

   Tsui, Yen-Chen; He, Minhao; Hu, Yuwen; Lake, Ethan; Wang, Taige; Watanabe, Kenji; Taniguchi, Takashi; Zaletel, Michael P; Yazdani, Ali (April 2024, Nature)

   Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2,3,4,5,6,7,8,9,10,11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice. 

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5. An all-epitaxial nitride heterostructure with concurrent quantum Hall effect and superconductivity

   https://doi.org/10.1126/sciadv.abf1388  

   Dang, Phillip; Khalsa, Guru; Chang, Celesta S.; Katzer, D. Scott; Nepal, Neeraj; Downey, Brian P.; Wheeler, Virginia D.; Suslov, Alexey; Xie, Andy; Beam, Edward; et al (February 2021, Science Advances)

   null (Ed.)

   Creating seamless heterostructures that exhibit the quantum Hall effect and superconductivity is highly desirable for future electronics based on topological quantum computing. However, the two topologically robust electronic phases are typically incompatible owing to conflicting magnetic field requirements. Combined advances in the epitaxial growth of a nitride superconductor with a high critical temperature and a subsequent nitride semiconductor heterostructure of metal polarity enable the observation of clean integer quantum Hall effect in the polarization-induced two-dimensional (2D) electron gas of the high-electron mobility transistor. Through individual magnetotransport measurements of the spatially separated GaN 2D electron gas and superconducting NbN layers, we find a small window of magnetic fields and temperatures in which the epitaxial layers retain their respective quantum Hall and superconducting properties. Its analysis indicates that in epitaxial nitride superconductor/semiconductor heterostructures, this window can be significantly expanded, creating an industrially viable platform for robust quantum devices that exploit topologically protected transport. 

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