Variable range hopping as the mechanism of the conductivity peak broadening in the quantum Hall regime

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.

Puddle-Induced Resistance Oscillations in the Breakdown of the Graphene Quantum Hall Effect

We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The ν=2 quantized plateau appears from fields B≃5  T and persists up to B≃80  T. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a 1/B periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus enlarging the quantum plateaus. These in-plane inhomogeneities, in the form of high carrier density graphene pockets, modulate the quantum Hall effect breakdown and decrease the breakdown current.

Quantum Hall resistance standards from graphene grown by chemical vapour deposition on silicon carbide

Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within 10⁻⁹ in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by Si sublimation, under higher magnetic fields. Here, we report on a graphene device grown by chemical vapour deposition on SiC, which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low dissipation, resulting from strongly localized bulk states at the magnetic length scale, over a wide magnetic field range. Our results show that graphene-based QHRS can replace their GaAs counterparts by operating in as-convenient cryomagnetic conditions, but over an extended magnetic field range. They rely on a promising hybrid and scalable growth method and a fabrication process achieving low-electron-density devices.

The quantum Hall effect in GaAs-based devices defines resistance standards accurate to within one part in 10⁻⁹ at magnetic fields close to 10 T. Here, Lafont et al. demonstrate such accuracies over an extended magnetic field range at 1.4 K in chemically vapour-deposited graphene on silicon carbide.

Non-universality of scaling exponents in quantum Hall transitions

We have investigated experimentally the scaling behaviour of quantum Hall transitions in GaAs/AlGaAs heterostructures of a range of mobility, carrier concentration, and spacer layer width. All three critical scaling exponents γ, κ and p were determined independently for each sample. We measure the localization length exponent to be γ ≈ 2.3, in good agreement with expected predictions from scaling theory, but κ and p are found to possess non-universal values. Results obtained for κ range from κ = 0.16 ± 0.02 to κ = 0.67 ± 0.02, and are found to be Landau level (LL) dependent, whereas p is found to decrease with increasing sample mobility. Our results demonstrate the existence of two transport regimes in the LL conductivity peak; universality is found within the quantum coherent transport regime present in the tails of the conductivity peak, but is absent within the classical transport regime found close to the critical point at the centre of the conductivity peak. We explain these results using a percolation model and show that the critical scaling exponent depends on certain important length scales that correspond to the microscopic description of electron transport in the bulk of a two-dimensional electron system.

Aryl functionalization as a route to band gap engineering in single layer graphene devices

Chemical functionalization is a promising route to band gap engineering of graphene. We chemically grafted nitrophenyl groups onto exfoliated single-layer graphene sheets in the form of substrate-supported or free-standing films. Our transport measurements demonstrate that nonsuspended functionalized graphene behaves as a granular metal, with variable range hopping transport and a mobility gap ∼0.1 eV at low temperature. For suspended graphene that allows functionalization on both surfaces, we demonstrate tuning of its electronic properties from a granular metal to a semiconductor in which transport occurs via thermal activation over a transport gap ∼80 meV from 4 to 300 K. This noninvasive and scalable functionalization technique paves the way for CMOS-compatible band gap engineering of graphene electronic devices.

Imaging transport resonances in the quantum Hall effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a dc bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than 4 orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.

Scaling and universality of integer quantum Hall plateau-to-plateau transitions

We have investigated the integer quantum Hall plateau-to-plateau transition in two-dimensional electrons confined to AlxGa(1-x)As-Al0.33Ga0.67As heterostructures over a broad range of Al concentration x. For x between 0.65% and 1.6%, where the dominant contribution to disorder is from the short-range alloy potential fluctuations, we observe a perfect power-law scaling in the temperature range from 30 mK to 1 K with a critical exponent kappa = 0.42 +/- 0.01.

Observation of microwave-induced zero-conductance state in Corbino rings of a two-dimensional electron system

Using Corbino samples we have observed oscillatory dc conductance in a high-mobility two-dimensional electron system when it is subjected to crossed microwave and magnetic fields. At the strongest of the oscillation minima the conductance is found to be vanishingly small, indicating a macroscopic insulating state associated with this minimum. With increasing voltage bias, a crossover from Ohmic to electron-heating regime is observed.

Diffusion thermopower of a two-dimensional hole gas in SiGe in a quantum Hall insulating state

Both the temperature dependence of resistivity and thermopower of a two-dimensional hole gas in SiGe show a reentrant metal-insulator transition at filling factor nu=1.5, but with strikingly different behavior of the two coefficients. As the temperature is decreased in the insulating state, the resistivity diverges exponentially while the thermopower decreases rapidly, suggesting that the insulating state is due to the presence of a mobility edge rather than a gap at the Fermi energy.

High frequency conductivity in the quantum hall regime

We have measured the complex conductivity sigma(xx) of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that sigma(xx) can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length xi. Even for large filling factor distances deltanu from the critical point we find xi approximately equals deltanu(-gamma) with a scaling exponent gamma = 2.3.