Non-ohmic to ohmic crossover in the breakdown of the quantum Hall states in graphene under broadband excitations

TL;DR

This work investigates the breakdown of the quantum Hall effect in high-m mobility graphene under broadband excitations (DC to 10 GHz) using Corbino devices. Conductance is described by Efros–Shklovskii variable range hopping, enabling extraction of hopping energies $T_0$ and the effective electronic temperature $T_{eff}$ from both temperature and field-driven measurements. A central finding is a universal crossover from non-ohmic, field-driven VRH to ohmic, Joule-heating–dominated transport, with the crossover voltage $U_c$ scaling as $U_c \propto T_0^{3/2}$ and the breakdown energy following $U_{BD} \propto T_0^{3/2}$, controlled by the localization length $\xi$. Importantly, breakdown shows negligible intrinsic frequency dependence from DC up to $10$ GHz, indicating bulk localization physics, not dynamical drive effects, governs the dissipation in graphene’s QH regime. These results unify low- and high-frequency breakdown and have broad implications for dissipation in topological quantum materials under microwave excitation.

Abstract

Graphene, through the coexistence of large cyclotron gaps and small spin and valley gaps, offers the possibility to study the breakdown of the quantum Hall effect across a wide range of energy scales. In this work, we investigate the breakdown of the QHE in high-mobility graphene Corbino devices under broadband excitation ranging from DC up to 10 GHz. We find that the conductance is consistently described by variable range hopping (VRH) and extract the hopping energies from both temperature and field-driven measurements. Using VRH thermometry, we are able to distinguish between a cold and hot electron regime, which are dominated by non-ohmic VRH and Joule heating, respectively. Our results demonstrate that breakdown in the quantum Hall regime of graphene is governed by a crossover from non-ohmic, field-driven VRH to ohmic, Joule-heating-dominated transport.

Figures (13)

• Figure 1: Sample layout and experimental setup: Microscope image of the device. The top contact is connected to a graphite back gate (grey contrast). The graphene Corbino ring is sandwiched between hBN flakes (shown in green). The blue flake is an additional hBN flake, avoiding shorts between the graphene and the central ohmic contact (right). The left ohmic contacts are grounded, and two are connected to RF sources via bias-tees. The conductance is obtained by voltage-biasing the central contact.
• Figure 2: Comparison of breakdown mechanisms under DC/RF excitation and temperature. (a–c) Conductance vs. filling factor $\nu$ for increasing DC bias voltages (a), increasing microwave power at 6GHz (b), and increasing temperature (c). (d–f) Conductance vs. DC bias voltage $U_{\rm DC}$ (d), microwave amplitude $U_{\rm RF}$ (e), and temperature $T$ (f) for different filling factors. The black lines in f) correspond to a fit with Eq. \ref{['eg:VRH_temp']} with $T_0$ and $\sigma_0$ as fitting parameters (with an offset for not fully developed gaps).
• Figure 3: Heating analysis (a) Effective electronic temperature $T_{\rm eff}$, extracted from the measured conductance using the VRH fit of Fig. \ref{['fig:results']}f), as a function of DC bias $U_{\rm DC}$ for four representative gaps. One observes $T_{\rm eff} \propto U$ for $\nu=6.4,10.2$ and $T_{\rm eff} \propto U^{1/2}$ for $\nu=4.0,8.1$, as indicated by dashed lines of slope 1 and $1/2$. (b) Power-law exponent $\beta$ from $T_{\rm eff} \propto U^{\beta}$ fits, plotted versus the hopping energy $T_0$ at the same $\nu$. Grey and blue regions indicate the expected ranges for Joule-heating–dominated and non-ohmic transport, respectively. (c) Same as a) for various filling factors within the $\nu=6$ gap. (d) Bias-dependent exponent $\beta$ from sliding-window fits: each fit uses six adjacent data points, with the exponent $\beta$ plotted at the mean $U$ if the MSE is $\textless 10\%$.
• Figure 4: Transition from non-ohmic to ohmic: (a) $T_{\rm eff}$ estimated from the conductance $\sigma(T)$ and $T_{\rm e}$ estimated from the Joule heating model ($\alpha=3$ and $\Sigma=1.9e-11W\per K^4$) vs the bias voltage $U$. The curves correspond to a filling factor of $\nu=6.6$. (b) Crossover voltage $U_{\rm c}$ vs. hopping energy $T_0$ for $\nu=6$, estimated from where $\beta$ crosses 0.83 (blue) or where $T_{\rm e}=0.8\,T_{\rm eff}$ (red). $U_{\rm c}$ increases with $T_0$, indicating that stronger localization requires higher fields. The black line corresponds to the breakdown voltage $U_{\rm BD}$ (where $\sigma=\sigma_{max}/2$).
• Figure S1: VRH fit of voltage dependence: Conductance vs. DC bias voltage $U_{\rm DC}$ for different filling factors. The black lines correspond to fits with Eq. \ref{['eq:VRH_field']} with $\alpha$, $U_0$, and $\sigma_0$ as fitting parameters (with an offset for not fully developed gaps). The fit results are shown in Tab. \ref{['tab:voltage-vrh-fit']}. The fitted exponents confirm that $\nu=6.5,10.2$ are dominated by non-ohmic VRH, while $\nu=4.0,8.0$ are ohmic (Joule-heated).