Quantum-Hall activation gaps in graphene

Phonon-mediated room-temperature quantum Hall transport in graphene

The quantum Hall (QH) effect in two-dimensional electron systems (2DESs) is conventionally observed at liquid-helium temperatures, where lattice vibrations are strongly suppressed and bulk carrier scattering is dominated by disorder. However, due to large Landau level (LL) separation (~2000 K at B = 30 T), graphene can support the QH effect up to room temperature (RT), concomitant with a non-negligible population of acoustic phonons with a wave-vector commensurate to the inverse electronic magnetic length. Here, we demonstrate that graphene encapsulated in hexagonal boron nitride (hBN) realizes a novel transport regime, where dissipation in the QH phase is governed predominantly by electron-phonon scattering. Investigating thermally-activated transport at filling factor 2 up to RT in an ensemble of back-gated devices, we show that the high B-field behaviour correlates with their zero B-field transport mobility. By this means, we extend the well-accepted notion of phonon-limited resistivity in ultra-clean graphene to a hitherto unexplored high-field realm.

Giant Magnetoresistance in a Chemical Vapor Deposition Graphene Constriction

Magnetic field-driven insulating states in graphene are associated with samples of very high quality. Here, this state is shown to exist in monolayer graphene grown by chemical vapor deposition (CVD) and wet transferred on Al₂O₃ without encapsulation with hexagonal boron nitride (h-BN) or other specialized fabrication techniques associated with superior devices. Two-terminal measurements are performed at low temperature using a GaAs-based multiplexer. During high-throughput testing, insulating properties are found in a 10 μm long graphene device which is 10 μm wide at one contact with an ≈440 nm wide constriction at the other. The low magnetic field mobility is ≈6000 cm² V^-1 s^-1. An energy gap induced by the magnetic field opens at charge neutrality, leading to diverging resistance and current switching on the order of 10⁴ with DC bias voltage at an approximate electric field strength of ≈0.04 V μm^-1 at high magnetic field. DC source-drain bias measurements show behavior associated with tunneling through a potential barrier and a transition between direct tunneling at low bias to Fowler-Nordheim tunneling at high bias from which the tunneling region is estimated to be on the order of ≈100 nm. Transport becomes activated with temperature from which the gap size is estimated to be 2.4 to 2.8 meV at B = 10 T. Results suggest that a local electronically high quality region exists within the constriction, which dominates transport at high B, causing the device to become insulating and act as a tunnel junction. The use of wet transfer fabrication techniques of CVD material without encapsulation with h-BN and the combination with multiplexing illustrates the convenience of these scalable and reasonably simple methods to find high quality devices for fundamental physics research and with functional properties.

Robust Quantum Oscillation of Dirac Fermions in a Single-Defect Resonant Transistor

The massless nature of Dirac Fermions produces large energy gaps between Landau levels (LLs), which is promising for topological devices. While the energy gap between the zeroth and first LLs reaches 36 meV in a magnetic field of 1 T in graphene, exploiting the quantum Hall effect at room temperature requires large magnetic fields (∼30 T) to overcome the energy level broadening induced by charge inhomogeneities in the device. Here, we report a way to use the robust quantum oscillations of Dirac Fermions in a single-defect resonant transistor, which is based on local tunneling through a thin (∼1.4 nm) hexagonal boron nitride (h-BN) between lattice-orientation-aligned graphene layers. A single point defect in the h-BN, selected by the orientation-tuned graphene layers, probes local LLs in its proximity, minimizing the energy broadening of the LLs by charge inhomogeneity at a moderate magnetic field and ambient conditions. Thus, the resonant tunneling between lattice-orientation-aligned graphene layers highlights the potential to spectroscopically locate the atomic defects in the h-BN, which contributes to the study on electrically tunable single photon source via defect states in h-BN.

Probing the low-temperature limit of the quantum anomalous Hall effect

Quantum anomalous Hall effect has been observed in magnetically doped topological insulators. However, full quantization, up until now, is limited within the sub-1 K temperature regime, although the material's magnetic ordering temperature can go beyond 100 K. Here, we study the temperature limiting factors of the effect in Cr-doped (BiSb)2Te3 systems using both transport and magneto-optical methods. By deliberate control of the thin-film thickness and doping profile, we revealed that the low occurring temperature of quantum anomalous Hall effect in current material system is a combined result of weak ferromagnetism and trivial band involvement. Our findings may provide important insights into the search for high-temperature quantum anomalous Hall insulator and other topologically related phenomena.

Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe_{2} Superconductor

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (NbSe_{2}) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

Epitaxial graphene for quantum resistance metrology

Graphene-based quantised Hall resistance standards promise high precision for the unit ohm under less exclusive measurement conditions, enabling the use of compact measurement systems. To meet the requirements of metrological applications, national metrology institutes developed large-area monolayer graphene growth methods for uniform material properties and optimized device fabrication techniques. Precision measurements of the quantized Hall resistance showing the advantage of graphene over GaAs-based resistance standards demonstrate the remarkable achievements realized by the research community. This work provides an overview over the state-of-the-art technologies in this field.

Electron-Hole Symmetry Breaking in Charge Transport in Nitrogen-Doped Graphene

Graphitic nitrogen-doped graphene is an excellent platform to study scattering processes of massless Dirac Fermions by charged impurities, in which high mobility can be preserved due to the absence of lattice defects through direct substitution of carbon atoms in the graphene lattice by nitrogen atoms. In this work, we report on electrical and magnetotransport measurements of high-quality graphitic nitrogen-doped graphene. We show that the substitutional nitrogen dopants in graphene introduce atomically sharp scatters for electrons but long-range Coulomb scatters for holes and, thus, graphitic nitrogen-doped graphene exhibits clear electron-hole asymmetry in transport properties. Dominant scattering processes of charge carriers in graphitic nitrogen-doped graphene are analyzed. It is shown that the electron-hole asymmetry originates from a distinct difference in intervalley scattering of electrons and holes. We have also carried out the magnetotransport measurements of graphitic nitrogen-doped graphene at different temperatures and the temperature dependences of intervalley scattering, intravalley scattering, and phase coherent scattering rates are extracted and discussed. Our results provide an evidence for the electron-hole asymmetry in the intervalley scattering induced by substitutional nitrogen dopants in graphene and shine a light on versatile and potential applications of graphitic nitrogen-doped graphene in electronic and valleytronic devices.

Unconventional Correlation between Quantum Hall Transport Quantization and Bulk State Filling in Gated Graphene Devices

We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in graphene and related topological states in other two-dimensional electron systems.

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.

Landau Levels of Majorana Fermions in a Spin Liquid

Majorana fermions, originally proposed as elementary particles acting as their own antiparticles, can be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here we propose a physical system which realizes Landau levels-highly degenerate single-particle states usually resulting from an orbital magnetic field acting on charged particles-for Majorana fermions. This is achieved in a variant of a quantum spin system due to Kitaev which is distorted by triaxial strain. This strained Kitaev model displays a spin-liquid phase with charge-neutral Majorana-fermion excitations whose spectrum corresponds to that of Landau levels, here arising from a tailored pseudomagnetic field. We show that measuring the dynamic spin susceptibility reveals the Landau-level structure by a remarkable mechanism of probe-induced bound-state formation.

Quantum resistance metrology using graphene

In this paper, we review the recent extraordinary progress in the development of a new quantum standard for resistance based on graphene. We discuss the unique properties of this material system relating to resistance metrology and discuss results of the recent highest-ever precision direct comparison of the Hall resistance between graphene and traditional GaAs. We mainly focus our review on graphene expitaxially grown on SiC, a system which so far resulted in the best results. We also briefly discuss progress in the two other graphene material systems, exfoliated graphene and chemical vapour deposition graphene, and make a critical comparison with SiC graphene. Finally, we discuss other possible applications of graphene in metrology.

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

We report the phase space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30 T. At 2 K, breakdown currents (I(c)) almost 2 orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state (ρ(xx)=0) shows a [1-(T/T(c))2] dependence and persists up to T(c)>45  K at 29 T. With magnetic field I(c) was found to increase ∝B(3/2) and T(c)∝B2. As the Fermi energy pproaches the Dirac point, the ν=2 quantized Hall plateau appears continuously from fields as low as 1 T up to at least 19 T due to a strong magnetic field dependence of the carrier density.

Influence of Landau level mixing on the properties of elementary excitations in graphene in strong magnetic field

Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the properties of magnetoexcitons and magnetoplasmons-elementary electron-hole excitations in graphene in quantizing magnetic field. We show that, at small enough background dielectric screening, the mixing leads to very essential change of magnetoexciton and magnetoplasmon dispersion laws in comparison with the lowest Landau level approximation.PACS: 73.22.Pr; 71.35.Ji; 73.43.Mp; 71.70.Gm.

Local compressibility measurements of correlated states in suspended bilayer graphene

Bilayer graphene has attracted considerable interest due to the important role played by many-body effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors ν= ± 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zero-field ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of broken-symmetry states at ν=0, ± 1, and ± 2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.

Density of states and zero Landau Level probed through capacitance of graphene

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels.

Metal to insulator transition on the N=0 Landau level in graphene

The magnetotransport in single layer graphene has been experimentally investigated in magnetic fields up to 18 T as a function of temperature. A pronounced T dependence is observed for T≲50  K, which is either metallic, or insulating, depending on the filling factor ν. The metal-insulator transition (MIT) occurs at |ν{c}|∼0.65 and in the regime of the dissipative transport, where the longitudinal resistance Rxx>1/2R{K}. The critical resistivity (Rxx per square) is ρ{xx}(ν{c})≈1/2R{K} and is correlated with the appearance of zero plateau in Hall conductivity σ{xy}(ν) and peaks in σ{xx}(ν). This leads us to construct a universal low-T (n, B) phase diagram of this quantum phase transition.

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.

Pseudomagnetic fields and ballistic transport in a suspended graphene sheet

We study a suspended graphene sheet subject to the electric field of a gate underneath. We compute the elastic deformation of the sheet and the corresponding effective gauge field, which modifies the electronic transport. In a clean system the two-terminal conductance of the sample is reduced below the ballistic limit and is almost totally suppressed at low carrier concentrations in samples under tension. Residual disorder restores a small finite conductivity.