Graphene Quantum Hall Effect Reveals up to Tenfold Variation in Localization Length, Challenging Universal Scaling

The quantum Hall effect, a phenomenon where electrons in strong magnetic fields exhibit quantized conductance, typically undergoes phase transitions governed by universal scaling laws, predicting how disorder affects electron localisation. However, recent experiments consistently reveal deviations from this expected behaviour, even in exceptionally clean materials. Aifei Zhang from Université Paris-Saclay, alongside Torsten Röper from Universität zu Köln and Manjari Garg from the Indian Institute of Technology Roorkee, and their colleagues, including Kenji Watanabe and Takashi Taniguchi from the National Institute for Materials Science, now systematically investigates this non-universality in broken-symmetry quantum Hall states of graphene. Their measurements demonstrate significant variations, up to tenfold differences, in the minimum localisation length, clearly indicating a breakdown of the expected universal scaling, and suggesting that the co-existence of localised states from successive energy levels plays a crucial role in determining electron behaviour.

Graphene Quantum Hall Localization and Disorder Effects

Scientists are investigating how electrons become localized within graphene quantum Hall systems, focusing on the influence of material imperfections and how this impacts electrical conductivity. They aim to understand the underlying reasons for localization, how it manifests in experiments, and why experimental results sometimes differ from theoretical predictions. A central goal is to refine existing theoretical models to better describe electron behavior in these unique materials. The research demonstrates that disorder, or imperfections in the graphene structure, plays a dominant role in trapping electrons and hindering their movement.

The degree of disorder directly affects how easily electrons can conduct electricity, with a clear relationship between the distance an electron can travel before becoming localized and the observed variable-range hopping. Importantly, experimental results deviate from predictions based on standard three-dimensional models, indicating that the localization mechanism in graphene is more complex than previously thought. The team emphasizes the importance of long-range disorder in determining how electrons become localized, noting that short-range imperfections alone cannot fully explain the experimental observations. They also propose that disorder affecting the different valleys within graphene’s electronic structure may contribute to the observed localization, working to reconcile experimental observations with theoretical models to develop a more comprehensive understanding of localization in graphene. This research contributes to a deeper understanding of the fundamental mechanisms of localization in graphene and other two-dimensional materials, with implications for materials science and potentially leading to the development of new materials and devices. Understanding localization is also crucial for developing quantum computing devices based on graphene, as localized states can be used to store and manipulate quantum information, challenging existing theoretical models and providing insights for developing more accurate descriptions of electron behavior.

Graphene Electron Localization via Corbino Geometry

Scientists have developed a method to systematically investigate the distance over which electrons remain localized in high-quality graphene, addressing discrepancies observed in previous quantum Hall effect experiments. The team used encapsulated graphene flakes, layering them between hexagonal boron nitride to create a highly controlled environment for electron transport, precisely tuning the number of electrons using a graphite gate to explore various quantum Hall states under fixed magnetic field and disorder conditions. To isolate electrical conductivity within the graphene itself, the team fabricated devices with a Corbino geometry, featuring a central contact and three edge contacts, carefully depositing an additional hexagonal boron nitride flake to electrically isolate the central contact. This configuration allowed for exclusive measurement of conductivity within the graphene, minimizing interference from the edges, with sensitive measurements performed at low frequencies using a specialized refrigerator. The resulting data revealed well-defined points of zero conductivity at specific electron densities, indicating robust quantum Hall states originating from energy gaps and symmetry-broken states. Researchers observed a non-monotonous temperature dependence of the conductivity, particularly at certain electron densities, exploiting this behavior to extract the localization length and determine how it varies with electron density and temperature, providing insights into the nature of electron localization and clarifying discrepancies observed in past experiments.

Graphene Quantum Hall States Defy Predictions

Scientists have meticulously investigated the quantum Hall effect in graphene, revealing significant deviations from previously established theoretical predictions regarding electron localization. The research team systematically measured the localization length in broken-symmetry quantum Hall states, discovering variations of up to tenfold in the minimum localization length depending on the size of the energy gap within these states, demonstrating clear departures from universal scaling behavior expected from existing theories. The experiments were conducted on monolayer graphene flakes encapsulated within hexagonal boron nitride, allowing precise control over the number of electrons using a graphite gate. Utilizing a Corbino geometry with a central contact and edge contacts, the team probed exclusively the electrical conductivity of the graphene, minimizing edge effects, with measurements of conductivity performed across a range of magnetic fields and temperatures, revealing clear points of zero conductivity at specific electron densities indicating well-defined quantum Hall states for both energy gaps and symmetry-broken states, with sharp transitions observed between these states. Detailed analysis of the temperature dependence of the quantum Hall plateaus revealed a non-monotonous behavior, particularly at certain electron densities. The team observed that increasing temperature leads to finite conductivity on the plateaus, indicating a weakening of the insulating behavior, explaining these findings with a model based on the co-existence of localized states from successive energy levels, offering a new understanding of discrepancies observed in previous experiments and providing a framework for interpreting the observed variations in localization length and scaling exponents, paving the way for improved theoretical models and potentially enabling the development of novel electronic devices.

Quantum Hall Localization Lengths Deviate From Theory

Researchers have significantly advanced understanding of electron localization within the quantum Hall effect, demonstrating that the distance over which electrons remain localized deviates from previously established theoretical predictions based on universal scaling principles. By systematically measuring localization lengths in specific quantum Hall states, the team observed variations of up to tenfold, indicating that the behavior of localized electrons is more complex than anticipated. These findings suggest that the co-existence of localized states from closely spaced energy levels within the quantum Hall system plays a crucial role in determining the overall localization length, challenging the assumption of strictly universal behavior and providing a more nuanced picture of electron behavior in these strongly correlated systems. While the research offers a compelling explanation for observed non-universality, the authors acknowledge that a complete understanding requires further investigation into the breakdown mechanisms at high energy levels.