Electronic effects in scanning tunneling microscopy: Moiré pattern on a graphite surface

Topical review: electronic and optical properties of Kekulé and other short wavelength spatial modulated textures of graphene

A review of the electronic and optical properties of Kekulé and other short wavelength modulations textures on graphene is presented. Starting from the experimental realization of such textures, the review discusses the electronic and optical properties in terms of several theoretical models like the tight-binding Hamiltonian and effective low energy models based on the Dirac equation. Other surveyed subjects are, strain effects, valley engineering, Kekulé bilayers, zitterbewegung, Kekulé interfaces, valley birefringence and the skew valley scattering. Specific signatures in the optical and electronic conductivities of Kekule textures are next discussed using several approaches like linear response theory, the random phase approximation, and Floquet theory. Plasmons are also presented by considering the dielectric function. Finally, a discussion is presented on how Kekulé textures are related with highly correlated phases, including its importance in magic angle twisted bilayer graphene superconductivity and related quantum phases.

Van der Waals epitaxy of tunable moirés enabled by alloying

The unique physics in moiré superlattices of twisted or lattice-mismatched atomic layers holds great promise for future quantum technologies. However, twisted configurations are thermodynamically unfavourable, making accurate twist angle control during growth implausible. While rotationally aligned, lattice-mismatched moirés such as WSe2/WS2 can be synthesized, they lack the critical moiré period tunability, and their formation mechanisms are not well understood. Here, we report the thermodynamically driven van der Waals epitaxy of moirés with a tunable period from 10 to 45 nanometres, using lattice mismatch engineering in two WSSe layers with adjustable chalcogen ratios. Contrary to conventional epitaxy, where lattice-mismatch-induced stress hinders high-quality growth, we reveal the key role of bulk stress in moiré formation and its unique interplay with edge stress in shaping the moiré growth modes. Moreover, the superlattices display tunable interlayer excitons and moiré intralayer excitons. Our studies unveil the epitaxial science of moiré synthesis and lay the foundations for moiré-based technologies.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Interface coupling in Au-supported MoS2-WS2 heterobilayers grown by pulsed laser deposition

Van der Waals heterostructures of transition metal dichalcogenides (TMDs) are promising systems for engineering functional layered 2D materials with tailored properties. In this work, we study the growth of WS₂/MoS₂ and MoS₂/WS₂ heterobilayers by pulsed laser deposition (PLD) under ultra-high vacuum conditions. Using Au(111) as growth substrate, we investigated the heterobilayer morphology and structure at the nanoscale by in situ scanning tunneling microscopy. Our experiments show that the heterostructure growth can be controlled with high coverage and thickness sensitivity by tuning the number of laser pulses in the PLD process. Raman spectroscopy complemented our investigation, revealing the effect of the interaction with the metallic substrate on the TMD vibrational properties and a strong interlayer coupling between the MoS₂ and WS₂ layers. The transfer of the heterobilayers on a silica substrate via a wet etching process shows the possibility to decouple them from the native metallic substrate and confirms that the interlayer coupling is not substrate-dependent. This work highlights the potential of the PLD technique as a method to grow TMD heterostructures, opening to new perspectives in the synthesis of complex 2D layered materials.

Uncovering Topological Edge States in Twisted Bilayer Graphene

Twisted bilayer graphene (t-BLG) has recently been introduced as a rich physical platform displaying flat electronic bands, strongly correlated states, and unconventional superconductivity. Studies have hinted at an unusual Z₂ topology of the moiré Dirac bands of t-BLG. However, direct experimental evidence of this moiré band topology and associated edge states is still lacking. Herein, using superconducting quantum interferometry, we reconstructed the spatial supercurrent distribution in t-BLG Josephson junctions and revealed the presence of edge states located in the superlattice band gaps. The absence of edge conduction in high resistance regions just outside the superlattice band gap confirms that the edge transport originates from the filling of electronic states located inside the band gap and further allows us to exclude several other edge conduction mechanisms. These results confirm the unusual moiré band topology of twisted bilayer graphene and will stimulate further research to explore its consequences.

Recent Progress on the Scanning Tunneling Microscopy and Spectroscopy Study of Semiconductor Heterojunctions

The band alignment, interface states, interface coupling, and carrier transport of semiconductor heterojunctions (SHs) need to be well understood for the design and fabrication of various important semiconductor structures and devices. Scanning tunneling microscopy (STM) with high spatial resolution and scanning tunneling spectroscopy (STS) with high energy resolution are significantly contributing to the understanding on the important properties of SHs. In this work, the recent progress on the use of STM and STS to study lateral, vertical and bulk SHs is reviewed. The spatial structures of SHs with atomically flat surface have been examined with STM. The electronic band structures (e. g., the band offset, interface state, and space charge region) of SHs are measured with STS. Combined with the spatial structures and the tunneling spectra features, the mechanism for the carrier transport in the SH may be proposed.

Moiré, Euler and self-similarity - the lattice parameters of twisted hexagonal crystals

A real-space approach for the calculation of the moiré lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides is presented. Apparent moiré lattices continuously form for all rotation angles, and their lattice parameter to a good approximation follows a hyperbolical angle dependence. Moiré crystals, i.e. moiré lattices decorated with a basis, require more crucial assessment of the commensurabilities and lead to discrete solutions and a non-continuous angle dependence of the moiré-crystal lattice parameter. In particular, this lattice parameter critically depends on the rotation angle, and continuous variation of the angle can lead to apparently erratic changes of the lattice parameter. The solutions form a highly complex pattern, which reflects number-theoretical relations between formation parameters of the moiré crystal. The analysis also provides insight into the special case of a 30° rotation of the constituting lattices, for which a dodecagonal quasicrystalline structure forms.

Tailoring spintronic and opto-electronic characteristics of bilayer AlN through MnO x clusters intercalation; an ab initio study

Adopting ab initio density functional theory (DFT) technique, the spintronic and opto-electronic characteristics of MnO x (i.e., Mn, MnO, MnO2, MnO3 and MnO4) clusters intercalated bilayer AlN (BL/AlN) systems are investigated in this paper. In terms of electron transfer, charge transfer occurs from BL/AlN to the MnO x clusters. MnO x clusters intercalation induces magnetic behavior in the non-magnetic AlN system. The splitting of electronic bands occurs, thus producing spintronic trends in the electronic structure of BL/AlN system. Further, MnO x intercalation converts insulating BL/AlN to a half metal/semiconductor material during spin up/down bands depending upon the type of impurity cluster present in its lattice. For instance, Mn, MnO and MnO2 intercalation in BL/AlN produces a half metallic BL/AlN system as surface states are available at the Fermi Energy (E F) level for spin up and down band channels, accordingly. Whereas, MnO3 and MnO4 intercalation produces a conducting BL/AlN system having a 0.5 eV and 0.6 eV band gap during the spin down band channel, respectively. During spin up band channels these systems behave as semiconductors with band gaps of 1.4 eV and 1.2 eV, respectively. In terms of optical characteristics (i.e., absorption coefficient, reflectivity and energy loss spectrum (ELS)), it was found that MnO x intercalation improves the absorption spectrum in the low electron energy range and absorption peaks are observed in the 0-3 eV energy range, which are not present in the absorption spectrum of pure BL/AlN. The static reflectivity parameter of BL/AlN is increased after MnO x intercalation and the ELS parameter obtains significant peak intensities in the 0-2 eV energy range, whereas for pure BL/AlN, ELS contains negligible value in this energy range. Outcomes of this study indicate that, MnO x clusters intercalation in BL/AlN is a suitable technique to tailor its spintronic and opto-electronic trends. Thus, experimental investigation can be carried out on the systems discussed in this work, so as to fabricate practical layered AlN systems that are functional in the field of nano-technology.

Abnormal conductivity in low-angle twisted bilayer graphene

Controlling the interlayer twist angle offers a powerful means for tuning the electronic properties of two-dimensional (2D) van der Waals materials. Typically, the electrical conductivity would increase monotonically with decreasing twist angle owing to the enhanced coupling between adjacent layers. Here, we report a nonmonotonic angle-dependent vertical conductivity across the interface of bilayer graphene with low twist angles. More specifically, the vertical conductivity enhances gradually with decreasing twist angle up to a crossover angle at θ_c ≈ 5°, and then it drops notably upon further decrease in the twist angle. Revealed by density functional theory calculations and scanning tunneling microscopy, the abnormal behavior is attributed to the unusual reduction in average carrier density originating from local atomic reconstruction. The impact of atomic reconstruction on vertical conductivity is unique for low-angle twisted 2D van der Waals materials and provides a strategy for designing and optimizing their electronic performance.

Stacking-configuration-enriched essential properties of bilayer graphenes and silicenes

First-principles calculations show that the geometric and electronic properties of silicene-related systems have diversified phenomena. Critical factors of group-IV monoelements, like buckled/planar structures, stacking configurations, layer numbers, and van der Waals interactions of bilayer composites, are considered simultaneously. The theoretical framework developed provides a concise physical and chemical picture. Delicate evaluations and analyses have been made on the optimal lattices, energy bands, and orbital-projected van Hove singularities. They provide decisive mechanisms, such as buckled/planar honeycomb lattices, multi-/single-orbital hybridizations, and significant/negligible spin-orbital couplings. We investigate the stacking-configuration-induced dramatic transformations of essential properties by relative shift in bilayer graphenes and silicenes. The lattice constant, interlayer distance, buckling height, and total energy essentially depend on the magnitude and direction of the relative shift: AA → AB → AA' → AA. Apparently, sliding bilayer systems are quite different between silicene and graphene in terms of geometric structures, electronic properties, orbital hybridizations, interlayer hopping integrals, and spin interactions.

Moiré Band Topology in Twisted Bilayer Graphene

Recently twisted bilayer graphene (t-BLG) has emerged as a strongly correlated physical platform. Besides the apparent significance of band flatness, band topology may be another critical element in t-BLG and yet receives much less attention. Here we report the compelling evidence for nontrivial noninteracting Moiré band topology in t-BLG through a systematic nonlocal transport study and a K-theory examination. The nontrivial topology manifests itself as two pronounced nonlocal responses in the electron and hole superlattice gaps. We show that the nonlocal responses are robust to the twist angle and edge termination, exhibiting a universal scaling law. We elucidate that, although Berry curvature is symmetry-trivialized, two nontrivial Z₂ invariants characterize the Moiré Dirac bands, validating the topological origin of the observed nonlocal responses. Our findings not only provide a new perspective for understanding the strongly correlated t-BLG but also suggest a potential strategy to achieve topological metamaterials from trivial vdW materials.

Moiré Potential, Lattice Corrugation, and Band Gap Spatial Variation in a Twist-Free MoTe2/MoS2 Heterobilayer

To have a fully first-principles description of the moiré pattern in transition-metal dichalcogenide heterobilayers, we have carried out density functional theory calculations on a MoTe₂(9 × 9)/MoS₂(10 × 10) stacking, which has a superlattice larger than an exciton yet not large enough to justify a continuum model treatment. Lattice corrugation is found to be significant in both monolayers, yet its effect on the electronic properties is marginal. We reveal that the variation of the average local potential near Mo atoms in both MoTe₂ and MoS₂ layers displays a conspicuous moiré pattern. They are the intralayer moiré potentials correlating closely with the spatial variation of the valence band maximum and conduction band minimum. The interlayer moiré potential, defined as the difference between the two intralayer moiré potentials, changes roughly in proportion to the band gap variation in the moiré cell. This finding might be instructive in chemical engineering of van der Waals bilayers.

Evidence for Magnetic Skyrmions at the Interface of Ferromagnet/Topological-Insulator Heterostructures

The heterostructures of the ferromagnet (Cr₂Te₃) and topological insulator (Bi₂Te₃) have been grown by molecular beam epitaxy. The topological Hall effect as evidence of the existence of magnetic skyrmions has been observed in the samples in which Cr₂Te₃ was grown on top of Bi₂Te₃. Detailed structural characterizations have unambiguously revealed the presence of intercalated Bi bilayer nanosheets right at the interface of those samples. The atomistic spin-dynamics simulations have further confirmed the existence of magnetic skyrmions in such systems. The heterostructures of ferromagnet and topological insulator that host magnetic skyrmions may provide an important building block for next generation of spintronics devices.

Confined states in graphene quantum blisters

Bilayer graphene samples may exhibit regions where the two layers are locally delaminated forming a so-called quantum blister in the graphene sheet. Electron and hole states can be confined in this graphene quantum blisters (GQB) by applying a global electrostatic bias. We scrutinize the electronic properties of these confined states under the variation of interlayer bias, coupling, and blister's size. The spectra display strong anti-crossings due to the coupling of the confined states on upper and lower layers inside the blister. These spectra are layer localized where the respective confined states reside on either layer or equally distributed. For finite angular momentum, this layer localization can be at the edge of the blister and corresponds to degenerate modes of opposite momenta. Furthermore, the energy levels in GQB exhibit electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we demonstrate that confinement in GQB persists even in the presence of a variation in the inter-layer coupling.

Stacking-enriched magneto-transport properties of few-layer graphenes

The quantum Hall effects in sliding bilayer graphene and a AAB-stacked trilayer system are investigated using the Kubo formula and the generalized tight-binding model.

Criticality of the phase transition on stage two in a lattice-gas model of a graphite anode in a lithium-ion battery

Herein, a Monte Carlo study within the canonical assembly has been applied to elucidate the lithium-ion phase transition order of a stage II lithium–graphite intercalation compound (LiC₁₂).

Super flexibility and stability of graphene nanoribbons under severe twist

The structure and properties of nanostructured materials formed upon deformation are determined to a great extent by the states of stress and strain and the regimes of deformation. The nanostructures and properties of the graphene nanoribbons (GNRs) subjected to severe twist deformation were studied using molecular dynamics (MD) simulations. The GNRs show superflexibility and withstanding severe twisting, which leads to GNR nanostructures transforming from flat to twisted and then getting thoroughly coiled and fail. The appearance of a decreasing Young's moduli of the GNRs was observed with increasing rotation in general. The chirality has little effect on the Young's moduli of flat GNRs, whereas the degree of the GNR aspect ratio does. The severely twisted GNRs follow a similar rule but with slightly decreased Young's moduli (∼0.1 TPa), which demonstrates that the twisted GNRs maintain their stiff nature. The electronic properties of the GNRs under severely twisted conditions also show slight changes studied by density-functional theory (DFT) simulations. The stable mechanical properties and structure changes of GNRs under severely twisted conditions makes them a good candidate in some polymers, enhancing the load transfer and interfacial bonding by adding the twisted GNRs.

Evolution of Moiré Profiles from van der Waals Superstructures of Boron Nitride Nanosheets

Two-dimensional (2D) van der Waals (vdW) superstructures, or vdW solids, are formed by the precise restacking of 2D nanosheet lattices, which can lead to unique physical and electronic properties that are not available in the parent nanosheets. Moiré patterns formed by the crystalline mismatch between adjacent nanosheets are the most direct features for vdW superstructures under microscopic imaging. In this article, transmission electron microscopy (TEM) observation of hexagonal Moiré patterns with unusually large micrometer-sized lateral areas (up to ~1 μm²) and periodicities (up to ~50 nm) from restacking of liquid exfoliated hexagonal boron nitride nanosheets (BNNSs) is reported. This observation was attributed to the long range crystallinity and the contaminant-free surfaces of these chemically inert nanosheets. Parallel-line-like Moiré fringes with similarly large periodicities were also observed. The simulations and experiments unambiguously revealed that the hexagonal patterns and the parallel fringes originated from the same rotationally mismatched vdW stacking of BNNSs and can be inter-converted by simply tilting the TEM specimen following designated directions. This finding may pave the way for further structural decoding of other 2D vdW superstructure systems with more complex Moiré images.

Interlayer interaction and related properties of bilayer hexagonal boron nitride: ab initio study

Properties of hexagonal boron nitride bilayer related to interlayer interaction (width and formation energy of dislocations, shear mode frequency, etc.) are estimated by approximation of potential energy surface by first Fourier harmonics.

Strong slip-induced anomalous enhancement and red-shifts in wide-range optical absorption of graphite under uniaxial pressure

Natural graphite shows little optical response. Based on first-principles calculations, we demonstrate, for the first time, that an in-plane pressure-induced slip between atomic layers causes a strong anomalous enhancement and large red-shifts in the infrared and far infrared optical absorption by graphite. Specifically, a slip along the armchair direction induces an absorption feature that redshifts from ∼ 3 eV to ∼ 0.15 eV, while its intensity increases by an order of magnitude, due to an electron density delocalization effect with slip. Our results provide a way to detect and measure the magnitude of the in-plane slip of graphite under compression and also open up potential applications in electronics and photonics.

Precisely aligned graphene grown on hexagonal boron nitride by catalyst free chemical vapor deposition

To grow precisely aligned graphene on h-BN without metal catalyst is extremely important, which allows for intriguing physical properties and devices of graphene/h-BN hetero-structure to be studied in a controllable manner. In this report, such hetero-structures were fabricated and investigated by atomic resolution scanning probe microscopy. Moiré patterns are observed and the sensitivity of moiré interferometry proves that the graphene grains can align precisely with the underlying h-BN lattice within an error of less than 0.05°. The occurrence of moiré pattern clearly indicates that the graphene locks into h-BN via van der Waals epitaxy with its interfacial stress greatly released. It is worthy to note that the edges of the graphene grains are primarily oriented along the armchair direction. The field effect mobility in such graphene flakes exceeds 20,000 cm²·V⁻¹·s⁻¹ at ambient condition. This work opens the door of atomic engineering of graphene on h-BN, and sheds light on fundamental research as well as electronic applications based on graphene/h-BN hetero-structure.

Terahertz conductivity of twisted bilayer graphene

Using terahertz time-domain spectroscopy, the real part of optical conductivity [σ(1)(ω)] of twisted bilayer graphene was obtained at different temperatures (10-300 K) in the frequency range 0.3-3 THz. On top of a Drude-like response, we see a strong peak in σ(1)(ω) at ~2.7 THz. We analyze the overall Drude-like response using a disorder-dependent (unitary scattering) model, then attribute the peak at 2.7 THz to an enhanced density of states at that energy, which is caused by the presence of a van Hove singularity arising from a commensurate twisting of the two graphene layers.

Phonon-mediated interlayer conductance in twisted graphene bilayers

Conduction between graphene layers is suppressed by momentum conservation whenever the layer stacking has a rotation. Here we show that phonon scattering plays a crucial role in facilitating interlayer conduction. The resulting dependence on orientation is radically different than previously expected, and far more favorable for device applications. At low temperatures, we predict diode-like current-voltage characteristics due to a phonon bottleneck. Simple scaling relationships give a good description of the conductance as a function of temperature, doping, rotation angle, and bias voltage, reflecting the dominant role of the interlayer beating phonon mode.

Unraveling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis

Extensive scanning tunneling microscopy and spectroscopy experiments complemented by first-principles and parametrized tight binding calculations provide a clear answer to the existence, origin, and robustness of van Hove singularities (vHs) in twisted graphene layers. Our results are conclusive: vHs due to interlayer coupling are ubiquitously present in a broad range (from 1° to 10°) of rotation angles in our graphene on 6H-SiC(000-1) samples. From the variation of the energy separation of the vHs with the rotation angle we are able to recover the Fermi velocity of a graphene monolayer as well as the strength of the interlayer interaction. The robustness of the vHs is assessed both by experiments, which show that they survive in the presence of a third graphene layer, and by calculations, which test the role of the periodic modulation and absolute value of the interlayer distance. Finally, we clarify the role of the layer topographic corrugation and of electronic effects in the apparent moiré contrast measured on the STM images.

Moire bands in twisted double-layer graphene

A moiré pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted two-layer graphene system, showing that in its continuum Dirac model the moiré pattern periodicity leads to moiré Bloch bands. The two layers become more strongly coupled and the Dirac velocity crosses zero several times as the twist angle is reduced. For a discrete set of magic angles the velocity vanishes, the lowest moiré band flattens, and the Dirac-point density-of-states and the counterflow conductivity are strongly enhanced.

Diffusion and drift of graphene flake on graphite surface

Diffusion and drift of a graphene flake on a graphite surface are analyzed. A potential energy relief of the graphene flake is computed using ab initio and empirical calculations. Based on the analysis of this relief, different mechanisms of diffusion and drift of the graphene flake on the graphite surface are considered. A new mechanism of diffusion and drift of the flake is proposed. According to the proposed mechanism, rotational transition of the flake from commensurate to incommensurate state takes place with subsequent simultaneous rotation and translational motion until a commensurate state is reached again, and so on. Analytic expressions for the diffusion coefficient and mobility of the flake corresponding to different mechanisms are derived in wide ranges of temperatures and sizes of the flake. The molecular dynamics simulations and estimates based on ab initio and empirical calculations demonstrate that the proposed mechanism can be dominant under certain conditions. The influence of structural defects on the diffusion of the flake is examined on the basis of calculations of the potential energy relief and molecular dynamics simulations. The methods of control over the diffusion and drift of graphene components in nanoelectromechanical systems are discussed. The possibility to experimentally determine the barriers to relative motion of graphene layers based on the study of diffusion of a graphene flake is considered. The results obtained can also be applied to polycyclic aromatic molecules on graphene and should be qualitatively valid for a set of commensurate adsorbate-adsorbent systems.

Separation-dependent electronic transparency of monolayer graphene membranes on III-V semiconductor substrates

Ultrahigh vacuum scanning tunneling microscopy and first-principles calculations have been carried out to study monolayer graphene nanomembranes deposited in situ onto UHV-cleaved GaAs(110) and InAs(110) surfaces. A bias-dependent semitransparency effect is observed in which the substrate atomic structure is clearly visible through the graphene monolayer. Statistical data analysis and density functional theory calculations suggest that this semitransparency phenomenon is due to the scanning tunneling microscope tip pushing the graphene membrane away from its equilibrium location and closer to the substrate surface, causing their electronic states to intermix.

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.

Localization of dirac electrons in rotated graphene bilayers

For Dirac electrons the Klein paradox implies that the confinement is difficult to achieve with an electrostatic potential although it can be of great importance for graphene-based devices. Here, ab initio and tight-binding approaches are combined and show that the wave function of Dirac electrons can be localized in rotated graphene bilayers due to the Moire pattern. This localization of wave function is maximum in the limit of the small rotation angle between the two layers.

Tailoring the local interaction between graphene layers in graphite at the atomic scale and above using scanning tunneling microscopy

With recent developments in carbon-based electronics, it is imperative to understand the interplay between the morphology and electronic structure in graphene and graphite. We demonstrate controlled and repeatable vertical displacement of the top graphene layer from the substrate mediated by the scanning tunneling microscopy (STM) tip-sample interaction, manifested at the atomic level as well as over superlattices spanning several tens of nanometers. Besides the full-displacement, we observed the first half-displacement of the surface graphene layer, confirming that a reduced coupling rather than a change in lateral layer stacking is responsible for the triangular/honeycomb atomic lattice transition phenomenon, clearing the controversy surrounding it. Furthermore, an atomic scale mechanical stress at a grain boundary in graphite, resulting in the localization of states near the Fermi energy, is revealed through voltage-dependent imaging. A method of producing graphene nanoribbons based on the manipulation capabilities of the STM is also implemented.

Registry-induced electronic superstructure in double-walled carbon nanotubes, associated with the interaction between two graphene-like monolayers

Prior to the implementation of multi-walled carbon nanotubes in microelectronic devices, investigating their electronic structure down to the nanometer scale is necessary. In that prospect, we used scanning tunneling microscopy (STM) to study the detailed atomic scale structure of double-walled carbon nanotubes, each comprising two rolled monolayers of graphene. Atomically resolved STM images usually displayed a motif and periodicity similar to that found in graphite but, on selected regions, atomically resolved motifs with a clearly defined superstructure were observed. This phenomenon has been reported previously but without a suitable explanation. We discuss the origin of this behavior in terms of modified stacking sequences due to the mismatch in registry between the chiral angles of the inner and the outer shells, associated with the interaction between the two carbon monolayers. These phenomena must be taken into account for the realization of lateral interference devices based on carbon nanotubes or graphene layers.

Graphene bilayer with a twist: electronic structure

We consider a graphene bilayer with a relative small angle rotation between the layers--a stacking defect often seen in the surface of graphite--and calculate the electronic structure near zero energy in a continuum approximation. Contrary to what happens in an AB stacked bilayer and in accord with observations in epitaxial graphene, we find: (a) the low energy dispersion is linear, as in a single layer, but the Fermi velocity can be significantly smaller than the single-layer value; (b) an external electric field, perpendicular to the layers, does not open an electronic gap.