Real-space Imaging of Quantum Hall Quasiparticles
Jinghao Deng, Yiming Sun, Dimitri Pimenov, Takashi Taniguchi, Kenji Watanabe, Erich J Mueller, Xiaomeng Liu
Abstract
Quantum Hall systems host emergent quasiparticles with unusual charge, spin, and statistics, such as fractionally charged anyons. Although transport measurements have revealed many of their collective properties, identifying and visualizing individual quasiparticles remain elusive. Here we use scanning tunneling spectroscopy (STS) to image quantum Hall quasiparticles in graphene. Within incompressible quantum Hall states, we observe spatial variation of Landau level energies originating from electrostatic potentials created by charged defects in graphene and the underlying hexagonal boron nitride (hBN). For surface and near-surface defects, the Coulomb potential lifts the degeneracy of Landau orbitals, producing discrete energy splittings that reveal Landau orbital wavefunctions. In quantum Hall ferromagnetic states, quasiparticles bound to defect potentials produce distinct spatial and spectroscopic signatures that serve as hallmarks of the presence and number of localized excitations. In the fractional quantum Hall regime at one-third filling, our theoretical calculations predict discrete spectroscopic changes associated with the sequential addition of localized anyons, with a three-anyon bound state quantitatively reproducing our experimental data at . These observations establish spectroscopic fingerprints of quantum Hall quasiparticles and provide a pathway toward imaging and manipulating individual anyons in real space.
AI Impact Assessments
(1 model)Scientific Impact Assessment: "Real-space Imaging of Quantum Hall Quasiparticles"
1. Core Contribution
This paper reports the first direct real-space visualization of individual quantum Hall quasiparticles using scanning tunneling spectroscopy (STS) in monolayer graphene on hBN. The central advance is threefold: (i) imaging individual Landau orbitals through defect-induced orbital splitting at ν=2, (ii) detecting and distinguishing bound quasiparticle configurations in quantum Hall ferromagnetic states at ν=−1, and (iii) identifying spectroscopic signatures consistent with three bound anyonic quasiparticles at ν=5/3. The key conceptual insight is that charged defects in graphene and hBN act as natural nanoscale traps for quantum Hall quasiparticles, and that the number of trapped quasiparticles produces distinct, identifiable spectroscopic fingerprints—both in energy-resolved spectra and in spatially-resolved spectral weight.
This addresses a longstanding experimental gap: while transport measurements (shot noise, interferometry) have probed fractional charge and statistics indirectly, no technique had previously visualized individual quantum Hall quasiparticles in real space with the resolution needed to reveal their internal structure.
2. Methodological Rigor
The experimental methodology is exceptionally thorough. The authors employ careful tip preparation (charge-neutral tips verified via Haldane sash features), constant-height-setpoint protocols to ensure reliable spectral weight extraction, and multiple independent consistency checks. The observation of particle-hole symmetry between ν=5/3 and ν=−5/3 measurements (Fig. S11) provides compelling internal validation.
The theoretical framework is multi-layered and appropriate: exact diagonalization for integer quantum Hall states, and DMRG on the Haldane sphere for fractional states. The spectral function calculations use a sophisticated global Krylov method with ghost-state deflation, and results are cross-validated with an independent sequential excited-state approach. The agreement between theory and experiment is quantitative for the three-anyon bound state at ν=5/3, including both the energy sequence of orbital peaks and the screened Coulomb potential profile. Crucially, the authors demonstrate that zero, one, and two anyon configurations produce clear discrepancies with the data (Supplementary Fig. S10), strengthening the three-anyon interpretation.
The treatment of systematic effects is commendable. The tip screening model (metallic sphere with image charges), the chemical potential pinning mechanism explaining enlarged apparent gaps, and the careful estimation of subsurface defect depths all reflect deep understanding of potential artifacts. The explanation of why tunneling current—rather than gate voltage—controls quasiparticle occupation within incompressible states is a significant methodological insight for the STM community.
3. Potential Impact
Immediate field impact: This work establishes STS as a platform for detecting individual anyons, opening a fundamentally new experimental avenue in quantum Hall physics. The "quasiparticle microscope" concept—using the dichotomy between surface and subsurface defect spectra to detect bound quasiparticles—is elegant and broadly applicable.
Toward topological quantum computing: The authors explicitly note the possibility of combining visualization with tip-induced manipulation for anyon braiding demonstrations. If realized, this would constitute a qualitatively different approach to demonstrating non-Abelian statistics compared to interferometric methods.
Extensions to non-Abelian states: The methodology naturally extends to even-denominator fractional quantum Hall states (ν=5/2) and fractional Chern insulators in moiré systems, where non-Abelian anyons are theorized.
Materials science implications: The characterization of charged defect distributions in hBN—revealing their depths, charge states, and density—provides valuable information for the van der Waals heterostructure community, where such defects limit device quality.
Spectral weight sum rules: The demonstration that integrated dI/dV faithfully reproduces local electron/hole density, including the excess charge distribution of anyon bound states, establishes a quantitative link between STS observables and many-body wavefunctions.
4. Timeliness & Relevance
This work arrives at a critical moment. Recent interferometry experiments have provided evidence for anyonic braiding statistics, and there is intense interest in fractional Chern insulators in moiré materials. A real-space probe capable of imaging individual anyons fills a major experimental gap and could accelerate progress toward topological quantum computation. The graphene platform is particularly timely given its accessibility and the rapid improvements in device quality.
5. Strengths & Limitations
Key strengths:
Notable limitations:
Overall assessment: This is a landmark experimental and theoretical achievement that opens a new chapter in quantum Hall physics. The combination of atomic-resolution imaging, quantitative many-body theory, and clear physical interpretation makes this work exceptionally impactful. The pathway from visualization to manipulation of individual anyons, while speculative, is credibly outlined.
Generated Jun 25, 2026
Comparison History (31)
Paper 1 achieves a historic milestone in fundamental physics: the real-space imaging of individual fractional quantum Hall quasiparticles (anyons). While Paper 2 presents highly impactful findings on chiral superconductivity in multilayer graphene, Paper 1's methodology for visualizing and potentially manipulating anyons unlocks direct pathways for topological quantum computing. The ability to observe discrete spectroscopic signatures of anyon bound states transcends traditional transport measurements, offering broader, paradigm-shifting implications across quantum condensed matter physics and quantum information science.
Paper 2 achieves the first real-space imaging and spectroscopic fingerprinting of quantum Hall quasiparticles, including anyons, with combined experiment-theory validation. This positive, enabling result opens pathways toward visualizing and manipulating individual anyons—directly relevant to topological quantum computing—with broad appeal. Paper 1 is rigorous and settles an important debate, but a null result (absence of the transition) ruling out a predicted phenomenon typically has narrower reach and less generative follow-on impact than a novel imaging capability that unlocks new manipulation of exotic quasiparticles.
Paper 2 likely has higher impact: it provides direct, spatially resolved thermodynamic evidence of TRS breaking consistent with chiral superconductivity in rhombohedral graphene, addressing a major open question with strong methodological rigor (nanoscale SQUID-on-tip). It also demonstrates deterministic ultra-low-current control and reversible chirality switching, enabling near-term device concepts (low-power, reconfigurable electronics) and broad relevance across superconductivity, topology, spin/valley (isospin) physics, and 2D materials. Paper 1 is highly novel for anyon imaging, but its applications are more long-term and specialized.
Both papers are high-impact condensed matter results. Paper 1 demonstrates the first coherent control of a Majorana parity qubit, a milestone long pursued for topological quantum computing after years of controversy over Majorana claims. Achieving coherent time-domain qubit operation directly advances fault-tolerant quantum computing, a field of enormous investment and cross-disciplinary interest. Paper 2's real-space imaging of anyons is elegant and novel, but Paper 1's demonstration of qubit control has more transformative, timely, and applied significance for quantum technologies.
Paper 2 likely has higher impact: it reports new experimental capability (STS real-space/spectroscopic imaging of quantum Hall quasiparticles in graphene) with clear methodological rigor and concrete signatures, extending into the fractional regime with theory–experiment agreement and implications for anyon manipulation—relevant to fundamental physics and quantum information. Paper 1 is a perspective/survey proposing “AI magnonics” and outlining future directions; it is timely and broadly relevant but less novel in primary results and typically lower immediate impact than a breakthrough experimental demonstration.
Paper 2 demonstrates higher potential scientific impact due to its broad, cross-disciplinary applicability and paradigm-shifting approach to discovery. While Paper 1 offers a profound fundamental physics breakthrough in imaging anyons, Paper 2 introduces a fully autonomous, embodied AI system capable of hypothesis generation and closed-loop physical experimentation. This framework not only accelerates quantum materials research but serves as a generalizable foundation for automated, self-driving laboratories across multiple scientific disciplines, scoring exceptionally high on novelty, timeliness, and breadth of future real-world applications.
Paper 1 provides groundbreaking experimental evidence of non-Abelian anyons, including Fibonacci anyons, via direct thermodynamic measurements of fractional entropy. This represents a monumental leap for topological quantum computing, offering a novel method to characterize quantum states that bypasses complex transport measurement limitations. While Paper 2 presents remarkable real-space imaging of quasiparticles, Paper 1's findings have broader immediate implications for quantum information processing and universal fault-tolerant quantum computing, fulfilling highly sought-after theoretical predictions with immense real-world application potential.
Paper 1 likely has higher impact because it demonstrates a scalable, manufacturing-compatible route (300 mm pilot line EUV lithography) to high-fidelity SiMOS spin qubits with wafer-scale uniformity and strong, quantified performance (GST up to ~99.9% 1Q, ~99.1% 2Q). This directly addresses a key bottleneck for large-scale quantum processors and has clear near-term industrial relevance, breadth (quantum computing + semiconductor manufacturing), and timeliness. Paper 2 is highly novel and important for fundamental physics, but its immediate real-world scalability and cross-industry leverage are less direct.
Paper 2 provides direct real-space imaging of fractional quantum Hall quasiparticles and anyons, addressing a longstanding challenge with major implications for topological quantum computing and fundamental physics of anyonic statistics. The quantitative agreement between theory and experiment for a three-anyon bound state is a significant achievement. While Paper 1's q-SNOM is methodologically novel and technically impressive, Paper 2 tackles a more foundational, widely-sought goal (visualizing/manipulating individual anyons) with broader impact across condensed matter and quantum information communities.
Paper 2 has higher impact potential due to its strong novelty (real-space STS fingerprints of integer, ferromagnetic, and fractional quantum Hall quasiparticles/anyons), broad relevance across condensed matter, quantum information, and materials science, and clear pathways to real-world applications (anyon imaging/manipulation for topological quantum computing). It combines experiment with quantitative theory and targets a timely, high-profile problem (identifying individual anyons). Paper 1 is solid and rigorous but more incremental and materials-specific, with narrower cross-field reach.