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1. Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids

   https://doi.org/10.1038/s42005-022-00946-8  

   Bochniak, Arkadiusz; Nussinov, Zohar; Seidel, Alexander; Ortiz, Gerardo (July 2022, Communications Physics)

   Abstract Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. We present a second-quantization framework that reveals an exact fusion mechanism for particle fractionalization in FQH fluids, and uncovers the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level. We show the first exact analytic computation of the quasielectron Berry connections leading to its fractional charge and exchange statistics, and perform Monte Carlo simulations that numerically confirm the fusion mechanism for quasiparticles. We express the sequence of (bosonic and fermionic) Laughlin second-quantized states, highlighting the lack of local condensation, and present a rigorous constructive subspace bosonization dictionary for the bulk fluid. Finally, we establish universal long-distance behavior of edge excitations by formulating a conjecture based on the DNA, or root state, of the FQH fluid. 

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2. A highly correlated topological bubble phase of composite fermions

   https://doi.org/10.1038/s41567-023-01939-2  

   Shingla, Vidhi; Huang, Haoyun; Kumar, Ashwani; Pfeiffer, Loren N.; West, Kenneth W.; Baldwin, Kirk W.; Csáthy, Gábor A. (May 2023, Nature Physics)

   Strong interactions and topology drive a wide variety of correlated ground states. Some of the most interesting of these ground states, such as fractional quantum Hall states and fractional Chern insulators, have fractionally charged quasiparticles. Correlations in these phases are captured by the binding of electrons and vortices into emergent particles called composite fermions. Composite fermion quasiparticles are randomly localized at high levels of disorder and may exhibit charge order when there is not too much disorder in the system. However, more complex correlations are predicted when composite fermion quasiparticles cluster into a bubble, and then these bubbles order on a lattice. Such a highly correlated ground state is termed the bubble phase of composite fermions. Here we report the observation of such a bubble phase of composite fermions, evidenced by the re-entrance of the fractional quantum Hall effect. We associate this re-entrance with a bubble phase with two composite fermion quasiparticles per bubble. Our results demonstrate the existence of a new class of strongly correlated topological phases driven by clustering and charge ordering of emergent quasiparticles. 

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3. Integrability of the $\nu =4/3$ fractional quantum Hall edge states

   https://doi.org/10.22331/q-2022-06-14-736  

   Hu, Yichen; Lian, Biao (June 2022, Quantum)

   We investigate the homogeneous chiral edge theory of the filling ν = 4 / 3 fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge 2 e 3 chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each conserved charge and momentum sector, indicating the existence of hidden conserved quantities and the possibility that the generic edge theory of the ν = 4 / 3 fractional quantum Hall state is integrable. We further show that a global symmetry preserving irrelevant nonlinear kinetic term will lead to the transition of LSS from Poisson to Wigner-Dyson at high energies. This further supports the possibility that the model without irrelevant terms is integrable. 

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4. High spatial resolution charge sensing of quantum Hall states

   https://doi.org/10.1073/pnas.2424781122  

   Chiu, Cheng-Li; Wang, Taige; Fan, Ruihua; Watanabe, Kenji; Taniguchi, Takashi; Liu, Xiaomeng; Zaletel, Michael P; Yazdani, Ali (February 2025, Proceedings of the National Academy of Sciences)

   Charge distribution offers a unique fingerprint of important properties of electronic systems, including dielectric response, charge ordering, and charge fractionalization. We develop an architecture for charge sensing in two-dimensional electronic systems in a strong magnetic field. We probe local change of the chemical potential in a proximitized detector layer using scanning tunneling microscopy, allowing us to infer the chemical potential and the charge profile in the sample. Our technique has both high energy (<0.3 meV) and spatial (<10 nm) resolution exceeding that of previous studies by an order of magnitude. We apply our technique to study the chemical potential of quantum Hall liquids in monolayer graphene under high magnetic fields and their responses to charge impurities. The chemical potential measurement provides a local probe of the thermodynamic gap of quantum Hall ferromagnets and fractional quantum Hall states. The screening charge profile reveals spatially oscillatory response of the quantum Hall liquids to charge impurities and is consistent with the composite Fermi liquid picture close to the half-filling. Our technique also paves the way to map moiré potentials, probe Wigner crystals, and investigate fractional charges in quantum Hall and Chern insulators. 

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5. Moiré synaptic transistor with room-temperature neuromorphic functionality

   https://doi.org/10.1038/s41586-023-06791-1  

   Yan, Xiaodong; Zheng, Zhiren; Sangwan, Vinod K; Qian, Justin H; Wang, Xueqiao; Liu, Stephanie E; Watanabe, Kenji; Taniguchi, Takashi; Xu, Su-Yang; Jarillo-Herrero, Pablo; et al (December 2023, Nature)

   The convergence of topology and correlations represents a highly coveted realm in the pursuit of novel quantum states of matter [1, 2]. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order [3– 10], not possible in quantum Hall and Chern insulator systems. However, the QSH insulator with quantized edge conductance remains rare, let alone that with significant correlations. In this work, we report a novel dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator that aligns with single-particle band structure calculations, manifesting enhanced nonlocal transport and quantized helical edge conductance. Interestingly, upon introducing electrons from charge neutrality, TaIrTe4 only shows metallic behavior in a small range of charge densities but quickly goes into a new insulating state, entirely unexpected based on TaIrTe4’s single-particle band structure. This insulating state could arise from a strong electronic instability near the van Hove singularities (VHS), likely leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state, marked by the revival of nonlocal transport and quantized helical edge conduction. Our observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands via CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism [3–5, 11, 12]. 

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