Graphene Dirac Research Articles

Valley filters, accumulators, and switches induced in graphene quantum dots by lines of adsorbed hydrogen atoms

We present electronic structure and quantum transport calculations that predict conducting channels induced in graphene quantum dots by lines of adsorbed hydrogen atoms to function as highly efficient, experimentally realizable valley filters, accumulators and switches. The underlying physics is a novel property of graphene Dirac point resonances (DPRs) that is revealed here, namely, that an electric current passing through a DPR-mediated conducting channel in a given direction is carried by electrons of em only one of the two graphene valleys. Our predictions apply to lines of hydrogen atoms adsorbed on graphene quantum dots that are either free standing or supported on a hexagonal boron nitride substrate.

Symmetry-enforced stability of interacting Weyl and Dirac semimetals

The nodal and effectively relativistic dispersion featuring in a range of novel materials including two- dimensional graphene and three-dimensional Dirac and Weyl semimetals has attracted enormous interest during the past decade. Here, by studying the structure and symmetry of the diagrammatic expansion, we show that these nodal touching points are in fact perturbatively stable to all orders with respect to generic two-body interactions. For effective low-energy theories relevant for single and multilayer graphene, type-I and type-II Weyl and Dirac semimetals as well as Weyl points with higher topological charge, this stability is shown to be a direct consequence of a spatial symmetry that anti-commutes with the effective Hamiltonian while leaving the interaction invariant. A more refined argument is applied to the honeycomb lattice model of graphene showing that its Dirac points are also perturbatively stable to all orders. We also give examples of nodal Hamiltonians that acquire a gap from interactions as a consequence of symmetries different from those of Weyl and Dirac materials.

Graphene Dirac point tuned by ferroelectric polarization field

Graphene has received numerous attention for future nanoelectronics and optoelectronics. The Dirac point is a key parameter of graphene that provides information about its carrier properties. There are lots of methods to tune the Dirac point of graphene, such as chemical doping, impurities, defects, and disorder. In this study, we report a different approach to tune the Dirac point of graphene using a ferroelectric polarization field. The Dirac point can be adjusted to near the ferroelectric coercive voltage regardless its original position. We have ensured this phenomenon by temperature-dependent experiments, and analyzed its mechanism with the theory of impurity correlation in graphene. Additionally, with the modulation of ferroelectric polymer, the current on/off ratio and mobility of graphene transistor both have been improved. This work provides an effective method to tune the Dirac point of graphene, which can be readily used to configure functional devices such as p–n junctions and inverters.

Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions

We develop an analytical mode-matching technique for the tight-binding model to describe electron transport across graphene P-N junctions. This method shares the simplicity of the conventional mode-matching technique for the low-energy continuum model and the accuracy of the tight-binding model over a wide range of energies. It further reveals an interesting phenomenon on a sharp P-N junction: the disappearance of the well-known Klein tunneling (i.e., perfect transmission) at normal incidence and the appearance of perfect transmission at oblique incidence due to trigonal warping at energies beyond the linear Dirac regime. We show that this phenomenon arises from the conservation of a generalized pseudospin in the tight-binding model. We expect this effect to be experimentally observable in graphene and other Dirac fermions systems, such as the surface of three-dimensional topological insulators.

Dirac-Weyl points’ manipulation using linear polarised laser field in Floquet crystals for various Graphene superlattices

We investigate the changes in the energy spectrum of the graphene monolayer subjected to linear polarised laser beam and external periodically modulated static field (electric and magnetic). Floquet theory and the resonance approximation are used to analyse the energy spectrum and, in particular, the creation and the destruction of the Dirac-Weyl points. We found that at certain conditions the graphene is transformed into the two-dimensional Weyl metals, where each of the two original graphene Dirac cones is split into pairs of the Weyl cones. We also show that altering the laser’s beam incidence(tilting) angle may lead to appearing and disappearing of the pairs of Weyl points, the opening gap in the spectrum, and its efficient manipulation.

Helical Level Structure of Dirac Potential Wells.

In graphene and other massless two-dimensional Dirac materials, Klein tunneling compromises electron confinement, and momentum-space contours can be assigned a Berry phase which is either zero or π. Consequently, in such systems the energy spectrum of circular potential wells exhibits an interesting discontinuity as a function of magnetic field B: for a given angular momentum the ladder of eigen-resonances is split at an energy-dependent critical field B c. Here we show that introducing a mass term Δ in the Hamiltonian bridges this discontinuity in such a way that states below B c are adiabatically connected to states above B c whose principal quantum number differs by unity depending on the sign of Δ. In the B-Δ plane, the spectrum of these circular resonators resembles a spiral staircase, in which a particle prepared in the ∣n, m⟩ resonance state can be promoted to the ∣n± 1, m⟩ state by an adiabatic circuit of the Hamiltonian about B c, the sign depending on the direction of the circuit. We explain the phenomenon in terms of the evolving Berry phase of the orbit, which in such a circuit changes adiabatically by 2π.

Dirac fermions and pseudomagnetic fields in two-dimensional electron gases with triangular antidot lattices

We investigate theoretically the electronic properties of two-dimensional electron gases (2DEGs) with regular and distorted triangular antidot lattices. We show that the triangular antidot lattices embedded in 2DEGs behave like artificial graphene and host Dirac fermions. By introducing the Wannier representation, we obtain a tight-binding Hamiltonian including the second-nearest-neighboring hopping, which agrees well with the numerically exact solutions. Based on the tight-binding model, we find that spatially nonuniform distortions of the antidot lattices strongly modify the electronic structures, generate pseudomagnetic fields and the well-defined Landau levels. In contrast to graphene, we can design the nonuniform distortions to generate various configurations of pseudomagnetic fields. We show that the snake orbital states arise by designing the $\ifmmode\pm\else\textpm\fi{}\mathbf{B}$ pseudomagnetic field configuration. We find that the disorders of antidot lattices during fabrication would not affect the basic feature of the Dirac electrons, but they lead to a reduction in conductance in strong disorder cases.

Analytic solution for gauged Dirac-Weyl equation in (2 + 1)-dimensions

A gauged Dirac-Weyl equation in -dimensions is considered. This equation has the particularity to describe the states of a graphene Dirac matter. In particular we are interested in matter interacting with a Chern-Simons gauge field. We show that exact self-dual solutions are admitted. These solutions are the same as those supported by nonrelativistic matter interacting with a Chern-Simons gauge field.

Quantum interference on electron scattering in graphene by carbon impurities in underlying h -BN

Electronic structures and transport properties of graphene on $h$-BN with carbon impurities are investigated by first-principles calculation and the tight-binding model. We show that the coupling between the impurity level and the graphene's Dirac cone sensitively depends on the impurity position, and in particular, it nearly vanishes when the impurity is located right below the center of the six membered ring of graphene. The Bloch phase factor at the Brillouin zone edge plays a decisive role in the cancellation of the hopping integrals. The impurity position dependence on the electronic structures of graphene on $h$-BN is investigated by the first-principles calculation, and its qualitative feature is well explained by a tight-binding model with graphene and a single impurity site. We also propose a simple one-dimensional chain-impurity model to analytically describe the role of the quantum interference in the position-dependent coupling.

Transport signatures of Kondo physics and quantum criticality in graphene with magnetic impurities

Localized magnetic moments have been predicted to develop in graphene samples with vacancies or adsorbates. The interplay between such magnetic impurities and graphene's Dirac quasiparticles leads to remarkable many-body phenomena, which have so far proved elusive to experimental efforts. In this article, we study the thermodynamic, spectral and transport signatures of quantum criticality and Kondo physics of a dilute ensemble of atomic impurities in graphene. We consider vacancies and adatoms that either break or preserve graphene's $C_{3v}$ and inversion symmetries. In a neutral graphene sample, all cases display symmetry-dependent quantum criticality, leading to enhanced impurity scattering for asymmetric impurities, in a manner analogous to bound-state formation by nonmagnetic resonant scatterers. Kondo correlations emerge only in the presence of a back gate, with estimated Kondo temperatures well within the experimentally accessible domain for all impurity types. For symmetry-breaking impurities at charge neutrality, quantum criticality is signaled by $T^{-2}$ resistivity scaling, leading to full insulating behavior at low temperatures, while low-temperature resistivity plateaus appear both in the non-critical and Kondo regimes. By contrast, the resitivity contribution from symmetric vacancies and hollow-site adsorbates vanishes at charge neutrality and for arbitrary back gate voltages, respectively. This implies that local probing methods are required for the detection of both Kondo and quantum critical signatures in these symmetry-preserving cases.

Graphene contacts to a HfSe2/SnS2 heterostructure.

Two-dimensional (2D) heterostructures and all-2D contacts are of high interest for electronic device applications, and the SnS2/HfSe2 bilayer heterostructure with graphene contacts has some unique, advantageous properties. The SnS2/HfSe2 heterostructure is interesting because of the strong intermixing of the two conduction bands and the large work function of the SnS2. The band lineup of the well separated materials indicates a type II heterostructure, but the conduction band minimum of the SnS2/HfSe2 bilayer is a coherent superposition of the orbitals from the two layers with a spectral weight of 60% on the SnS2 and 40% on the HfSe2 for AA stacking. These relative weights can be either increased or reversed by an applied vertical field. A 3×3 supercell of graphene and a 2×2 supercell of SnS2/HfSe2 have a lattice mismatch of 0.1% and both the SnS2/HfSe2 conduction band at M and the graphene Dirac point at K are zone-folded to Γ. Placing graphene on the SnS2/HfSe2 bilayer results in large n-type charge transfer doping of the SnS2/HfSe2 bilayer, on the order of 1013/cm2, and the charge transfer is accompanied by a negative Schottky barrier contact for electron injection from the graphene into the SnS2/HfSe2 bilayer conduction band. Binding energies and the anti-crossing gaps of the graphene and the SnS2/HfSe2 electronic bands both show that the coupling of graphene to the HfSe2 layer is significantly larger than its coupling to the SnS2 layer. A tunneling Hamiltonian estimate of the contact resistance of the graphene to the SnS2/HfSe2 heterostructure predicts an excellent low-resistance contact.

Tuning charge and correlation effects for a single molecule on a graphene device.

The ability to understand and control the electronic properties of individual molecules in a device environment is crucial for developing future technologies at the nanometre scale and below. Achieving this, however, requires the creation of three-terminal devices that allow single molecules to be both gated and imaged at the atomic scale. We have accomplished this by integrating a graphene field effect transistor with a scanning tunnelling microscope, thus allowing gate-controlled charging and spectroscopic interrogation of individual tetrafluoro-tetracyanoquinodimethane molecules. We observe a non-rigid shift in the molecule's lowest unoccupied molecular orbital energy (relative to the Dirac point) as a function of gate voltage due to graphene polarization effects. Our results show that electron–electron interactions play an important role in how molecular energy levels align to the graphene Dirac point, and may significantly influence charge transport through individual molecules incorporated in graphene-based nanodevices.

Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how can we compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the low-energy electronic scattering off this linear defect. We also compute the effective generalized potential seen by the Dirac fermions at the grain boundary region.

Indirect Interlayer Bonding in Graphene-Topological Insulator van der Waals Heterostructure: Giant Spin-Orbit Splitting of the Graphene Dirac States.

van der Waals (vdW) heterostructures of two-dimensional materials exhibit properties and functionalities that can be tuned by stacking order and interlayer coupling. Although direct covalent bonding is not expected at the heterojunction, the formation of an interface nevertheless breaks the symmetries of the layers, and the orthogonal requirement of the wave functions can lead to indirect interfacial coupling, creating new properties and functionalities beyond their constituent layers. Here, we fabricate graphene/topological insulator vdW heterostructure by transferring chemical vapor deposited graphene onto Bi2Se3 grown by molecular beam epitaxy. Using scanning tunneling microscopy/spectroscopy, we observe a giant spin-orbit splitting of the graphene Dirac states up to 80 meV. Density functional theory calculations further reveal that this splitting of the graphene bands is a consequence of the breaking of inversion symmetry and the orthogonalization requirement on the overlapping wave functions at the interface, rather than simple direct bonding. Our findings reveal two intrinsic characteristics-the symmetry breaking and orthogonalization of the wave functions at the interface-that underlines the properties of vdW heterostructures.

Electronic structure of transferred graphene/h-BN van der Waals heterostructures with nonzero stacking angles by nano-ARPES

In van der Waals heterostructures, the periodic potential from the Moiré superlattice can be used as a control knob to modulate the electronic structure of the constituent materials. Here we present a nanoscale angle-resolved photoemission spectroscopy (nano-ARPES) study of transferred graphene/h-BN heterostructures with two different stacking angles of 2.4° and 4.3° respectively. Our measurements reveal six replicas of graphene Dirac cones at the superlattice Brillouin zone (SBZ) centers. The size of the SBZ and its relative rotation angle to the graphene BZ are in good agreement with Moiré superlattice period extracted from atomic force microscopy (AFM) measurements. Comparison to the epitaxial graphene/h-BN with 0° stacking angles suggests that the interaction between graphene and h-BN decreases with increasing stacking angle.

Controlled thermodynamics for tunable electron doping of graphene on Ir(111)

The electronic properties and surface structures of K-doped graphene supported on Ir(111) are characterized as a function of temperature and coverage by combining low-energy electron diffraction, angle-resolved photoemission spectroscopy, and density functional theory (DFT) calculations. Deposition of K on graphene at room temperature (RT) yields a stable $(\ensuremath{\surd}3\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}3)$ R30\ifmmode^\circ\else\textdegree\fi{} surface structure having an intrinsic electron doping that shifts the graphene Dirac point by ${E}_{D}=1.30\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ below the Fermi level. Keeping the graphene substrate at 80 K during deposition generates instead a $(2\ifmmode\times\else\texttimes\fi{}2)$ phase, which is stable until full monolayer coverage. Further deposition of K followed by RT annealing develops a double-layer K-doped graphene that effectively doubles the K coverage and the related charge transfer, as well as maximizing the doping level $({E}_{D}=1.61\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$. The measured electron doping and the surface reconstructions are rationalized by DFT calculations. These indicate a large thermodynamic driving force for K intercalation below the graphene layer. The electron doping and Dirac point shifts calculated for the different structures are in agreement with the experimental measurements. In particular, the ${\mathrm{K}}_{4s}$ bands are shown to be sensitive to both the K intercalation and periodicity and are therefore suggested as a fingerprint for the location and ordering of the K dopants.

Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

Graphene/h-BN has emerged as a model van der Waals heterostructure, and the band structure engineering by the superlattice potential has led to various novel quantum phenomena including the self-similar Hofstadter butterfly states. Although newly generated second generation Dirac cones (SDCs) are believed to be crucial for understanding such intriguing phenomena, so far fundamental knowledge of SDCs in such heterostructure, e.g. locations and dispersion of SDCs, the effect of inversion symmetry breaking on the gap opening, still remains highly debated due to the lack of direct experimental results. Here we report first direct experimental results on the dispersion of SDCs in 0$^\circ$ aligned graphene/h-BN heterostructure using angle-resolved photoemission spectroscopy. Our data reveal unambiguously SDCs at the corners of the superlattice Brillouin zone, and at only one of the two superlattice valleys. Moreover, gaps of $\approx$ 100 meV and $\approx$ 160 meV are observed at the SDCs and the original graphene Dirac cone respectively. Our work highlights the important role of a strong inversion symmetry breaking perturbation potential in the physics of graphene/h-BN, and fills critical knowledge gaps in the band structure engineering of Dirac fermions by a superlattice potential.

Exact solution of the Dirac–Weyl equation in graphene under electric and magnetic fields

In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q -parameters under an electrostatic potential. In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used. We have also investigated the thermodynamic properties by using the Hurwitz zeta function method for one of the states. Finally, some of the numerical results are also shown.

Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures.

Chirality is a fundamental property of electrons with the relativistic spectrum found in graphene and topological insulators. It plays a crucial role in relativistic phenomena, such as Klein tunneling, but it is difficult to visualize directly. Here, we report the direct observation and manipulation of chirality and pseudospin polarization in the tunneling of electrons between two almost perfectly aligned graphene crystals. We use a strong in-plane magnetic field as a tool to resolve the contributions of the chiral electronic states that have a phase difference between the two components of their vector wave function. Our experiments not only shed light on chirality, but also demonstrate a technique for preparing graphene's Dirac electrons in a particular quantum chiral state in a selected valley.

Extremely Large Gate Modulation in Vertical Graphene/WSe2 Heterojunction Barristor Based on a Novel Transport Mechanism.

A WSe2 -based vertical graphene-transition metal dichalcogenide heterojunction barristor shows an unprecedented on-current increase with decreasing temperature and an extremely high on/off-current ratio of 5 × 10(7) at 180 K (3 × 10(4) at room temperature). These features originate from a trap-assisted tunneling process involving WSe2 defect states aligned near the graphene Dirac point.