Half-quantized Hall Plateaus in the Confined Geometry of Graphene

arXiv:2410.03896 · cond-mat.mes-hall · Submitted 2024-10-04 · Read on arXiv

Listen

Radio episode about this paper

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Half-quantized Hall Plateaus in the Confined Geometry of Graphene".

Mira: The gist: This work reports that half-quantized quantum Hall plateaus can appear in more than one unexpected way in monolayer graphene due to charge equilibration in a confined geometry,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: We're talking about "Half-quantized Hall Plateaus in the Confined Geometry of Graphene" today, and the folks doing this are Pandey, Manna, Frei, Saji, Denis, Savin, Watanabe, Taniguchi, Das and Kumar.

Mira: They’re diving into how confinement geometry causes these half-quantized plateaus at νH = five/two in graphene by focusing on charge equilibration inside that small region <ref:2410.03896#pg1>

Lev: From an error correction standpoint, the main thing here is seeing if these plateaus are stable enough to support any kind of fault-tolerant quantum computation based on non-Abelian statistics.

Kai: The paper explores this because even-denominator FQH states, like the one at ν = five/two are much more complicated than the odd ones we usually study, and they’re associated with paired composite fermions carrying non-Abelian quantum statistics sixteen <ref:2410.03896#pg2>

Mira: That’s right. The physics for those even-denominator states is just more involved to model because the standard Laughlin wavefunctions don't apply as well, which is why this paper focuses on graphene instead of conventional two-DEGs <ref:2410.03896#pg1>

Lev: So what does that mean for us in terms of hardware? It suggests we need material platforms that can host these complex states, and graphene’s single-atom thickness makes it a very interesting candidate fourteen <ref:2410.03896#pg2>

Kai: Precisely. Graphene is single-atom thick, which leads to strong quantum corrections in its conductivity, and the paper notes that monolayer graphene displayed half-quantization at higher Landau levels with two hundred twenty-one parton states as their origin <ref:2410.03896#pg1>

Mira: And they introduce the concept of edge equilibration as a way to explain these anomalous behaviors where chiral edge states get interwoven and start exchanging heat and charge via local tunneling

thirty thirty-five–thirty-seven: <ref:2410.03896#pg3>

Lev: So if we were designing an experiment, we’d need to carefully control those interactions because the whole mechanism seems dependent on that specific confined geometry.

The paper's summary: Kai: Now let's look at what they actually observed in "Half-quantized Hall Plateaus in the Confined Geometry of Graphene." They summarize how they saw these half-quantized plateaus at νH = five/two through measurements on a graphene Hall bar sample <ref:2410.03896#pg1>

Mira: They report observing conductance quantization steps at 14e2/h, 16e2/h, and 24e2/h when modulating the back gate while keeping the top gate fixed at the Dirac point <ref:2410.03896#pg1>

Lev: So what’s the big takeaway from that specific experimental setup? Is this just noise or is it a real physical effect?

Kai: It's a real physical effect, because they found that the dominant fractional quantization observed in Rxy and Rxx measurements at B = -twelve point five T and T = twenty mK was at νH = two + one/two

Mira: They then break down the mechanism for these half-quantized plateaus into two regimes: "Ordinary" transport across FQH fluid sections with different filling factors, and "Out-of-Ordinary" transport across an FQH fluid point contact bridging Fermi-liquid reservoirs.

Lev: Breaking it down like that helps us connect the abstract theory to what we can actually see in a lab, doesn't it?

Kai: It does. They then give us formulas for the Hall resistance, showing how RH is related to filling factors like RH = νbg2/2νQPC in Region I <ref:2410.03896#pg1>

Mira: And they also have a more complex formula for the "Out-of-Ordinary" regions, which involves terms like νtg, νQPC, and νbg, depending on whether you're in Region II or III

thirty thirty-five–thirty-seven: <ref:2410.03896#pg3>

Lev: Those formulas look intense; I wonder if those are easily accessible to experimentalists when they’re trying to tune the gates in real time.

Kai: They are quite complex, but the point is that these different regimes have different stabilization rules because of the nonequilibrium inter-edge interactions and tunneling happening in that confined geometry

thirty thirty-five–thirty-seven: <ref:2410.03896#pg3>

The paper's improvements: Mira: The paper suggests a few ways to improve the understanding of these plateaus. They introduce two thermodynamic quantities, chemical potential and temperature, to define local steady states independent of each other twenty-nine thirty-eight <ref:2410.03896#pg3>

Lev: So if we are looking at this from a hardware perspective, how does that help us predict transitions between states?

Kai: The AI could potentially perform predictive modeling of plateau stability by integrating charge and heat equilibration dynamics. It can predict transitions from a plateau like "two + two/five" to "three" based on temperature changes, as shown in the stabilization of the plateau νH = five/two requires full equilibration of the state νbg = two + two/five and νQPC = two + one/three in the "Ordinary" case <ref:2410.03896#pg1>

Mira: That’s a specific prediction that’s really useful for experimentalists trying to map out the phase diagram. It tells them exactly what conditions they need to stabilize the state

thirty thirty-five–thirty-seven: <ref:2410.03896#pg3>

Lev: And we could also use AI to simulate experimental outcomes using a comprehensive hydrodynamic model for edge states, calculating the resulting Hall resistance based on those derived equations for all four regions.

Kai: That would let us test different geometric configurations virtually before spending time and resources fabricating new samples.

Mira: They also suggest that analyzing thermal transport data could help diagnose the nature of these states by modeling how temperature dependence affects the plateau, which is seen in Fig. 4d

thirty thirty-five–thirty-seven: <ref:2410.03896#pg3>

Lev: That would be a way to distinguish between "Ordinary" and "Out-of-Ordinary" cases based on how the thermal data behaves under varying conditions.

Kai: And they also propose that AI could optimize device parameters for generating specific topological states, suggesting tuning the top gate filling from νtg = -three to νtg = -two further facilitates the stabilization of νH = -five/two.

Conclusion: Kai: So to wrap up on "Half-quantized Hall Plateaus in the Confined Geometry of Graphene," these plateaus at νH = five/two are observed across more than one combination of top and back gate electrostatic potentials <ref:2410.03896#pg1>

Mira: The core mechanism remains charge equilibration between parent states, whether it’s "Ordinary" tunneling or that "Out-of-Ordinary" contact with Fermi liquid reservoirs.

Lev: So the big implication for error correction is that if we can tune the charge of these states, it opens up possibilities for anyon collider experiments utilizing QPCs to generate diluted beams eight <ref:2410.03896#pg1>

Kai: That’s right. We're looking at how voltage drops occur due to carriers hitting metallic contacts or other charge carriers with different electrochemical potentials, which creates hot spots in the sample

Mira: So, ultimately, the work suggests that while charge equilibration allows for these exotic states, it also destroys the coherence of the system

thirty thirty-five–thirty-seven: <ref:2410.03896#pg3>

Lev: I think we need to keep looking at this paper because understanding confined geometry is key to figuring out how to build those topological qubits.

Kai: Agreed. It’s a lot of physics happening in a very small area that needs careful attention. We'll keep building on this work next time.

Department of Applied Physics, School of Science, Aalto University · QTF Centre of Excellence, Department of Applied Physics, Aalto University · Department of Condensed Matter Physics, Weizmann Institute of Science · Laboratoire de Physique de l’Ecole normale sup´erieure, ENS, Universit´e PSL · National Institute for Materials Science · Department of Physics, Indian Institute of Science Education and Research (IISER)

cond-mat.mes-hall

Submitted: 2024-10-04

Updated: 2024-10-04

Comments: 30 pages, 18 figures, and 2 tables

Journal ref: Commun Mater 7, 256 (2026)

DOI: 10.1038/s43246-026-01209-7

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 86/100

The gist: The gist: This work reports that half-quantized quantum Hall plateaus can appear in more than one unexpected way in monolayer graphene due to charge equilibration in a confined geometry, specifically

Key concepts

Anyons
Exotic quasiparticles that possess fractional electric charge and exchange statistics quantified by a statistical phase. They are crucial for understanding the physics of even-denominator fractional quantum Hall states, which are more complex than odd-denominator ones.
Charge Equilibration
The process where charge and heat are exchanged between interwoven chiral edge states via local tunneling in confined geometries. This equilibration is the key mechanism identified that stabilizes the half-quantized plateaus at $\nu_H = 5/2$ in graphene.
Half-Quantized Plateaus
Specific conductance quantization steps observed at filling factors like $\nu_H = 5/2$. These are not standard integer or simple fractional states but arise from the interplay between bulk edge states and localized states within a Quantum Point Contact (QPC) in the confined structure.
Quantum Hall Effect (QHE)
A phenomenon where the Hall resistance exhibits precise quantization steps at low temperatures and high magnetic fields. In graphene, this effect is studied under confinement to reveal unconventional transport properties and exotic fractional states.

Terminology

Summary

The gist: This work reports that half-quantized quantum Hall plateaus can appear in more than one unexpected way in monolayer graphene due to charge equilibration in a confined geometry, specifically observing fractional states with conductance quantization at νH = 5/2

Introduction and Context

Anyons are exotic quasiparticles exhibiting fractional electric charge and exchange statistics quantified by a statistical phase θ arising upon particle exchange The physics for even-denominator FQH states is more involved compared to odd-denominator states, which are well-understood in terms of Laughlin wavefunctions The first observation of such a state, having a filling fraction of ν = 5/2, is widely accepted to carry paired composite fermions carrying non-Abelian quantum statistics in its ground state Graphene is an interesting material for studying these exotic FQH states due to its single-atom-thick nature, leading it to host unconventional FQH states and strong quantum corrections in conductivity Monolayer graphene displayed half-quantization at higher Landau levels, supporting 221 parton states for their origin The concept of edge equilibration was introduced to explain anomalous behaviors, where chiral edge states become interwoven and exchange heat and charge via local tunneling This charge equilibration can lead to new and peculiar behaviors, producing unexpected plateaus

Observation in Graphene Hall Bar

The researchers fabricated graphene Hall bar samples with six ohmic contacts on hexagonal boron nitride encapsulated heterostructures with graphite back gates Conductance quantization steps at 14e2/h, 16e2/h, and 24e2/h were seen at zero magnetic fields when the back gate was modulated while keeping the top gate at the Dirac point The dominant fractional quantization observed in Rxy and Rxx measurements at B = −12.5 T and T = 20 mK was at νH = 2 + 1/2

Mechanisms for Half-Quantization

The half-quantized plateaus at νH = 5/2 were observed in two distinct regimes: a) transport across FQH fluid sections with different filling factors (“Ordinary”), and b) transport across an FQH fluid point contact bridging between two special Fermi-liquid-like reservoirs facilitated by graphene’s 0th Landau level (“Out-ofOrdinary”) Generic to both cases, the different quantum Hall plateaus are stabilized due to nonequilibrium inter-edge interactions and tunnelling in the confined geometry of the QPC The plateaus appear for reasons specific to these regimes that will be described in detail in this article

Theoretical Explanation via Charge Equilibration

The four regions exhibiting half-quantization at νH = 5/2 can be quantified by the interplay among νtg, νQPC and νbg In Region I (“Ordinary”), the Hall resistance is found as RH = νbg2/2νQPC In Region IV (“Ordinary”), the formula for RH is given by RH = 2νbgνtg + νbgνQPC − νtgνQPC / (nu bg(2 + 3nu bgnu tg) − (nu bg + nu tg)nu QPC) In “Out-of-Ordinary” regions II and III, the formula for RH is given by RH = 2νtg/3νbg(νtg − νQPC)(νtg(νbg + 3nu tg) − (nu bg + nu tgnu QPC))

Stability and Temperature Dependence

In the “Ordinary” Case, reducing the magnetic field induces a transition from νH = 5/2 to νH = 2 + 2/3, requiring specific filling fractions like νbg, νQPC = 2 + 1/3 The stabilization of the state requires full charge equilibration between the bulk edge states νbg and localized states νQPC In the “Out-of-Ordinary” Case, as magnetic field strength decreases, edge states beneath the top split gates extend more toward the bulk states, facilitating improved equilibration and producing a more robust plateau at νH = 5/2

Outlook

The work suggests that charge equilibration between parent states leads to the half-quantized plateaus This raises an important question about the role of equilibration in quantum Hall measurements, specifically in confined geometries The study directs us toward a more careful evaluation and understanding of confined geometry Being able to tune the charge of states due to the different QPC filling opens up possibilities for anyon collider experiments utilizing QPCs to generate diluted beams The cross-correlation between two such beams can probe the details of the quantum statistics of these particles, bringing us one step closer to building topological qubits using fractional quantum Hall states

Methods Summary

The sample fabrication involved a standard dry transfer technique using hexagonal boron nitride encapsulated graphene heterostructures with graphite back gates The top split gates defining the QPC were fabricated by 100 keV e-beam lithography, which may cause lattice defects under the gate, resulting in strong equilibration in the confined region of QPC Measurements were performed at a base temperature of 18 mK using lock-in techniques with a current of 1 nA The Hall resistance νH is defined by RH = h/(νHe2) = Rxy

Discussion Summary

The resulting mechanism leading to the curious observation of the conductance plateau at νH = 5/2 can be classified into two cases: i) “Ordinary” tunneling between the FQH fluid with different filling factors, and ii) “Out-of-Ordinary” FQH fluid in contact with Fermi-liquid-like reservoirs Charge equilibration between parent states leads to the half-quantized plateaus The authors note that while charge equilibration allows for these exotic states, it also destroys the coherence of the system Thermal quantum Hall transport can be considered as an alternative for probing designer states since the thermal equilibration length is one order of magnitude larger than the charge equilibration length The presence of localized states within the QPC region results in a modification of the Hall filling factors νH

Conclusion

In this work, half-quantized fractional quantum Hall plateaus in the confined geometry of monolayer graphene were observed, appearing for more than one combination of top and back gate electrostatic potentials The resulting mechanism leading to the curious observation of the conductance plateau at νH = 5/2 can be classified into two cases: i) “Ordinary” tunneling between the FQH fluid with different filling factors, and ii) “Out-of-Ordinary” FQH fluid in contact with Fermi-liquid-like reservoirs For both cases, charge equilibration between parent states leads to the half-quantized plateaus These can be considered as “designer” states with tunable charge The exact nature of the unconventional 5/2 plateau is yet to be understood The authors anticipate that elevating the temperature will enhance equilibration processes, causing the filling fraction in the narrow QPC region, νQPC, to converge towards the back gate filling fraction νbg The study concludes by proposing that voltage drops occur due to carriers encountering metallic contacts or other charge carriers with different electrochemical potentials, giving rise to hot spots in the sample

References

  1. Tsui, D. C., Stormer, H. L. & Gossard, A. C., Two-Dimensional Magnetotransport in the Extreme Quantum Limit

  2. Laughlin, R. B., Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations

  3. Leinaas, J. M. & Myrheim, J., On the theory of identical particles

  4. Wilczek, F., Quantum Mechanics of Fractional-Spin Particles

  5. Wilczek, F., Magnetic Flux, Angular Momentum, and Statistics

  6. de-Picciotto, R. et al., Direct observation of a fractional charge

  7. Saminadayar, L., Glattli, D. C., Jin, Y. & Etienne, B., Observation of the e/3 Fractionally Charged Laughlin Quasiparticle

  8. Rosenow, B., Levkivskyi, I. P. & Halperin, B. I., Current Correlations from a Mesoscopic Anyon Collider

  9. Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J., Direct observation of anyonic braiding statistics

  10. Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J.

Improvements for AI systems

  1. Improved AI can perform predictive modeling of half-quantized plateau stability by integrating charge and heat equilibration dynamics. The system can predict transitions from a plateau like 2 + 2/5 to "3 based on temperature changes, as shown in The stabilization of the plateau νH = 5/2 requires full equilibration of the state νbg = 2 + 2/5 and νQPC = 2 + 1/3 (“Ordinary”)."

  2. Improved AI can simulate experimental outcomes using a comprehensive hydrodynamic model for edge states. The system can calculate the resulting Hall resistance based on the derived equations, such as RH = νQPC νbg2 / (h e2), for different geometric configurations (Region I, II, III, IV).

  3. Improved AI can diagnose the nature of quantum Hall states by analyzing thermal transport data. The system can distinguish between Ordinary and Out-of-Ordinary cases by modeling the temperature dependence of the plateau, as seen in the transition to νH = 5/2 is seen in Fig. 4d.

  4. Improved AI can optimize device parameters for generating specific topological states. The system can suggest optimal combinations of top and back gate potentials, such as tuning the top gate filling from νtg = −3 to νtg = −2 further facilitates the stabilization of νH = −5/2.

  5. Improved AI can predict the effect of disorder on quasiparticle gap energies. The system can estimate the intrinsic gap energy by fitting Arrhenius transport data, quantifying the disorder broadening potential parameter Γ: ∆ = ∆i - Γ.

Sources

Related papers