We report room temperature scanning tunneling microscopy and spectroscopy study of bilayer graphene prepared by mechanical exfoliation on SiO$_2$/Si surface and electrically contacted with gold pads using a mechanical mask. The bulk conductivity shows contribution from regions of varying electron density indicating significant charge inhomogeneity. Large scale topographic images show ripple like structures with a roughness of $\sim$1nm while the small scale atomic resolution images show graphite-like triangular lattice. Local dI/dV-V tunnel spectra have an asymmetric V-shape with the minima location showing significant spatial variation indicating inhomogeneity in electron density of order 10$^{11}$ cm-2. The minima in spectra at a fixed location also shifts linearly with the gate voltage with a slope consistent with the field induced carrier density.
Boltzmann transport theory fails near the linear band-crossing of single-layer graphene and near the quadratic band-crossing of bilayer graphene. We report on a numerical study which assesses the role of inter-band coherence in transport when the Fermi level lies near the band-crossing energy of bilayer graphene. We find that interband coherence enhances conduction, and that it plays an essential role in graphene's minimum conductivity phenomena. This behavior is qualitatively captured by an approximate theory which treats inter-band coherence in a relaxation-time approximation. On the basis o…
We develop a fully self-consistent model to describe scanning tunneling spectroscopy (STS) measurements of Bernal-stacked bilayer graphene (BLG), and we compare the results of our model to experimental measurements. Our results show that the STS tip acts as a top gate that changes the BLG bandstructure and Fermi level, while simultaneously probing the voltage-dependent tunneling density of states (TDOS). These effects lead to differences between the TDOS and the local density of states (LDOS); in particular, we show that the bandgap of the BLG appears larger than expected in STS measurements, …
Nanoscale twisted bilayer graphene (TBG) is quite instable and will change its structure to Bernal (or AB-stacking) bilayer with a much lower energy. Therefore, the lack of nanoscale TBG makes its electronic properties not accessible in experiment up to now. In this work, a special confined TBG is obtained in the overlaid area of two continuous misoriented graphene sheets. The width of the confined region of the TBG changes gradually from about 22 nm to 0 nm. By using scanning tunnelling microscopy, we studied carefully the structure and the electronic properties of the nanoscale TBG. Our resu…
The existence of strong trigonal warping around the K point for the low energy electronic states in multilayer (N$\geq$2) graphene films and graphite is well established. It is responsible for phenomena such as Lifshitz transitions and anisotropic ballistic transport. The absolute orientation of the trigonal warping with respect to the center of the Brillouin zone is however not agreed upon. Here, we use quasiparticle scattering experiments on a gated bilayer graphene/hexagonal boron nitride heterostructure to settle this disagreement. We compare Fourier transforms of scattering interference m…
We use low-temperature scanning gate microscopy (SGM) to investigate the breakdown of the quantum Hall regime in an exfoliated bilayer graphene flake. SGM images captured during breakdown exhibit intricate patterns of "hotspots" where the conductance is strongly affected by the presence of the tip. Our results are well described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering between localized Landau levels.
We have performed low temperature scanning tunneling spectroscopy measurements on exfoliated bilayer graphene on SiO2. By varying the back gate voltage we observed a linear shift of the Dirac point and an opening of a band gap due to the perpendicular electric field. In addition to observing a shift in the Dirac point, we also measured its spatial dependence using spatially resolved scanning tunneling spectroscopy. The spatial variation of the Dirac point was not correlated with topographic features and therefore we attribute its shift to random charged impurities.
We use Scanning Gate Microscopy to demonstrate the presence of localized states arising from potential inhomogeneities in a 50nm-wide, gate-defined conducting channel in encapsulated bilayer graphene. When imaging the channel conductance under the influence of a local tip-induced potential, we observe ellipses of enhanced conductance as a function of the tip position. These ellipses allow us to infer the location of the localized states and to study their dependence on the displacement field. For large displacement fields, we observe that localized states tend to occur halfway into the channel…
Twisted graphene layers produce a moiré pattern (MP) structure with a predetermined wavelength for given twist angle. However, predicting the membrane corrugation amplitude for any angle other than pure AB-stacked or AA-stacked graphene is impossible using first-principles density functional theory (DFT) due to the large supercell. Here, within elasticity theory we define the MP structure as the minimum energy configuration, thereby leaving the height amplitude as the only unknown parameter. The latter is determined from DFT calculations for AB and AA stacked bilayer graphene in order to elimi…
Twist, as a simple and unique degree of freedom, could lead to enormous novel quantum phenomena in bilayer graphene. A small rotation angle introduces low-energy van Hove singularities (VHSs) approaching the Fermi level, which result in unusual correlated states in the bilayer graphene. It is reasonable to expect that the twist could also affect the electronic properties of few-layer graphene dramatically. However, such an issue has remained experimentally elusive. Here, by using scanning tunneling microscopy/spectroscopy (STM/STS), we systematically studied a twisted trilayer graphene (TTG) w…
We probe the local inhomogeneities in the electronic properties of exfoliated graphene due to the presence of charged impurities in the SiO2 substrate using a combined scanning tunneling and electrostatic force microscope. Contact potential difference measurements using electrostatic force microscopy permit us to obtain the average charge density but it does not provide enough resolution to identify individual charges. We find that the tunneling current decay constant, which is related to the local tunneling barrier height, enables one to probe the electronic properties of graphene distorted a…
We study an epitaxial graphene monolayer with bilayer inclusions via magnetotransport measurements and scanning gate microscopy at low temperatures. We find that bilayer inclusions can be metallic or insulating depending on the initial and gated carrier density. The metallic bilayers act as equipotential shorts for edge currents, while closely spaced insulating bilayers guide the flow of electrons in the monolayer constriction, which was locally gated using a scanning gate probe.
Molecular and atomic imaging required the development of electron and scanning probe microscopies to surpass the physical limits dictated by diffraction. Nano-infrared experiments and pico-cavity tip-enhanced Raman spectroscopy imaging later demonstrated that radiation in the visible range can surpass this limit by using scanning probe tips to access the near-field regime. Here we show that ultimate resolution can be obtained by using scanning microwave imaging microscopy to reveal structures with feature sizes down to 1~nm using a radiation of 0.1~m in wavelength. As a test material we use tw…
We probe the local inhomogeneities of the electronic properties of graphene at the nanoscale using scanning probe microscopy techniques. First, we focus on the study of the electronic inhomogeneities caused by the graphene-substrate interaction in graphene samples exfoliated on silicon oxide. We find that charged impurities, present in the graphene-substrate interface, perturb the carrier density significantly and alter the electronic properties of graphene. This finding helps to understand the observed device-to-device variation typically observed in graphene-based electronic devices. Second,…
Self-assembled monolayers (SAMs) of organic molecules are widely employed in surface chemistry and biology, and serve as ultra-fine lithographic resists. Due to their small thickness of only a few nanometers, the analysis of patterned monolayer surfaces using conventional methods requires thorough point-by-point scanning using complicated equipment. In the work reported herein, patterned monolayers are simply and directly observed using a bright-field optical microscope. The monolayers modify the spectral reflectivity pattern of a silica-on-silicon thin film, and introduce a contrast between b…
Graphite crystals used to prepare graphene-based heterostructures are generally assumed to be defect free. We report here scanning tunneling microscopy results that show graphite commonly used to prepare graphene devices can contain a significant amount of native defects. Extensive scanning of the surface allows us to determine the concentration of native defects to be 6.6$\times$10$^8$ cm$^{-2}$. We further study the effects of these native defects on the electronic properties of Bernal-stacked bilayer graphene. We observe gate-dependent intravalley scattering and successfully compare our exp…
In bilayer systems electron-hole (e-h) pairs with spatially separated components (i.e., with electrons in one layer and holes in the other) can be condensed to a superfluid state when the temperature is lowered. This article deals with the influence of randomly distributed inhomogeneities on the superfluid properties of such bilayer systems in a strong perpendicular magnetic field. Ionized impurities and roughenings of the conducting layers are shown to decrease the superfluid current density of the e-h pairs. When the interlayer distance is smaller than or close to the magnetic length, the fl…
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of one-dimensional nanomaterials offers the lateral stacking offset as an additional parameter for modulating the resulting material properties. Here, we report that the edge states of twisted bilayer zigzag graphene nanoribbons (TBZGNRs) can be tuned with both the twist angle and the stacking offset. Strong edge state variations in the stacking region are first reve…
Doping twisted bilayer graphene away from charge neutrality leads to an enormous buildup of charge inhomogeneities within each Moiré unit cell. Here we show, using unbiased real-space self-consistent Hartree calculations on a relaxed lattice, that Coulomb interactions smoothen this charge imbalance by changing the occupation of earlier identified `ring' orbitals in the AB/BA region and `center' orbitals at the AA region. For hole doping, this implies an increase of the energy of the states at the ${\bf Γ}$ point, leading to a further flattening of the flat bands and a pinning of the Van Hove s…
A perpendicular electric field breaks the layer symmetry of Bernal-stacked bilayer graphene, resulting in the opening of a band gap and a modification of the effective mass of the charge carriers. Using scanning tunneling microscopy and spectroscopy, we examine standing waves in the local density of states of bilayer graphene formed by scattering from a bilayer/trilayer boundary. The quasiparticle interference properties are controlled by the bilayer graphene band structure, allowing a direct local probe of the evolution of the band structure of bilayer graphene as a function of electric field…
We have mapped the Dirac point in exfoliated monolayer and bilayer graphene using spatially resolved scanning tunneling spectroscopy (STS) measurements at low temperature. The Dirac point shifts in energy at different locations in graphene. However, a cross correlation with the topography shows no correlation indicating that topographic features such as ripples are not the primary source of the variation. Rather, we attribute the shift of the Dirac point to random charged impurities located near the graphene. Our findings emphasize the need to advance exfoliated graphene sample preparation to …
Scanning tunneling spectroscopy at very low temperature on homogeneously disordered superconducting Titanium Nitride thin films reveals strong spatial inhomogeneities of the superconducting gap $Δ$ in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature $T_c$ towards zero, enhancement of spatial fluctuations in $Δ$, and growth of the $Δ/T_c$ ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.
We investigate the atomic-scale tunneling characteristics of bilayer graphene on silicon carbide using the scanning tunneling microscopy. The high-resolution tunneling spectroscopy reveals an unexpected negative differential resistance (NDR) at the Dirac energy, which spatially varies within the single unit cell of bilayer graphene. The origin of NDR is explained by two near-gap van Hove singularities emerging in the electronic spectrum of bilayer graphene under a transverse electric field, which are strongly localized on two sublattices in different layers. Furthermore, defects near the tunne…
Nanoscale electronic transport gives rise to a number of intriguing physical phenomena that are accompanied by distinct spatial patterns of current flow. Here, we report on sensitive magnetic imaging of two-dimensional current distributions in bilayer graphene at room temperature. By combining dynamical modulation of the source-drain current with ac quantum sensing of a nitrogen-vacancy center in a diamond probe, we acquire magnetic field and current density maps with excellent sensitivities of 4.6 nT and 20 nA/$μ$m, respectively. The spatial resolution is 50-100 nm. We further introduce a set…
Charge carriers in bilayer graphene occupy two parabolic continua of electron-like and hole-like states which differ by the alignment between carrier pseudospin and its momentum, the property known as chirality. Due to chirality conservation, a strong confining potential can host unusual bound states: electron levels cloaked into the hole continuum. The energy levels and the wave functions of the cloaked states can be obtained by solving the Schrödinger equation for a massive non-chiral particle in the p-wave channel in two dimensions. Eventually, cloaked states slowly decay into the continuum…
The interlayer coupling of twisted bilayer graphene could markedly affect its electronic band structure. A current challenge required to overcome in experiment is how to precisely control the coupling and therefore tune the electronic properties of the bilayer graphene. Here, we describe a facile method to modulate the local interlayer coupling by adsorption of single molecule magnets onto the twisted bilayer graphene and report the characterization of its electronic band structure using scanning tunneling microscopy and spectroscopy. The low-energy Van Hove singularities (VHSs) and superlatti…
Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHS…
We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2x1:H surface. Room temperature, ultra-high vacuum (UHV) tunnelling spectroscopy measurements of nanometer-sized single-layer graphene reveal a size dependent energy gap ranging from 0.1-1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunnelling microscopy (STM) topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nano…
We theoretically propose to directly observe the chiral nature of charge carriers in graphene mono- and bilayers within a controlled scattering experiment. The charge located on a capacitively coupled scanning probe microscope (SPM) tip acts as a scattering center with controllable position on the graphene sheet. Unambiguous features from the chirality of the particles in single and bilayer graphene arise in the ballistic transport in the presence of such a scattering center. To theoretically model the scattering from the smooth potential created by the SPM tip, we develop the scattering forma…
Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bila…
Developing van der Waals (vdW) homojunction devices requires materials with narrow bandgaps and simultaneously high hole and electron mobilities for bipolar transport, as well as methods to image and study spatial variations in carrier type and associated conductivity with nanometer spatial resolution. Here we demonstrate the general capability of near-field scanning microwave microscopy (SMM) to image and study the local carrier type and associated conductivity in operando by studying ambiploar field effect transistors (FETs) of the 1D vdW material tellurium in 2D form. To quantitatively unde…
The AB-BA domain wall in gapped graphene bilayers is a rare naked structure hosting topological electronic states. Here we show, for the first time, direct imaging of its topological edge states by using scanning tunneling microscope. The simultaneously obtained atomic-resolution images of the domain wall provide us unprecedented opportunities to measure the spatially-varying edge states within it. The one-dimensional conducting channels are observed to be mainly located around the two edges of the domain wall, which is reproduced quite well by our theoretical calculations. Our experiment furt…
Bilayer graphene contains, compared to graphene monolayer, an additional graphene sheet and, therefore, extra degrees of freedom, making it a unique system for complex electronic states to emerge. Here, we show that there are two types of domain walls, i.e., coupling domain wall and potential domain wall, in gapped graphene bilayers, which make microscopic electronic properties of the bilayers varying spatially. The coupling domain wall separates two graphene bilayer regions with different interlayer coupling strengths and the potential domain wall is a boundary separating two adjacent regions…
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monola…
We report on microscopic measurements of the low-energy electronic structures both at zigzag and armchair edges of bilayer graphene using scanning tunneling microscopy and spectroscopy (STM and STS). We have found that, both in the absence and in the presence of a magnetic field, an almost zero-energy peak in density of states was localized at zigzag edges, as expected for the surface states at zigzag edges of bilayer graphene. In the quantum Hall regime, we have observed clearly Landau levels bending away from the charge neutrality point near both the zigzag and armchair edges. Such a result …
Graphene, as an atomic-thick ultrasoft membrane, almost has no resistance against out-of-plane deformations and, therefore, it is always wrinkled to a certain degree. Recently, corrugated structures and their effects on the electronic properties of monolayer graphene have been studied extensively. However, similar experimental studies in bilayer graphene have yet to be reported. Here, we show that corrugations in bilayer graphene can generate incommensurate stacking solitons (domain walls) between commensurate Bernal-stacked domains. By using scanning tunneling microscopy, we microscopically s…
Plasma enhanced chemical vapor deposition (PECVD) techniques have been shown to be an efficient method to achieve single-step synthesis of high-quality monolayer graphene (MLG) without the need of active heating. Here we report PECVD-growth of single-crystalline hexagonal bilayer graphene (BLG) flakes and mm-size BLG films with the interlayer twist angle controlled by the growth parameters. The twist angle has been determined by three experimental approaches, including direct measurement of the relative orientation of crystalline edges between two stacked monolayers by scanning electron micros…
Graphene hybrid planar structures consisting of two regions with different quantum Hall (QH) states exhibit unusual transport properties1-5, originating from chiral edge states equilibration at the interface of the two different regions6. Here we present a sub-nanometre-resolved scanning tunnelling microscopy (STM) and spectroscopy (STS) study of a monolayer-bilayer graphene planar junction in the QH regime. The atomically well-defined interface of such a junction allows us to spatially resolve the interface electronic properties. Around the interface, we detect Landau quantization of massless…
Influence of a nonmagnetic surface on the density of states in a spin-split superconductor, which is realized on the basis of a S/F bilayer, is investigated. It is demonstrated that if the ferromagnet magnetization has a defect in the form of a domain wall in the vicinity of the surface, the superconducting density of states is reconstructed manifesting the spin-split Andreev resonances. Formation of these resonances is not connected to any superconducting order parameter inhomogeneities. Andreev reflection processes forming the resonances occur at the inhomogeneity of the spin-split gap gener…
We have used scanning gate microscopy to explore the local conductivity of a current-annealed graphene flake. A map of the local neutrality point (NP) after annealing at low current density exhibits micron-sized inhomogeneities. Broadening of the local e-h transition is also correlated with the inhomogeneity of the NP. Annealing at higher current density reduces the NP inhomogeneity, but we still observe some asymmetry in the e-h conduction. We attribute this to a hole doped domain close to one of the metal contacts combined with underlying striations in the local NP.
By combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy we reveal the structural and electronic properties of multilayer graphene on Ru(0001). We prove that large ethylene exposure allows to synthesize two distinct phases of bilayer graphene with different properties. The first phase has Bernal AB stacking with respect to the first graphene layer, displays weak vertical interaction and electron doping. The long-range ordered moiré pattern modulates the crystal potential and induces replicas of the Dirac cone and minigaps. The second phase has AA stacking sequen…
Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene (TBG) have been intensely studied. At small twist angle $θ$, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride (hBN), which we use as a TBG substrate, is …
The methods for realizing of non-Abelian gauge potentials have been proposed in many different systems in condensed matter1-5. The simplest realization among them may be in a graphene bilayer obtained by slightly relative rotation between the two layers4. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunnelling microscopy and spectroscopy. At a magic twisted angle, theta ~ (1.11+/-0.05)deg, a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, are observed in the tunnelling de…
We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photo-thermoelectric effect. Consistent with the photocurrent study, infrared nano-imaging experiments reveal optical conductivity features dominated by twist-angle dependent interband transitions. Our results p…
Recent studies show that two low-energy Van Hove singularities (VHSs) seen as two pronounced peaks in the density of states (DOS) could be induced in twisted graphene bilayer. Here, we report angle dependent VHSs of slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows \DeltaEvhs ~ \hbarνF\DeltaK between 1.0^{\circ} and 3.0^{\circ} (here νF ~ 1.1\times106 m/s is the Fermi velocity of monolayer graphene, \DeltaK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bi…
Artificially twisted heterostructures of semiconducting transition metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural reconstruction. Here we study twisted MoS2 bilayers in a wide range of twist angles near 0° using Scanning Tunneling Microscopy/Spectroscopy. We investigate the twist angle-dependence of the moiré pattern which is dominated by lattice reconstruction for small angles (<2°) leading to large triangular domains with rhombohedral stacking. Local spectroscopy measur…
We have performed an \it {ab initio} investigation of transition metals (TMs = Mo, Ru, Co, and Pt) embedded in twisted bilayer graphene (tBG) layers. Our total energy results reveal that, triggered by the misalignment between the graphene layers, Mo and Ru atoms may form a quasi-periodic (triangular) array of intercalated atoms. In contrast, the formation of those structures is not expected for the other TMs, Co and Pt atoms. The net magnetic moment (m) of Mo and Ru atoms may be quenched upon intercalation, depending on the stacking region (AA or AB). For instance, we find a magnetic moment of…
We report scanning tunneling microscopy (STM) and spectroscopy (STS) of twisted graphene bilayer on SiC substrate. For twist angle ~ 4.5o the Dirac point ED is located about 0.40 eV below the Fermi level EF due to the electron doping at the graphene/SiC interface. We observed an unexpected result that the local Dirac point around a nanoscaled defect shifts towards the Fermi energy during the STS measurements (with a time scale about 100 seconds). This behavior was attributed to the decoupling between the twisted graphene and the substrate during the measurements, which lowers the carrier densi…
Scanning tunneling microscopy (STM) images are obtained for the first time on few layer and twisted multilayer epitaxial graphene states synthesized on n+ 6H-SiC a-plane non-polar surface. The twisted graphene is determined to have a rotation angle of 5.4° between the top two layers, by comparing moiré patterns from stick and ball models of bilayer graphene to experimentally obtained images. Furthermore, the experimental moiré pattern shows dynamic behavior, continuously shuffling between two stable surface arrangements one bond length apart. The moiré pattern shifts by more than 1 nm, making …
In twisted bilayer graphene (TBG), a twist-angle-dependent competition between interlayer stacking energy and intralayer elastic energy results in flat rigid layers at large twist angles and lattice reconstruction at small twist angles. Despite enormous scientific interest and effort in the TBG, however, an experimental study of evolution from the rigid lattice to the reconstructed lattice as a function of twist angle is still missing. Here we present a scanning tunneling microscopy and spectroscopy study to reveal the twist-angle-dependent lattice reconstruction in the TBG. Our experiment dem…
Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of QD states determines the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment, all of which are relevant for quantum information processing. Despite its importance, the shape of BLG QD states remains experimentally unexamined. Here we report direct visualization of BLG QD states by using a scanning …
The creation of van der Waals heterostructures based on a graphene monolayer and other two-dimensional crystals has attracted great interest because atomic registry of the two-dimensional crystals can modify the electronic spectra and properties of graphene. Twisted graphene bilayer can be viewed as a special van der Waals structure composed of two mutual misoriented graphene layers, where the sublayer graphene not only plays the role of a substrate, but also acts as an equivalent role as the top graphene layer in the structure. Here we report the electronic spectra of slightly twisted graphen…
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs and cause semiconductor-metal tr…
We show that Friedel charge oscillation near an interface opens a gap at the Fermi energy for electrons with wave vectors perpendicular to the interface. If the Friedel gaps on two sides of the interface are different, a nonequlibrium effect - shifting of these gaps under bias - leads to asymmetric transport upon reversing the bias polarity. The predicted transport asymmetry is revealed by scanning tunneling potentiometry at monolayer-bilayer interfaces in epitaxial graphene on SiC (0001). This intriguing interfacial transport behavior opens a new avenue towards novel quantum functions such as…
