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 experimental results. Special attention is given to the interesting low magnetic field limit and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.
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.
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 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 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 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…
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 …
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…
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…
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…
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.
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…
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.
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…
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.
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas provide key access to the excitations of the bulk. Here we demonstrate controlled transmission of edge states in bilayer graphene. Controlled by an independent gate, the backscattering rate of the edge modes is continuously tuned from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more…
We determine conditions for the formation of compressible stripes near the quantum Hall effect (QHE) edges of top-gated epitaxial graphene on Si-terminated SiC (G/SiC) and compare those to graphene exfoliated onto insulating substrate in the field-effect-transistor (GraFET) geometry. For G/SiC, a large density of localised surface states on SiC just underneath graphene layer and charge transfer between them lead both to doping of graphene and to screening of potential profile near its edge. This suppresses formation of compressible stripes near QHE edges in graphene, making them much narrower …
We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that form in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that form between Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.
Strong Goos-Hänchen (GH) effect at a prism-graphene interface in the quantum Hall effect (QHE) condition is reported. Based on the full quantum description of the temperature-dependent surface conductivity of graphene present in the unconventional quantum Hall regime, magnetically strong tunable QHE GH shifts emerge. Our approach is based on deriving the generalized Fresnel coefficients with antisymmetric conductivity tensor for the Kerr phase of the incident linearly polarized light. Moreover, it is demonstrated that at low temperatures, GH shifts map plateaus as the intensity of the magnetic…
We apply Laughlin's gauge argument to analyze the $ν=0$ quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying $ν=0$ quantized Hall effect. We argue that this $ν=0$ graphene quantum Hall state is qualitati…
Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arc length of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short-circuit the bulk current paths and inhibit the observation of the quantized two-terminal resistance. Unlike competing theoretical proposals, this mechanism of disrupting the Hall quantization in suspended graphene is not caused by ill-chosen placement of the contacts, singular elastic strains, or a…
We report on a theoretical study of one-dimensional (1D) states localized at few-layer graphene system ribbon edges, and at interfaces between few-layer graphene systems with different valley Hall conductivities. These 1D states are topologically protected when valley mixing is neglected. We address the influence on their properties of stacking arrangement, interface structure, and external electric field perpendicular to the layers. We find that 1D states are generally absent at multilayer ribbon armchair direction edges, but present irrespective of crystallographic orientation at any interna…
The weak spin-orbit interaction in graphene was predicted to be increased, e.g., by hydrogenation. This should result in a sizable spin Hall effect (SHE). We employ two different methods to examine the spin Hall effect in weakly hydrogenated graphene. For hydrogenation we expose graphene to a hydrogen plasma and use Raman spectroscopy to characterize this method. We then investigate the SHE of hydrogenated graphene in the H-bar method and by direct measurements of the inverse SHE. Although a large nonlocal resistance can be observed in the H-bar structure, comparison with the results of the ot…
In the quantum Hall effect (QHE) regime, heat is carried by electrons in the edge states of Landau levels. Here, we study cooling of hot electrons propagating along the edge of graphene at the filling factor $ν=\pm2$, mediated by acoustic phonons. We determine the temperature profile extended from a hot spot, where the Hall current is injected into graphene from a metallic contact, taking into account specifics of boundary conditions for lattice displacements in graphene in a van der Waals heterostructure with an insulating substrate. Our calculations, performed using generic boundary conditio…
Nonlinear anomalous Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference in response to a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time reversal symmetric systems. Here, we investigate the family of second-order nonlinear anomalous Hall effects, the electrical, thermoelectric and thermal nonlinear Hall effects in the moiré system of twisted double bilayer graphene. We demonstrate that the nonlinear anomalous Hall signals can be used to probe the topological phase-transitions in moiré systems,…
The use of multiple current terminals on millimeter-scale graphene $p-n$ junction devices fabricated with Corbino geometries, or quantum Hall resistance dartboards, have enabled the measurement of several fractional multiples of the quantized Hall resistance at the $ν=2$ plateau ($R_H\approx 12906 Ω$). Experimentally obtained values agreed with corresponding numerical simulations performed with the LTspice circuit simulator. More complicated designs of the quantum Hall resistance dartboard were simulated to establish the potential parameter space within which these Corbino-type devices could o…
The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied we predict oscillations in the Hall and the bend resistance as function of the magnetic field which are a consequence o…
We consider intrinsic contributions to the spin Hall and spin Nernst effects in a bilayer graphene. The relevant electronic spectrum is obtained from the tight binding Hamiltonian, which also includes the intrinsic spin-orbit interaction. The corresponding spin Hall and spin Nernst conductivities are compared with those obtained from effective Hamiltonians appropriate for states in the vicinity of the Fermi level of a neutral bilayer graphene. Both conductivities are determined within the linear response theory and Green function formalism. The influence of an external voltage between the two …
We study nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateaus feature. The plateaus heights depend on the laser intensity and broadening of Landau levels, so that are not quantized exactly. This nonlinear effect remains robust against the significant broadening of Landau levels. We predict realization of an experiment through the observatio…
We study the spin Hall effect (SHE) in graphene using a realistic multi-orbital tight-binding model that includes the atomic spin-orbit interaction. The SHE is found to be induced by the spin-dependent Aharonov-Bohm phase. In the metallic case, the calculated values for the spin Hall conductivity (SHC) are much smaller than the quantized Hall conductivity for realistic parameter values of metallic graphene. In the insulating case, quantization of the SHC is violated due to the multi-orbital effect. The present study suggests that the SHE in a honeycomb lattice is enhanced by chemical doping, s…
Quantum Hall edge states offer avenues for quasiparticle interferometry, provided that the ratio between phase coherence length and quantum Hall interferometer (QHI) size is large enough. Maximizing this ratio by shrinking the QHI area favors Coulomb interactions, impairing clear interferences observation. Here, we use scanning gate spectroscopy to probe interference regime in antidots-based graphene nano-QHIs, free of localized states (LS). A simple Fabry-Perot model, without Coulomb interaction, reproduces the QHI phenomenology, even in the smallest QHI, highlighting the LS detrimental role.
In the framework of first-principles calculations, we investigate the structural and electronic properties of graphene in contact with as well as sandwiched between WS$_2$ and WSe$_2$ monolayers. We report the modification of the band characteristics due to the interaction at the interface and demonstrate that the presence of the dichalcogenides results in quantum spin Hall states in the absence of a magnetic field.
