🔬 mesoscale physics

Real-space Imaging of Quantum Hall Quasiparticles

This paper demonstrates the real-space imaging and spectroscopic identification of individual quantum Hall quasiparticles in graphene using scanning tunneling spectroscopy, revealing distinct signatures of localized anyons and providing a pathway toward manipulating them.

Original authors: Jinghao Deng, Yiming Sun, Dimitri Pimenov, Takashi Taniguchi, Kenji Watanabe, Erich J Mueller, Xiaomeng Liu

Published 2026-06-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jinghao Deng, Yiming Sun, Dimitri Pimenov, Takashi Taniguchi, Kenji Watanabe, Erich J Mueller, Xiaomeng Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a crowded dance floor where everyone is moving in perfect, synchronized circles. This is what happens to electrons in a special material called graphene when you put it under a very strong magnetic field. In this state, known as the Quantum Hall effect, the electrons form a rigid, invisible grid. They don't just move randomly; they occupy specific "dance steps" called Landau orbitals.

Usually, scientists can only guess what these electrons are doing by watching how electricity flows around the edges of the material. It's like trying to understand a complex dance routine by only watching the audience's applause. You know something is happening, but you can't see the individual dancers.

This paper is like finally getting a high-definition camera that can zoom in and film every single dancer in real-time. Here is how the researchers did it and what they found, using simple analogies:

1. The "Spotlight" and the "Hidden Bumps"

The researchers used a tool called a Scanning Tunneling Microscope (STM). Think of this as a super-sensitive needle that hovers just above the graphene surface. It acts like a flashlight that can detect the energy of the electrons.

As they scanned the surface, they discovered that the "dance floor" isn't perfectly flat. There are tiny, invisible bumps caused by charged defects (like a speck of dust or a missing atom) in the graphene or the layer underneath it.

The Analogy: Imagine a trampoline. If you place a heavy weight in the center, the fabric dips down. The electrons (the balls rolling on the trampoline) feel this dip. The researchers mapped these dips, creating a 3D map of the invisible electric landscape created by these tiny defects.

2. Splitting the "Dance Steps" (Orbital Splitting)

In a perfect, flat world, all the "dance steps" (Landau orbitals) at the same energy level would look identical. But when the needle got close to a defect, the researchers saw something amazing: the single energy level split into multiple distinct levels.

The Analogy: Imagine a choir singing a single note. If you bring a giant speaker right next to them, the sound waves interact, and the single note splits into different harmonics. The defect's electric field acted like that speaker, forcing the electrons to separate into different "orbits" based on how close they were to the defect. This allowed the team to actually see the shape of these invisible electron orbits for the first time.

3. Catching the "Mischievous Dancers" (Quasiparticles)

In some of these quantum states, the electrons act like a team where everyone is perfectly paired up. But sometimes, a "mischievous dancer" (a quasiparticle) gets trapped by one of those charged bumps.

The Integer Case (Whole Numbers): In one state, the researchers found that a defect could trap exactly one or two of these quasiparticles. It was like a magnet that could hold a specific number of metal balls. They could count them by looking at the energy signals.
The Fractional Case (The "Thirds"): This is the most exciting part. In a different state, the electrons behave as if they are made of smaller pieces. The quasiparticles here carry only one-third of an electron's charge.
- The Discovery: The researchers found a defect that was holding three of these "one-third" particles.
- The Analogy: Imagine you have a pizza. Usually, you cut it into whole slices. But in this quantum world, you can cut a slice into three tiny pieces. The researchers found a "trap" that was holding exactly three of these tiny pieces, which together made up one whole slice. They confirmed this by matching their experimental data with complex computer simulations, proving that these three tiny pieces were stuck together as a group.

4. Why This Matters (According to the Paper)

The paper claims that this is the first time scientists have been able to directly image these individual quasiparticles in real space.

Before this, we knew they existed because of indirect clues (like traffic jams in electricity flow).
Now, we can see them, count them, and see how they are trapped by defects.

The authors suggest that this technique turns the microscope into a "quasiparticle microscope." It doesn't just show us that these strange particles exist; it shows us exactly where they are and how many are there. This is a crucial step toward understanding how to control them, which is necessary for future technologies like topological quantum computing (a type of super-computer that uses these particles to store information).

In short: The researchers used a super-sensitive needle to map the invisible electric hills and valleys on a graphene sheet. They discovered that these hills act like traps, catching specific numbers of strange, fractional particles. They successfully photographed these traps and counted the particles inside, proving that these exotic quantum objects can be seen and manipulated one by one.

Technical Summary: Real-space Imaging of Quantum Hall Quasiparticles

Problem Statement
Quantum Hall systems host emergent quasiparticles with exotic properties, including fractional charges and anyonic statistics (e.g., skyrmions in ferromagnetic states and anyons in fractional states). While bulk transport measurements have successfully characterized collective properties such as fractional charge and anyonic statistics, they offer only indirect insights into the microscopic structure of individual quasiparticles. Previous attempts to visualize these entities, such as scanning single-electron transistor measurements, lack the spatial resolution required to resolve individual quasiparticles. Consequently, the direct real-space imaging of individual quantum Hall quasiparticles, their localization conditions, and their interactions remains an unresolved challenge essential for understanding their fundamental nature and potential manipulation for topological quantum computing.

Methodology
The authors employ Scanning Tunneling Microscopy and Spectroscopy (STM/STS) on high-quality monolayer graphene devices encapsulated in hexagonal boron nitride (hBN) with graphite back gates. The experiments are conducted under strong out-of-plane magnetic fields (12 T to 14.8 T) at a base temperature of ~400 mK.

Sample Preparation: Devices are fabricated using mechanical exfoliation and dry transfer techniques. Charge-neutral STM tips are carefully prepared to minimize tip-induced gating effects, which is critical for probing fragile symmetry-breaking and fractional states.
Measurement Strategy: The study focuses on mapping the energy of Landau levels (LLs) across the sample surface. By tracking the peak positions of the Zeroth Landau Level (ZLL) and higher LLs, the authors reconstruct the real-space electrostatic potential landscape created by charged defects.
Theoretical Framework: Theoretical analysis includes exact diagonalization for integer quantum Hall states (specifically the $\nu = -1$ ferromagnetic state) and Density Matrix Renormalization Group (DMRG) calculations for fractional quantum Hall states (specifically the $\nu = 5/3$ state). These models account for Coulomb interactions, defect potentials, and the specific boundary conditions of the experimental setup.

Key Contributions and Results

Mapping the Electrostatic Landscape and Orbital Splitting ( $\nu = 2$ ):
In the integer quantum Hall state at $\nu = 2$ , the authors map the electrostatic potential variations induced by charged defects in graphene and the hBN substrate. They observe that strong, near-surface Coulomb potentials lift the degeneracy of Landau orbitals. This "orbital splitting" allows for the direct visualization of individual Landau orbital wavefunctions ( $\psi_m$ ). By integrating the differential conductance ($dI/dV$) over specific energy windows, they reconstruct the probability densities of $m=0, 1, 2$ orbitals, which match theoretical expectations. Furthermore, they resolve valley symmetry breaking for surface defects, evidenced by a half-unit-cell shift in the spatial patterns of $K$ and $K'$ valley states.
Spectroscopic Signatures of Bound Quasiparticles in Ferromagnetic States ( $\nu = -1$ ):
In the quantum Hall ferromagnetic state at $\nu = -1$ , the authors demonstrate that charged defects can pin individual quasiparticles.
- Surface Defects: A surface $+e$ defect binds a localized electron (specifically a $K\downarrow$ state with $m=0$ ) for hole tunneling, screening the defect potential. For electron tunneling, the defect binds two electrons, leading to distinct spectral signatures and a suppression of spectral weight at the defect center.
- Subsurface Defects: Defects buried several nanometers beneath the surface generate weaker potentials that are insufficient to overcome the quantum Hall gap to nucleate an electron. Consequently, these defects exhibit orbital splitting patterns consistent with a bare Coulomb potential without quasiparticle binding.
- Mechanism: The authors propose a mechanism of "tunneling-induced chemical potential pinning." In incompressible states, the local chemical potential is pinned to the mobility edges of the extended states by the tunneling current, rendering gate voltage ineffective in altering the quasiparticle occupation near the tunneling site. This explains why the number of bound quasiparticles remains fixed despite gate voltage variations within the incompressible gap.
Imaging Anyon Bound States in Fractional Quantum Hall States ( $\nu = 5/3$ ):
Extending the approach to the fractional quantum Hall regime at $\nu = 5/3$ (corresponding to a hole filling of $\nu^* = 1/3$ ), the authors identify spectroscopic signatures consistent with the binding of multiple anyons.
- Three-Anyon Bound State: Experimental data near a $-e$ subsurface defect shows a screened Coulomb potential and an energy sequence of spectral peaks ( $m=0, 1, 2$ ) that quantitatively match DMRG simulations for a bound state containing three $+e/3$ anyon quasi-holes.
- Spectral Weight Analysis: The real-space density profile of the spectral weight reveals a pronounced peak near the defect center, indicating nearly complete depletion of local orbitals, alongside oscillatory structures in the charge density. These features are interpreted as evidence of an "anyon molecule" rather than a simple point charge.
- Quasi-electron Binding: For a $+e$ defect, the spectral weight is suppressed, indicating the binding of three quasi-electrons (total charge $-e$ ), though extracting the exact number is less reliable than for quasi-holes due to the lack of discrete spectroscopic features.

Significance
The paper establishes STM/STS as a powerful platform for the direct detection and visualization of localized quasiparticles in both integer and fractional quantum Hall states. By resolving the spectroscopic fingerprints of individual quasiparticles and their bound states, the work provides a microscopic understanding of how charged defects act as nanoscale traps for these excitations. The ability to distinguish between different numbers of bound anyons and to visualize their spatial wavefunctions represents a significant step toward the real-space manipulation of anyons, a prerequisite for topological quantum computation. The findings also offer insights into the role of charged defects in high-quality van der Waals heterostructures and the effects of tunneling processes on spectroscopic measurements in insulating quantum Hall states.

1. The "Spotlight" and the "Hidden Bumps"

2. Splitting the "Dance Steps" (Orbital Splitting)

3. Catching the "Mischievous Dancers" (Quasiparticles)

4. Why This Matters (According to the Paper)

More like this