Motivated by recent experiments and a theoretical analysis of the gap equation for the propagator of Dirac quasiparticles, we assume that the physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field is connected with the generation of both Dirac masses and spin gaps. The consequences of such a scenario for the existence of the gapless edge states with zigzag and armchair boundary conditions are discussed. In the case of graphene on a half-plane with a zigzag edge, there are gapless edge states in the spectrum only when the spin gap dominates over the mass gap. In the case of an armchair edge, however, the existence of the gapless edge states depends on the specific type of mass gaps.
General properties of long wavelength triangular graphene superlattice are studied. It is shown that Dirac points with and without gaps can arise at a number of high symmetry points of the Brillouin Zone. The existence of gaps can lead to insulating behavior at commensurate fillings. Strain and magnetic superlattices are also discussed.
We have investigated the magnetotransport properties of a single-layer graphene Hall bar with additional graphene side gates. The side gating in the absence of a magnetic field can be modeled by considering two parallel conducting channels within the Hall bar. This results in an average penetration depth of the side gate created field of approx. 90 nm. The side gates are also effective in the quantum Hall regime, and allow to modify the longitudinal and Hall resistances.
We determine the structure of band and gaps in graphene encapsulated in hexagonal boron nitride and subjected to magnetic field of Abrikosov lattice of vortices in the underlying superconducting film. The spectrum features one non-dispersive magnetic miniband at zero energy, separated by the largest gaps in the miniband spectrum from a pair of minibands resembling slightly broadened first Landau levels in graphene, suggesting the persistence of $ν= \pm 2$ quantum Hall effect states. Also, we identify occasional merging point of magnetic minibands which feature Dirac-type dispersion at the cons…
The Berry phase of π in graphene is derived in a pedagogical way. The ambiguity of how to calculate this value properly is clarified. Its connection with the unconventional quantum Hall effect in graphene is discussed.
We employ tip-enhanced infrared near-field microscopy to study the plasmonic properties of epitaxial quasi-free-standing monolayer graphene on silicon carbide. The near-field images reveal propagating graphene plasmons, as well as a strong plasmon reflection at gaps in the graphene layer, which appear at the steps between the SiC terraces. When the step height is around 1.5 nm, which is two orders of magnitude smaller than the plasmon wavelength, the reflection signal reaches 20% of its value at graphene edges, and it approaches 50% for step heights as small as 5 nm. This intriguing observatio…
We report observations of well developed half integer quantum Hall effect (QHE) on mono layer graphene films of 7 mm \times 7 mm in size. The graphene films are grown by chemical vapor deposition (CVD) on copper, then transferred to SiO_{2} /Si substrates, with typical carrier mobilities \approx 4000 cm^{2} /Vs. The large size graphene with excellent quality and electronic homogeneity demonstrated in this work is promising for graphene-based quantum Hall resistance standards, and can also facilitate a wide range of experiments on quantum Hall physics of graphene and practical applications expl…
We report on our accurate evaluation of spin polarizations of the ground state and particle-hole gaps for partially-filled lowest Landau level, observed in recent experiments on graphene subjected to ultra-high magnetic fields. We find that inter-electron interactions are important at these filling factors, characterized by the non-degenerate ground states and large particle-hole gaps at infinitely large wave vectors. The gaps are the largest for the quantum Hall states in the second Landau level. The weak appearance of quantum Hall plateaus in the experiments for certain filling factors in th…
We investigate the transport properties of high-quality single-layer graphene, epitaxially grown on a 6H-SiC(0001) substrate. We have measured transport properties, in particular charge carrier density, mobility, conductivity and magnetoconductance of large samples as well as submicrometer-sized Hall bars which are entirely lying on atomically flat substrate terraces. The results display high mobilities, independent of sample size and a Shubnikov-de Haas effect with a Landau level spectrum of single-layer graphene. When gated close to the Dirac point, the mobility increases substantially, and …
Quantum spin Hall effect was first predicted in graphene. However, the weak spin orbit interaction in graphene meant that the search for quantum spin Hall effect in graphene never fructified. In this work we show how to generate the quantum spin-valley Hall effect in graphene via quantum pumping by adiabatically modulating a magnetic impurity and an electrostatic potential in a monolayer of strained graphene. We see that not only exclusive spin polarized currents can be pumped in the two valleys in exactly opposite directions but one can have pure spin currents flowing in opposite directions i…
One of the most distinctive features of graphene is its huge inter-Landau-level splitting in experimentally attainable magnetic fields which results in the room-temperature quantum Hall effect. In this paper we calculate the longitudinal conductivity induced by two-phonon scattering in graphene in a quantizing magnetic field at elevated temperatures. It is concluded that the purely phonon-induced scattering, negligible for conventional semiconductor heterostructures under quantum Hall conditions, becomes comparable to the disorder-induced contribution to the dissipative conductivity of graphen…
We have measured the quantum Hall activation gaps in bilayer graphene at filling factors $ν=\pm4$ and $ν=\pm8$ in high magnetic fields up to 30 T. We find that energy levels can be described by a 4-band relativistic hyperbolic dispersion. The Landau level width is found to contain a field independent background due to an intrinsic level broadening and a component which increases linearly with magnetic field.
We demonstrate the anomalous Hall effect (AHE) in single-layer graphene exchange-coupled to an atomically flat yttrium iron garnet (YIG) ferromagnetic thin film. The anomalous Hall conductance has magnitude of ~0.09(2e2/h) at low temperatures and is measurable up to ~ 300 K. Our observations indicate not only proximity-induced ferromagnetism in graphene/YIG with large exchange interaction, but also enhanced spin-orbit coupling which is believed to be inherently weak in ideal graphene. The proximity-induced ferromagnetic order in graphene can lead to novel transport phenomena such as the quanti…
We present calculations of the quasiparticle energies and band gaps of graphene nanoribbons (GNRs) carried out using a first-principles many-electron Green's function approach within the GW approximation. Because of the quasi-one-dimension nature of a GNR, electron-electron interaction effects due to the enhanced screened Coulomb interaction and confinement geometry greatly influence the quasiparticle band gap. Compared with previous tight-binding and density functional theory studies, our calculated quasiparticle band gaps show significant self-energy corrections for both armchair and zigzag …
We calculate the electronic structure in quasiperiodic double-moiré systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number of minigaps, and they exhibit a recursive fractal structure similar to the Hofstadter butterfly when plotted against the twist angle. Each of the energy gaps can be characterized by a set of integers, which are associated with an area in the momentum space. The corresponding area is geometrically interpreted as a quasi Brillouin zone, which is a polygon enclos…
The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological protection of graphene edge channels is found regrettably less robust than in high mobility semi-conductors. Here, we explore graphene quantum Hall regime at the local scale, using a scanning gate microscope. We reveal the detrimental influence of antido…
Spin, anomalous, and valley Hall effects in graphene-based hybrid structures are studied theoretically within the Green function formalism and linear response theory. Two different types of hybrid systems are considered in detail: (i) graphene/boron nitride/cobalt(nickel), and (ii) graphene/YIG. The main interest is focused on the proximity-induced exchange interaction between graphene and magnetic substrate and on the proximity-enhanced spin-orbit coupling. The proximity effects are shown to have a significant influence on the electronic and spin transport properties of graphene. To find the …
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J=1 and J=2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including assessing the role of disorder in current exp…
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elu…
We have realized an integer quantum Hall system with superconducting contacts by connecting graphene to niobium electrodes. Below their upper critical field of 4 tesla, an integer quantum Hall effect coexists with superconductivity in the leads, but with a plateau conductance that is larger than in the normal state. We ascribe this enhanced quantum Hall plateau conductance to Andreev processes at the graphene-superconductor interface leading to the formation of so-called Andreev edge-states. The enhancement depends strongly on the filling-factor, and is less pronounced on the first plateau, du…
We obtain an analytical expression for the Hall conductivity in AAA-stacked trilayer graphene (TLG) within the linear response Kubo formalism. Interestingly, we find that the quantization of the Hall conductivity is severely dependent on the value of the chemical potential and the magnetic field. The origin of this unusual quantization, attributed to the Landau level spectrum of AAA-stacked TLG, is explained in detail. We show that is a characteristic of the multilayer graphene structures with AA stacking order.
Intrinsic spin Hall effect in the AA-stacked bilayer graphene is studied theoretically. The low-energy electronic spectrum for states in the vicinity of the Dirac points is obtained from the corresponding $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. The spin Hall conductivity in the linear response regime is determined within the Green function formalism. Conditions for the existence of spin Hall insulator phase are also analyzed, and it is shown that the spin Hall insulator phase can exist for a sufficiently large spin-orbit coupling, which opens a gap in the spectrum. The electric field perpendi…
The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is o…
Realization of the quantum-spin-Hall effect in graphene devices has remained an outstanding challenge dating back to the inception of the field of topological insulators. Graphene's exceptionally weak spin-orbit coupling -stemming from carbon's low mass- poses the primary obstacle. We experimentally and theoretically study artificially enhanced spin-orbit coupling in graphene via random decoration with dilute Bi2Te3 nanoparticles. Remarkably, multi-terminal resistance measurements suggest the presence of helical edge states characteristic of a quantum-spin-Hall phase; the magnetic-field and te…
We develop a theory of the valley Hall effect in high-quality graphene samples, in which strain fluctuation-induced random gauge potentials have been suggested as the dominant source of disorder. We find a near-quantized value of valley Hall conductivity in the band transport regime, which originates from an enhanced side jump of a Dirac electron when it scatters off the gauge potential. By assuming a small residue charge density our theory reproduces qualitatively the temperature- and gap-dependence of the observed valley Hall effect at the charge neutral point. Our study suggests that the va…
Quantum anomalous Hall state is expected to emerge in Dirac electron systems such as graphene under both sufficiently strong exchange and spin-orbit interactions. In pristine graphene, neither interaction exists; however, both interactions can be acquired by coupling graphene to a magnetic insulator (MI) as revealed by the anomalous Hall effect. Here, we show enhanced magnetic proximity coupling by sandwiching graphene between a ferrimagnetic insulator yttrium iron garnet (YIG) and hexagonal-boron nitride (h-BN) which also serves as a top gate dielectric. By sweeping the top-gate voltage, we o…
In this Letter, we put forward a resolution to the prolonged ambiguity in energy band gaps between theory and experiments of fabricated graphene nanoribbons (GNRs). Band structure calculations using density functional theory are performed on oxygen passivated GNRs supercells of customized edge configurations without disturbing the inherent sp2 hybridization of carbon atoms. Direct band gaps are observed for both zigzag and armchair GNRs, consistent with the experimental reports. In addition, band gap values of GNRs scattered about an average value curve for a given crystallographic orientation…
We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-Büttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by t…
By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall ferromagnetism (QHF) gaps and dynamically generated Dirac-like masses. The analysis is done for graphene ribbons with both zigzag and armchair edges. The characteristic features of the spectrum of the edge states in both these cases are described. In particular, the conditions for the existence of the gapless edge states are established. Implications of these results for…
The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain Hall conductance of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation value of the velocity operator, or classically, all carriers move in cycloids with the same average velocity. The magnitude of this velocity is just appropriate to generate the quantized Hall conductance which is in turn exactly independent of the external field. Electrical field changes each Landau level into a bundle of energies, whose overlap …
We have revealed from a numerical study that the optical Hall conductivity $σ_{xy}(ω)$ has a characteristic feature even in the ac ($\sim$ THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and in graphene in the quantum Hall (QHE) regime, although the plateau height is no longer quantized in ac. In graphene $σ_{xy}(ω)$ reflects the unusual Landau level structure. The effect remains unexpectedly robust against a significant strength of disorder, which we attribute to an effect of localization. We predict the ac quantum Hall measurements are fea…
Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity. In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to its values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in g…
We present electron transport measurements on lithographically defined and etched graphene nanoconstrictions with different aspect ratios including different lengths (L) and widths (W). A roughly length-independent disorder induced effective energy gap can be observed around the charge neutrality point. This energy gap scales inversely with the width even in regimes where the length of the constriction is smaller than its width (L<W). In very short constrictions, we observe both resonances due to localized states or charged islands and an elevated overall conductance level (0.1-1e2/h), which i…
When a graphene layer is stressed, the strain alters the phase an electron accumulates hopping between sites in a way that can be modeled as arising from a pseudo-magnetic vector potential. We examine the case of an oscillating graphene ribbon and explore a new effect - an oscillating resistance arising from an oscillating quantum Hall effect. This pseudo-magneto-resistance is large, and depends upon the frequency and the amplitude of the acoustic oscillations. We calculate the consequences for experiment.
We studied the magneto-transport in SiO2 substrate-supported monolayer graphene and the quantum phase transitions that characterize the quantum Hall regime, using magnetic fields up to 28T and temperatures down to 4K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals new non-universalities of the critical exponents of the plateau-insulator transition. These exponent depends on the type of disorder that governs the electrical transport, which knowledge is important for the design and fabrication of new graphene nano-devices.
Spin Hall effect due to random Rashba spin-orbit coupling in the two-dimensional honeycomb lattice of carbon atoms (graphene) is considered theoretically. Using the Green function method and diagrammatic technique we show that fluctuations of the Rashba interaction around zero average value give rise to nonzero spin Hall conductivity. Generally, the conductivity is not universal, but depends on the ratio of the total momentum and spin-flip relaxation rates.
Response of electronic systems in intense lights (AC electric fields) to DC source-drain fields is formulated with the Floquet method. We have then applied the formalism to graphene, for which we show that a non-linear effect of a circularly polarized light can open a gap in the Dirac cone, which leads to a photo-induced dc Hall current. This is numerically confirmed for a graphene ribbon attached to electrodes with the Keldysh Green's function.
The encapsulation of graphene in hexagonal boron nitride provides graphene on substrate with excellent material quality. Here, we present the fabrication and characterization of Hall sensor elements based on graphene boron nitride heterostructures, where we gain from high mobility and low charge charier density at room temperature. We show a detailed device characterization including Hall effect measurements under vacuum and ambient conditions. We achieve a current- and voltage-related sensitivity of up to 5700 V/AT and 3 V/VT, respectively, outpacing state-of- the-art silicon and III/V Hall s…
Observations of electron-hole asymmetry in transport through graphene devices at high magnetic field challenge prevalent models of the graphene quantum Hall effect. Here, we study this asymmetry both in conventional magnetotransport and in scanning gate microscopy maps measured in an encapsulated graphene constriction. We reveal that the presence of upstream modes and local doping in the vicinity of electrical contacts leads to a totally different picture of topological breakdown for electrons and holes, explaining the observed asymmetry.
Epitaxial graphene films were formed on the Si-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. A high-k gate stack on epitaxial graphene is realized by inserting a fully oxidized nanometer thin aluminum film as a seeding layer followed by an atomic-layer deposition process. The electrical properties of epitaxial graphene films are sustained after gate stack formation without significant degradation. At low temperatures, the quantum-Hall effect in Hall resistance is observed along with pronounced Shubnikov-de Hass oscillations in diagonal magneto-resistance …
A non-local Hall bar geometry is used to detect neutral-current Hall effects in graphene on silicon dioxide. Disorder is tuned by the addition of Au or Ir adatoms in ultra-high vacuum. A reproducible neutral-current Hall effect is found in both as-fabricated and adatom-decorated graphene. The Hall angle exhibits a complex but reproducible dependence on gate voltage and disorder, and notably breaks electron-hole symmetry. An exponential dependence on length between Hall and inverse-Hall probes indicates a neutral current relaxation length of approximately 300 nm. The short relaxation length and…
We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5 h/e^2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.
The development of functional composite nanomaterials based on graphene and metal nanoparticles (NPs) is currently the subject of intense research interest. In this study we report the preparation of novel type of graphene/Sn and graphene/SnOx (1 < x < 2) hybrid nanostructures and their investigation by scanning probe methods. First, we prepare Sn NPs by evaporating 7 - 8 nm tin on highly oriented pyrolytic graphite substrates. Graphene/Sn nanostructures are obtained by transferring graphene on top of the tin NPs immediately after evaporation. We show by scanning tunnelling microscopy (STM) an…
Recent reports of spin-orbit coupling enhancement in chemically modified graphene have opened doors to studies of the spin Hall effect with massless chiral fermions. Here, we theoretically investigate the interaction and impurity density dependence of the extrinsic spin Hall effect in spin-orbit coupled graphene. We present a nonperturbative quantum diagrammatic calculation of the spin Hall response function in the strong-coupling regime that incorporates skew scattering and anomalous impurity density-independent contributions on equal footing. The spin Hall conductivity dependence on Fermi en…
We have studied the electronic properties in aperiodic graphene superlattices of Thue-Morse sequence. Although the structure is aperiodic, an unusual Dirac point (DP) does exist and its location is exactly at the position of the zero-averaged wave number (zero-$\bar{k})$. Furthermore, the zero-$\bar{k}$ gap associated with the DP is robust against the lattice constants and the incident angles, and multi-DPs can appear under the suitable conditions. A resultant controllability of electron transport in Thue-Morse sequence is predicted, which may facilitate the development of many graphene-based …
By using four-terminal configurations, we investigated the dependence of longitudinal and diagonal resistances of a graphene p-n interface on the quantum-Hall edge-state equilibration position. The resistance of a p-n device in our four-terminal scheme is asymmetric with respect to the zero point where the filling factor ($ν$) of the entire graphene vanishes. This resistance asymmetry is caused by the chiral-direction-dependent change of the equilibration position and leads to a deeper insight into the equilibration process of the quantum-Hall edge states in a bipolar graphene system.
The microscopic approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness.
We have measured the quantum-Hall activation gaps in graphene at filling factors $ν=2$ and $ν=6$ for magnetic fields up to 32 T and temperatures from 4 K to 300 K. The $ν=6$ gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at $ν=2$ is strongly temperature and field dependent and approaches the expected value for sharp Landau levels for fields $B > 20$ T and temperatures $T > 100$ K. We explain this surprising behavior by a narrowing of the lowest Landau level.
We theoretically study the electronic band structure and the Hall effect in the negatively-curved three-dimensional (3D) graphene network in magnetic fields. We found that special energy regions appear above and below the zero-energy Landau level, where the 3D Hall conductivity is quantized even though the spectrum is not fully gapped. The energy regions are dominated by the chiral snake states traveling along the zero magnetic field contour on the 3D surface, and the quantization of the Hall conductivity crucially depends on the topology of the contour. The exclusive energy region for the chi…
Recent progress in preparing well controlled 2D van der Waals heterojunctions has opened up a new frontier in materials physics. In this paper we address the intriguing energy gaps that are sometimes observed when a graphene sheet is placed on a hexagonal boron nitride substrate, demonstrating that they are produced by an interesting interplay between structural and electronic properties, including electronic many-body exchange interactions. Our theory is able to explain the observed gap behavior by accounting first for the structural relaxation of graphene's carbon atoms when placed on a boro…
Much attention has been focused on ways of rendering graphene semiconducting. We study periodically gated graphene in a tight-binding model and find that, contrary to predictions based on the Dirac equation, it is possible to open a band gap at the Fermi level using electrostatic gating of graphene. However, comparing to other methods of periodically modulating graphene, namely perforated graphene structures, we find that the resulting band gap is significantly smaller. We discuss the intricate dependence of the band gap on the magnitude of the gate potential as well as the exact geometry of t…
Graphene is used as the thinnest possible spacer between gold nanoparticles and a gold substrate. This creates a robust, repeatable, and stable sub-nanometre gap for massive plasmonic field enhancements. White light spectroscopy of single 80 nm gold nanoparticles reveals plasmonic coupling between the particle and its image within the gold substrate. While for a single graphene layer, spectral doublets from coupled dimer modes are observed shifted into the near infra-red, these disappear for increasing numbers of layers. These doublets arise from plasmonic charge transfer, allowing the direct …
Precision quantum Hall resistance (QHR) measurements were performed on large-area epitaxial graphene device at low magnetic fields (B = 2 T - 8 T) at temperature T = 1.5 K. Hall resistance was measured using Cryogenic Current Comparator resistance bridge with high biasing current Isd = 40 micro ampere. The results showed that at B = 8 T the relative deviation of Hall resistance from the expected quantized value h/2e2 is within experimental uncertainty of 3.5 parts in 108 and remained below 0.35 parts per million (ppm) down to B = 3 T.
We demonstrate a device concept to fabricate resistance standards made of quantum Hall series arrays by using p-type and n-type graphene. The ambipolar nature of graphene allows fabricating series quantum Hall resistors without complex multi-layer metal interconnect technology, which is required when using conventional GaAs two-dimensional electron systems. As a prerequisite for a precise resistance standard we confirm the vanishing of longitudinal resistance across a p-n junction for metrological relevant current levels in the range of a few \muA.
We report on magnetotransport measurements of multi-terminal suspended graphene devices. Fully developed integer quantum Hall states appear in magnetic fields as low as 2 T. At higher fields the formation of longitudinal resistance minima and transverse resistance plateaus are seen corresponding to fractional quantum Hall states, most strongly for ν= 1/3. By measuring the temperature dependence of these resistance minima, the energy gap for the 1/3 fractional state in graphene is determined to be at ~20 K at 14 T.
We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\pm e/3$ at fractional fillings of $ν= \pm 1/3$. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against thermal excitation. The capability of localizing fractional quasiparticles on QH antidots brings promising opportunities for realizing anyon braiding and novel quantum electronics.
An approach to observe snake states in a graphene Hall bar containing a pn-junction is proposed. The magnetic field dependence of the bend resistance in a ballistic graphene Hall bar structure containing a tilted pn-junction oscillates as a function of applied magnetic field. We show that each oscillation is due to a specific snake state that moves along the pn-interface. Furthermore depending on the value of the magnetic field and applied potential we can control the lead in which the electrons will end up and hence control the response of the system.
