Graphene Quantum Hall States Exhibit Crossover to Ohmic Behaviour at 10GHz under Broadband Excitation

Graphene presents a unique opportunity to investigate the breakdown of the quantum Hall effect, due to the coexistence of large cyclotron gaps and smaller spin and valley gaps, allowing study across a broad range of energy scales. Torsten Röper, from the II. Physikalisches Institut, Universität zu Köln, alongside Aifei Zhang from Université Paris-Saclay, CEA, CNRS, SPEC, and Kenji Watanabe et al. from the National Institute for Materials Science, now demonstrate a crucial transition in how this breakdown occurs. The team investigates the quantum Hall effect in high-mobility graphene devices, using broadband excitations ranging from direct current up to 10 gigahertz, and finds that conductance consistently follows a pattern of variable range hopping. By carefully measuring hopping energies with both temperature and magnetic field, they distinguish between regimes where electrons remain cold and those where Joule heating dominates, revealing a crossover from non-ohmic, field-driven variable range hopping to ohmic, Joule-heating-dominated transport, fundamentally advancing understanding of breakdown in the quantum Hall regime.

This work explores this breakdown in high-mobility graphene Corbino devices, using broadband excitation ranging from DC up to 10GHz. Researchers aimed to understand how the quantum Hall effect responds to varying energy inputs, potentially revealing fundamental insights into electron behaviour within this material. The study utilizes Corbino devices, a specific geometry that enhances the observation of quantum Hall effects, and high-mobility graphene to ensure clear and measurable results.

Universal Variable Range Hopping Breakdown Observed

The research investigates the transition from non-ohmic, variable range hopping (VRH)-dominated conduction to ohmic, Joule heating-dominated conduction in a two-dimensional electron gas. The key finding is that the breakdown from VRH to ohmic conduction is governed by the hopping energy and is independent of carrier type and magnetic field. The effective electronic temperature scales with applied bias following a power law, and the exponent changes as the bias increases, indicating a transition in the dominant conduction mechanism. This crossover between VRH and ohmic conduction is explained by comparing the electrostatic potential energy with the electronic temperature.

Researchers observed that the exponent in the relationship between electronic temperature and applied bias indicates the conduction mechanism, with a value of approximately 1 signifying VRH and 0. 5 indicating Joule heating. A sliding window technique tracked the evolution of this exponent as a function of bias and hopping energy, revealing a systematic decrease with increasing bias. The crossover occurs when the electrostatic potential energy balances the electronic temperature, and the observed behaviour is mirrored in both electron- and hole-doped states, confirming that the VRH-based breakdown mechanism is universal and independent of carrier type.

Variable Range Hopping and Graphene Breakdown

Scientists investigated the breakdown of the quantum Hall effect in high-mobility graphene Corbino devices, probing electron behaviour under broadband excitation ranging from DC up to 10GHz. Experiments described the conductance using variable range hopping theory, allowing the team to extract hopping energies from both temperature and field-driven measurements. Through VRH thermometry, researchers distinguished between a cold electron regime, dominated by non-ohmic VRH, and a hot electron regime, governed by Joule heating, providing insight into the energy landscape of charge carriers. The data demonstrates a crossover from non-ohmic, field-driven VRH to ohmic, Joule-heating-dominated transport, revealing that the breakdown mechanism in graphene is not singular but dependent on the strength of electron localization. Researchers established an effective electronic temperature by analysing conductance calibration curves, observing its dependence on applied bias and systematically tracking the breakdown mechanism across varying localization strengths. Measurements across a broad range of filling factors enabled the team to resolve this crossover, previously overlooked in studies focused solely on large cyclotron gaps.

Graphene’s Quantum Hall Breakdown Explained by Localization

This research demonstrates a systematic understanding of how the quantum Hall effect breaks down in graphene, revealing a crossover from non-ohmic, field-driven variable range hopping to ohmic transport dominated by Joule heating. Through detailed measurements across a broad range of energies and magnetic fields, scientists established that this breakdown is governed by the material’s localization length, the distance over which electrons can travel before being scattered, and that larger cyclotron gaps, which exhibit smaller localization lengths, can withstand higher bias fields. The findings clarify the role of heating across various energy scales and provide a unified explanation for observed slope changes in previous studies. The team’s work confirms that the breakdown mechanism is intrinsic to the bulk material, rather than being driven by external factors or frequency-dependent effects, as demonstrated by the absence of measurable frequency dependence from DC to 10GHz. This understanding of dissipation in graphene establishes a foundation for further investigation of quantum materials under high-frequency excitation and offers a sensitive probe of bulk conduction and localization in topological systems.