Special CPM Seminar

Revisiting quantum Hall transport with graphene

Keyan Bennaceur

Commissariat à l'énergie atomique (CEA)
Saclay

Graphene offers a new set of parameters to revisit the quantum phase transition of localization in the Quantum Hall regime. In particular charge carriers are described with a massless Dirac equation which leads to considerably higher Landau level (LL) spacing than in conventional 2DEGs, allowing to probe hopping transport in a single LL and localization on a wider energy range compared to conventional 2DEGs. In addition, for large localization length, the Coulomb energy paid for electron hopping can be screened by a highly doped silicon backgate.

We investigated the localization by measuring the longitudinal resistivity as a function of temperature and bias current. On the minima which correspond to the Hall plateaus the resistivity follows a variable range hopping (VRH) law with coulomb interactions, the Efros-Shklovskii law (E-S) [1], where ρ_xx ∝ exp(-√(T₀/T)) . At high energy (typically for temperature above 100K) thermal activation to the next LL becomes possible, giving ρ_xx ∝ exp (-Δ/kT). VRH law was also observed in the evolution of ρ_xx with bias current where it acts as an effective temperature.

Extracting the T₀ from VRH allows to obtain the localization length and probe the universal scaling exponent given by the quantum percolation theory. We find the exponent to be 7/3, just like in conventional 2DEG.

Approaching the Hall plateau transition, when the localization length becomes larger than the interaction screening length set by the nearby gate, we were able to observe for the first time a cross-over from Efros-Shklovskii VRH conduction regime with Coulomb interactions to a Mott VRH regime without interactions [2]. Measurement of the scaling exponents of the conductance peak widths with both temperature and current bias give the first validation of the Polyakov-Shklovskii scenario [3] that VRH alone is sufficient to describe conductance in the Quantum Hall regime.

References:
[1] A.L Efros, B.I Shklovskii J. Phys. C, 8, 249 (1975).
[2] I. L. Aleiner and B. I. Shklovskii, Phys. Rev. B, 49, 13721 (1994).
[3] D. G. Polyakov and B. I. Shklovskii, Phys. Rev. Lett., 70, 3796 (1993).