🔬 mesoscale physics

Spin polarisation signatures of Fractionally Charged Skyrmions in Fractional Quantum Hall states

This paper reports the first observation of complete suppression of oscillator strength in fully polarized fractional quantum Hall states and identifies a depolarization law ( $S=\nu^*$ ) as evidence for the existence of Minimal Fractionally Charged Skyrmions formed by bound spin-flip and quasiparticle excitations.

Original authors: Odysseas Williams, Stefan Faelt, Christian Reichl, Werner Wegscheider

Published 2026-06-10

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CC BY 4.0

Original authors: Odysseas Williams, Stefan Faelt, Christian Reichl, Werner Wegscheider

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

The Big Picture: A Dance of Electrons

Imagine a crowded dance floor where the dancers are electrons. Usually, these electrons move around randomly. But if you put them in a very cold environment and apply a strong magnetic field (like a giant, invisible magnet), they suddenly stop dancing randomly and start moving in perfect, synchronized patterns. This is called the Fractional Quantum Hall (FQH) state.

In this state, the electrons act like a single, giant super-organism. The scientists in this paper wanted to know: Are all the dancers spinning in the same direction (fully polarized), or are some spinning the opposite way (depolarized)?

The Tool: A "Light Microscope" for Electrons

To see how the electrons are spinning, the researchers didn't use a regular microscope. They used a special trick involving light and mirrors.

The Trap: They built a tiny "cage" made of mirrors (a microcavity) containing a thin layer of Gallium Arsenide (a semiconductor).
The Light: They shone light into this cage. The light bounces back and forth, creating a standing wave.
The Interaction: When the light hits the electrons, they get excited. If the electrons are spinning in a specific way, they "grab" onto the light and form a hybrid particle called a polariton.
The Clue: By measuring how strongly the light couples to the electrons, the scientists could tell exactly how many electrons were spinning "up" versus "down."

The First Discovery: The "Silent" Spot

The researchers looked at what happens when they try to excite the lowest-energy electrons.

The Analogy: Imagine trying to push a swing. If the swing is empty, you can push it easily. If the swing is already full of people, you can't push it at all.
The Result: At certain specific "filling factors" (which is just a fancy way of saying "how crowded the dance floor is"), the light coupling completely vanished. The light couldn't excite the electrons at all.
What it means: This silence proved that the electrons had formed a special, tightly bound group called a singlet trion. It's like a trio of dancers (two electrons and one "hole" or empty spot) holding hands so tightly that they refuse to let the light separate them. This was the first time this specific "silence" was seen in these fractional states.

The Second Discovery: The "Skyrmion" Swirls

Once the scientists knew the electrons were fully spinning in one direction (fully polarized) at certain densities, they started changing the density slightly.

The Analogy: Imagine a perfectly calm, blue ocean (all electrons spinning the same way). If you drop a stone in it, you don't just get one ripple; you get a swirling vortex that spreads out.
The Result: As they moved away from the perfect "quantized" densities, the electrons didn't just flip one by one. Instead, they started flipping in a coordinated, swirling pattern.
The Name: The scientists call these swirling patterns Skyrmions. Think of them as "magnetic tornadoes" made of electron spins.

The New Finding: "Minimal" Swirls

The most exciting part of the paper is what they found about the size of these swirls in the fractional states (like 1/3, 2/5, etc.).

The Old Idea: Scientists thought these swirls might be huge, complex monsters involving many electrons flipping at once.
The New Discovery: The data shows these swirls are actually Minimal Fractionally Charged Skyrmions (MFCS).
The Metaphor: Instead of a massive hurricane, these are like tiny, precise eddies. They are formed by binding a single "spin-flip" (one electron turning around) to a single "quasiparticle" (a ripple in the electron crowd).
The Rule: The researchers found a simple rule for how these swirls behave: The number of spins that flip is directly related to the "effective" number of dancers on the floor. It's a very neat, predictable pattern that holds true across different samples.

Why This Matters

This paper is like finding a new rulebook for how electrons behave in these exotic states.

It confirms a theory: It proves that the "Composite Fermion" theory (which treats electrons as if they are carrying little magnetic flags) works very well.
It reveals the structure: It shows that the excitations (the "ripples" in the electron sea) aren't just random single flips, but organized, bound groups (trions and skyrmions).
It's a new tool: It proves that using light in a cavity is a super-sensitive way to measure the spin of electrons, better than many previous methods.

In short: The scientists used a special light trick to watch electrons dance. They found that when the dance floor gets crowded in specific ways, the electrons form tight-knit groups and create tiny, organized magnetic swirls, rather than just flipping randomly. This helps us understand the fundamental rules of how matter behaves at the quantum level.

Technical Summary: Spin Polarisation Signatures of Fractionally Charged Skyrmions in Fractional Quantum Hall States

Problem and Context
The nature of elementary excitations in Fractional Quantum Hall (FQH) states remains a subject of debate. While the Composite Fermion (CF) theory successfully maps fractional fillings to integer fillings in pseudo-Landau levels ( $\Lambda$ Ls), the specific nature of excitations—whether they are simple single-particle CFs or more complex collective states—requires further elucidation. Previous work established that the integer quantum Hall state at $\nu=1$ is ferromagnetic, with its elementary excitations being Skyrmions (extended spin textures) rather than isolated spin flips, evidenced by symmetric depolarisation away from $\nu=1$ . However, in the FQH regime ( $1/3 \le \nu \le 1$ ), the continuous evolution of spin polarisation ( $P$ ) with filling factor is less understood, with existing experiments reporting conflicting results. Specifically, it is unclear if FQH states exhibit Skyrmionic behaviour analogous to $\nu=1$ and what the nature of the bound states forming these excitations might be.

Methodology
The authors investigated spin polarisation and low-energy excitations using cavity-polariton spectroscopy on two high-mobility, n-doped GaAs quantum well (QW) samples coupled to optical microcavities (designated 2 $\lambda$ and 3 $\lambda$ ).

Sample Fabrication: The devices were grown via Molecular Beam Epitaxy (MBE) with electron mobilities exceeding $30 \times 10^6$ cm $^2$ V $^{-1}$ s $^{-1}$ . The samples feature a central 30 nm GaAs QW hosting a 2D electron gas (2DEG), surrounded by Distributed Bragg Reflectors (DBRs). The cavity lengths differ (2 $\lambda$ vs. 3 $\lambda$ ), resulting in different electron densities ( $n_e \approx 1.05 \times 10^{11}$ cm $^{-2}$ for 2 $\lambda$ and $0.52 \times 10^{11}$ cm $^{-2}$ for 3 $\lambda$ ).
Measurement Technique: The team measured normal-incidence reflection spectra while sweeping the perpendicular magnetic field ( $B$ ) and cavity energy. By reversing the sign of $B$ , they separated spectra for $\sigma^+$ and $\sigma^-$ circular polarisations.
Data Extraction: The spectra were fitted with a coupled-oscillator model to extract excitation energies ( $E_n$ ) and Rabi splittings ( $\Omega_n$ ), which characterize the optical coupling strength between cavity photons and matter excitations. The spin polarisation $P$ was derived from the coupling strength of the lowest-energy excitation ( $\Omega_0$ ), which the authors identify as a singlet trion in the fully polarised regime.

Key Contributions and Results

Suppression of Oscillator Strength: The authors report the first observation of the complete suppression of the oscillator strength (coupling energy $\Omega_0$ ) for the lowest-energy interband excitation at fractional fillings ( $1/3 \le \nu \le 1$ ). This suppression, previously only seen at $\nu=1$ , indicates the formation of singlet trions (a hole bound to two electrons of opposite spin) rather than simple interband transitions. This phenomenon allows for the direct extraction of the minority-spin population ( $n_\downarrow$ ).
Spin Polarisation Mapping: Using the relation $\Omega_0^2 \propto n_\downarrow$ $Ω_{0}^{2} \propto n_{↓}$ , the authors extracted the spin polarisation $P$ $P$ across the filling factor range.
- Partially Polarised States: At lower magnetic fields, the data shows abrupt transitions consistent with CF $\Lambda$ L crossings. For instance, at $\nu=2/3$ , the system transitions from unpolarised ( $P=0$ ) to fully polarised ( $P=1$ ). At $\nu=3/5$ and $\nu=4/7$ , partially polarised states with $P=1/3$ and $P=1/2$ respectively are observed, aligning with CF theory predictions.
- Fully Polarised States: At higher magnetic fields, states such as $\nu=2/5, 3/7, 4/9$ (sample 3 $\lambda$ ) and $\nu=2/3, 3/5, 4/7$ (sample 2 $\lambda$ ) are found to be fully polarised ( $P=1$ ). This is attributed to the dominance of Zeeman energy over the CF cyclotron gap.
Skyrmionic Depolarisation and MFCS: Away from these fully polarised integer CF fillings ( $\nu^*$ $ν^{*}$ ), the authors observe a symmetric depolarisation. The number of spin flips per added magnetic flux quantum, $S$ $S$ , follows an empirical law $S = \nu^*$ $S = ν^{*}$ .
- This behaviour is interpreted as evidence for Minimal Fractionally Charged Skyrmions (MFCS). Unlike the integer-charge Skyrmions at $\nu=1$ , these MFCS are formed by binding a spin-flip excitation (a hole in the highest occupied $\Lambda$ L bound to a CF in a spin-reversed $\Lambda$ L) to either a CF particle or a CF hole.
- The data fits the $S=\nu^*$ curve closely for $2 \le \nu^* \le 4$ , suggesting that the elementary excitations are collective bound states rather than single CFs.

Significance and Claims
The paper claims that cavity-polariton spectroscopy is a powerful tool for probing FQH spin physics, offering a continuous measurement of spin polarisation that reveals details inaccessible to transport measurements. The primary significance lies in:

Direct Evidence of Bound States: The complete suppression of optical coupling provides direct evidence for singlet trion formation in the FQH regime.
Identification of MFCS: The observation of symmetric depolarisation following $S=\nu^*$ provides strong evidence that the elementary excitations in fully polarised FQH states are Minimal Fractionally Charged Skyrmions. This challenges the description of excitations as independent single-particle CFs and highlights the importance of collective spin-reversal excitations.
Validation of CF Theory: The results support the Composite Fermion framework, particularly regarding $\Lambda$ L crossings and the transition between partially and fully polarised states, while extending the understanding of excitation hierarchies beyond the single-quasiparticle picture.

The authors remain modest regarding the range of validity, noting that the MFCS picture breaks down in the range $1 < \nu^* < 2$ (likely due to the influence of larger Skyrmions from the $\nu=1$ state and higher-order fractions like $\nu=4/11$ ) and that a detailed microscopic description of the multi-CF bound states remains beyond the scope of the current work.