Phase space for the breakdown of the quantum Hall effect in epitaxial graphene

Accurate graphene quantum Hall arrays for the new International System of Units

Graphene quantum Hall effect (QHE) resistance standards have the potential to provide superior realizations of three key units in the new International System of Units (SI): the ohm, the ampere, and the kilogram (Kibble Balance). However, these prospects require different resistance values than practically achievable in single graphene devices (~12.9 kΩ), and they need bias currents two orders of magnitude higher than typical breakdown currents I_C ~ 100 μA. Here we present experiments on quantization accuracy of a 236-element quantum Hall array (QHA), demonstrating R_K/236 ≈ 109 Ω with 0.2 part-per-billion (nΩ/Ω) accuracy with I_C ≥ 5 mA (~1 nΩ/Ω accuracy for I_C = 8.5 mA), using epitaxial graphene on silicon carbide (epigraphene). The array accuracy, comparable to the most precise universality tests of QHE, together with the scalability and reliability of this approach, pave the road for wider use of graphene in the new SI and beyond.

The 2019 redefinition of the International System of Units requires a 100 Ω quantum resistance standard for the ideal electrical realization of the kilogram via the Kibble Balance. Here, the authors report the realization of an array of 236 graphene quantum Hall bars, demonstrating a quantized resistance of 109 Ω with an accuracy of 0.2 nΩ/Ω over an extended range of bias currents.

Highly sensitive broadband binary photoresponse in gateless epitaxial graphene on 4H-SiC

Due to weak light-matter interaction, standard chemical vapor deposition (CVD)/exfoliated single-layer graphene-based photodetectors show low photoresponsivity (on the order of mA/W). However, epitaxial graphene (EG) offers a more viable approach for obtaining devices with good photoresponsivity. EG on 4H-SiC also hosts an interfacial buffer layer (IBL), which is the source of electron carriers applicable to quantum optoelectronic devices. We utilize these properties to demonstrate a gate-free, planar EG/4H-SiC-based device that enables us to observe the positive photoresponse for (405-532) nm and negative photoresponse for (632-980) nm laser excitation. The broadband binary photoresponse mainly originates from the energy band alignment of the IBL/EG interface and the highly sensitive work function of the EG. We find that the photoresponsivity of the device is > 10 A/W under 405 nm of power density 7.96 mW/cm² at 1 V applied bias, which is three orders of magnitude greater than the obtained values of CVD/exfoliated graphene and higher than the required value for practical applications. These results path the way for selective light-triggered logic devices based on EG and can open a new window for broadband photodetection.

Recent Studies on Dispersion of Graphene-Polymer Composites

Graphene is an excellent 2D material that has extraordinary properties such as high surface area, electron mobility, conductivity, and high light transmission. Polymer composites are used in many applications in place of polymers. In recent years, the development of stable graphene dispersions with high graphene concentrations has attracted great attention due to their applications in energy, bio-fields, and so forth. Thus, this review essentially discusses the preparation of stable graphene-polymer composites/dispersions. Discussion on existing methods of preparing graphene is included with their merits and demerits. Among existing methods, mechanical exfoliation is widely used for the preparation of stable graphene dispersion, the theoretical background of this method is discussed briefly. Solvents, surfactants, and polymers that are used for dispersing graphene and the factors to be considered while preparing stable graphene dispersions are discussed in detail. Further, the direct applications of stable graphene dispersions are discussed briefly. Finally, a summary and prospects for the development of stable graphene dispersions are proposed.

Epitaxial Graphene on 4H-SiC (0001) as a Versatile Platform for Materials Growth: Mini-Review

Material growth on a dangling-bond-free interface such as graphene is a challenging technological task, which usually requires additional surface pre-treatment steps (functionalization, seed layer formation) to provide enough reactive sites. Being one of the most promising and adaptable graphene-family materials, epitaxial graphene on SiC, due to its internal features (substrate-induced n-doping, compressive strain, terrace-stepped morphology, bilayer graphene nano-inclusions), may provide pre-conditions for the enhanced binding affinity of environmental species, precursor molecules, and metal atoms on the topmost graphene layer. It makes it possible to use untreated pristine epitaxial graphene as a versatile platform for the deposition of metals and insulators. This mini-review encompasses relevant aspects of magnetron sputtering and electrodeposition of selected metals (Au, Ag, Pb, Hg, Cu, Li) and atomic layer deposition of insulating Al2O3 layers on epitaxial graphene on 4H-SiC, focusing on understanding growth mechanisms. Special deliberation has been given to the effect of the deposited materials on the epitaxial graphene quality. The generalization of the experimental and theoretical results presented here is hopefully an important step towards new electronic devices (chemiresistors, Schottky diodes, field-effect transistors) for environmental sensing, nano-plasmonics, and biomedical applications.

Landau Velocity for Collective Quantum Hall Breakdown in Bilayer Graphene

Breakdown of the quantum Hall effect (QHE) is commonly associated with an electric field approaching the inter-Landau-level (LL) Zener field, the ratio of the Landau gap and the cyclotron radius. Eluded in semiconducting heterostructures, in spite of extensive investigation, the intrinsic Zener limit is reported here using high-mobility bilayer graphene and high-frequency current noise. We show that collective excitations arising from electron-electron interactions are essential. Beyond a noiseless ballistic QHE regime a large super-Poissonian shot noise signals the breakdown via inter-LL scattering. The breakdown is ultimately limited by collective excitations in a regime where phonon and impurity scattering are quenched. The breakdown mechanism can be described by a Landau critical velocity as it bears strong similarities with the roton mechanism of superfluids. In addition, we show that breakdown is a precursor of an electric-field induced QHE-metal transition.

Gyrotropic Zener tunneling and nonlinear IV curves in the zero-energy Landau level of graphene in a strong magnetic field

We have investigated tunneling current through a suspended graphene Corbino disk in high magnetic fields at the Dirac point, i.e. at filling factor ν = 0. At the onset of the dielectric breakdown the current through the disk grows exponentially before ohmic behaviour, but in a manner distinct from thermal activation. We find that Zener tunneling between Landau sublevels dominates, facilitated by tilting of the source-drain bias potential. According to our analytic modelling, the Zener tunneling is strongly affected by the gyrotropic force (Lorentz force) due to the high magnetic field.

Asymmetric Electron-Hole Decoherence in Ion-Gated Epitaxial Graphene

We report on asymmetric electron-hole decoherence in epitaxial graphene gated by an ionic liquid. The observed negative magnetoresistance near zero magnetic field for different gate voltages, analyzed in the framework of weak localization, gives rise to distinct electron-hole decoherence. The hole decoherence rate increases prominently with decreasing negative gate voltage while the electron decoherence rate does not exhibit any substantial gate dependence. Quantitatively, the hole decoherence rate is as large as the electron decoherence rate by a factor of two. We discuss possible microscopic origins including spin-exchange scattering consistent with our experimental observations.

Quantum Hall effect in epitaxial graphene with permanent magnets

We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.

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.

Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube

We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.

Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene

Epitaxial graphene has proven itself to be the best candidate for quantum electrical resistance standards due to its wide quantum Hall plateaus with exceptionally high breakdown currents. However one key underlying mechanism, a magnetic field dependent charge transfer process, is yet to be fully understood. Here we report measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to an almost linear increase in carrier density with magnetic field. This behaviour is strong evidence for field dependent charge transfer from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels we model the densities of donor states and predict the field dependence of charge transfer in excellent agreement with experimental results, thus providing a guide towards engineering epitaxial graphene for applications such as quantum metrology.

Insulator-quantum Hall transitionin monolayer epitaxial graphene

We report on magneto-transport measurements on low-density, large-area monolayer epitaxial graphene devices grown on SiC. We observe temperature (T)-independent crossing points in the longitudinal resistivity ρxx, which are signatures of the insulator-quantum Hall (I-QH) transition, in all three devices. Upon converting the raw data into longitudinal and Hall conductivities σxx and σxy, in the most disordered device, we observed T-driven flow diagram approximated by the semi-circle law as well as the T-independent point in σxy near e2/h. We discuss our experimental results in the context of the evolution of the zero-energy Landau level at low magnetic fields B. We also compare the observed strongly insulating behaviour with metallic behaviour and the absence of the I-QH transition in graphene on SiO2 prepared by mechanical exfoliation.

Rapid epitaxy-free graphene synthesis on silicidated polycrystalline platinum

Large-area synthesis of high-quality graphene by chemical vapour deposition on metallic substrates requires polishing or substrate grain enlargement followed by a lengthy growth period. Here we demonstrate a novel substrate processing method for facile synthesis of mm-sized, single-crystal graphene by coating polycrystalline platinum foils with a silicon-containing film. The film reacts with platinum on heating, resulting in the formation of a liquid platinum silicide layer that screens the platinum lattice and fills topographic defects. This reduces the dependence on the surface properties of the catalytic substrate, improving the crystallinity, uniformity and size of graphene domains. At elevated temperatures growth rates of more than an order of magnitude higher (120 μm min(-1)) than typically reported are achieved, allowing savings in costs for consumable materials, energy and time. This generic technique paves the way for using a whole new range of eutectic substrates for the large-area synthesis of 2D materials.

Hot carrier relaxation of Dirac fermions in bilayer epitaxial graphene

Energy relaxation of hot Dirac fermions in bilayer epitaxial graphene is experimentally investigated by magnetotransport measurements on Shubnikov-de Haas oscillations and weak localization. The hot-electron energy loss rate is found to follow the predicted Bloch-Grüneisen power-law behaviour of T(4) at carrier temperatures from 1.4 K up to ∼100 K, due to electron-acoustic phonon interactions with a deformation potential coupling constant of 22 eV. A carrier density dependence n(e)(-1.5) in the scaling of the T(4) power law is observed in bilayer graphene, in contrast to the n(e)(-0.5) dependence in monolayer graphene, leading to a crossover in the energy loss rate as a function of carrier density between these two systems. The electron-phonon relaxation time in bilayer graphene is also shown to be strongly carrier density dependent, while it remains constant for a wide range of carrier densities in monolayer graphene. Our results and comparisons between the bilayer and monolayer exhibit a more comprehensive picture of hot carrier dynamics in graphene systems.

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.