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The electronic density of states of two-dimensional (2D) Au quantum dot superlattice are explored by using cryogenic scanning tunneling microscopy and scanning tunneling spectroscopy. The 2D Au superlattice opens up a gap in its electronic density of states. The single-electron transfer of a single Au quantum dot can be effectively inhibited by this “artificial” forbidden gap. This finding opens a route toward modulating electronic energy band of solid on the basis of 2D metal quantum dot superlattice, which may generate materials with electronic properties for possible future electronic devices. [ABSTRACT FROM AUTHOR]

The electronic local density of states of a single Co3O4 semiconductor nanowire with the diameter of 3 nm is explored using low-temperature scanning tunneling microscopy and spectroscopy. The energy gap between the conduction band and valence band of the nanowire is about 1.7 eV, which is slightly enhanced compared to the bulk value, ∼1.5 eV, due to the quantum confinement effect. Two surface states are observed locating near the Fermi level in the band gap. [ABSTRACT FROM AUTHOR]

Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ ≈ (1.11 ± 0.05)°, a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δE ≈ νF/D ≈ 70 meV (here νF is the Fermi velocity of graphene and D is the period of the moir'e patterns). This indicates that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the moiré patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 106 m/s to zero by simply reducing the twisted angle of about 2°. [ABSTRACT FROM AUTHOR]

Electronic properties of surface areas decoupled from graphite are studied using scanning tunneling microscopy and spectroscopy. We show that it is possible to identify the decoupled graphene monolayer, the Bernal bilayer, and the Bernal trilayer on a graphite substrate according to their tunneling spectra in a high magnetic field. The decoupled monolayer and bilayer exhibit Landau quantization of massless and massive Dirac fermions, respectively. The substrate generates a sizable band gap ~35 meV in the Bernal bilayer, therefore, the eightfold degenerate Landau level at the charge neutrality point is split into two valley-polarized quartets polarized on each layer. In the decoupled Bernal trilayer, we find that both massless and massive Dirac fermions coexist and its low-energy band structure can be described quite well by taking into account only the nearest-neighbor intra- and interlayer hopping parameters. A strong correlation between the Fermi velocity of the massless Dirac fermions and the effective mass of the massive Dirac fermions is observed in the graphene trilayer. Our result demonstrates that the surface of graphite provides a natural ideal platform to probe the electronic spectra of graphene layers. [ABSTRACT FROM AUTHOR]

Recently, rhombohedral trilayer graphene (r-TLG) has attracted much attention because of its low-energy flat bands, which are predicted to result in many strongly correlated phenomena. However, there has been a need for more experimental evidence for these flat bands in the r-TLG, since the supporting substrates usually have strong destructive effects on the low-energy band structure of graphene systems. Here, we demonstrate that it is possible to directly probe the stacking order and electronic spectrum of the r-TLG on a graphite surface with scanning tunneling microscopy around a monoatomic step edge of the top graphene layer. The tunneling spectra of the r-TLG exhibit four adjacent peaks, which are generated by the low-energy flat bands, flanking the charge neutrality point. Based on these spectra, the true energy gap and the energy gap at the K point of the r-TLG are determined as about 9 and 23 meV, respectively. The observed features are well reproduced by a low-energy effective Hamiltonian. [ABSTRACT FROM AUTHOR]

The creation of van der Waals heterostructures based on a graphene monolayer and other two-dimensional crystals has attracted great interest because the atomic registry of the two-dimensional crystals can modify the electronic spectra and properties of graphene. A twisted graphene bilayer can be viewed as a special van der Waals structure composed of two mutually misoriented graphene layers, where the sublayer graphene not only plays the role of a substrate, but also acts in an equivalent role as the top graphene layer in the structure. Here we report the electronic spectra of slightly twisted graphene bilayers studied by scanning tunneling microscopy and spectroscopy. Our experiment demonstrates that twist-induced van Hove singularities are ubiquitously present for rotation angles θ of less than about 3.5∘ , corresponding to moiré -pattern periods D longer than 4 nm. However, they totally vanish for θ>5.5 ∘ (D < 2.5 nm). Such a behavior indicates that the continuum models, which capture moiré-pattern periodicity more accurately at small rotation angles, are no longer applicable at large rotation angles. [ABSTRACT FROM AUTHOR]

Despite the fact that structures and properties of tilt grain boundaries of graphite surface and graphene have been extensively studied, their effect on the structures and electronic spectra of graphene layers has not been fully addressed. Here we study effects of one-dimensional tilt grain boundaries on structures and electronic spectra of graphene multilayers by scanning tunneling microscopy and spectroscopy. A tilt grain boundary of a top graphene sheet in graphene multilayers leads to a twist between consecutive layers and generates superstructures (Moiré patterns) on one side of the boundary. Our results demonstrate that the twisting changes the electronic spectra of Bernal graphene bilayer and graphene trilayers dramatically. We also study quantum-confined twisted graphene bilayer generated between two adjacent tilt grain boundaries and find that the band structure of such a system is still valid even when the number of superstructures is reduced to two in one direction. It implies that the electronic structure of this system is driven by the physics of a single Moiré spot. [ABSTRACT FROM AUTHOR]

Physical properties of two-dimensional van der Waals (vdWs) structures depend sensitively on both stacking orders and interlayer interactions. Yet, in most cases studied to date, the interlayer interaction is considered to be a "static" property of the vdWs structures. Here we demonstrate that applying a scanning tunneling microscopy (STM) tip pulse on twisted bilayer graphene (TBG) can induce sub-Ångstrom fluctuations of the interlayer separation in the TBG, which are equivalent to dynamic vertical external pressure of about 10 GPa on the TBG. The sub-Ångstrom fluctuations of the interlayer separation result in large oscillations of the energy separations between two van Hove singularities (VHSs) in the TBG. The period of the oscillations of the VHSs spacing is extremely long, about 500-1000 sec, attributing to tip-induced local stress in the atomic-thick TBG. Our result provides an efficient method to tune and measure the physical properties of the vdWs structures dynamically. [ABSTRACT FROM AUTHOR]

Theoretical research has predicted that a ripple of graphene generates an effective gauge field on its low-energy electronic structure and could lead to Landau quantization. Here, we demonstrate using a combination of an experimental method (scanning tunneling microscopy) and a theoretical approach (tight-binding approximation) that Landau levels will form when the effective pseudomagnetic flux per ripple Φ~(h²/la)Φ0 is larger than the flux quantum Φ0 (here, h is the height, l is the width of the ripple, and a is the nearest C-C bond length). The strain-induced gauge field in the ripple only results in one-dimensional (1D) Landau-level quantization along the ripple. Such 1D Landau quantization does not exist in two-dimensional systems in an external magnetic field. Its existence offers a unique opportunity to realize interesting electronic properties in strained graphene. [ABSTRACT FROM AUTHOR]

Recent studies show that periodic potentials can generate superlattice Dirac points at energies ±ħvF G 2 in graphene (where ħ is the reduced Planck constant, vp is the Fermi velocity of graphene, and G is the reciprocal superlattice vector). Here, we perform scanning tunneling microscopy and spectroscopy studies of a corrugated graphene monolayer on Rh foil. We show that the quasiperiodic ripples of nanometer wavelength in the corrugated graphene give rise to weak one-dimensional electronic potentials and thereby lead to the emergence of the superlattice Dirac points. The position of the superlattice Dirac point is space dependent and shows a wide distribution of values. We demonstrate that the space-dependent superlattice Dirac points are closely related to the space-dependent Fermi velocity, which may arise from the effect of the local strain and the strong electron-electron interaction in the corrugated graphene. [ABSTRACT FROM AUTHOR]

Recent studies show that two low-energy van Hove singularities (VHSs) seen as two pronounced peaks in the density of states could be induced in a twisted graphene bilayer. Here, we report angle-dependent VHSs of a slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows ΔEvhs ~ hvFΔK between 1.0° and 3.0° [here vF ~1.l X 106 m/s is the Fermi velocity of monolayer graphene, and ΔK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer]. This result indicates that the rotation angle between graphene sheets does not result in a significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle θ ~ 1.3°, the observed ΔEvhs ~ 0.11 eV is much smaller than the expected value hvFΔK ~ 0.28 eV at 1.3°. The origin of the reduction of ΔEvhs at 1.3° is discussed. [ABSTRACT FROM AUTHOR]

Using cryogenic scanning tunneling microscopy and scanning tunneling spectroscopy+ single-electron tunneling of Au nanoparticles (NPs) with 1.4 nm in radius was studied. We observe a gap ΔV ~ 2e/C (C is the capacitance of the Au particle and e the charge of an electron) around zero bias in the tunneling-conductancc spectrum, followed by a series of discrete single-electron tunneling peaks with peak spacing of EC ~ e/C at both negative and positive bias. Experimental data are well explained by taking into account both the shift o1 conductance peaks and the effect of exchange interaction of electrons on the single-electron tunneling of Au NPs. A conductance peak near zero bias was suppressed by the exchange-type zero-bias anomaly, which results in the gap Δ V ~ 2EC. According to our experiment and analysis, the shift of conductance peaks of Au NPs is attributed to self-biased gate and/or tip-induced gate. [ABSTRACT FROM AUTHOR]

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θc. Experimentally, the θc is demonstrated to be very close to the magic angle (θ≈1.08°). Here we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunneling microscopy (STM). Our experiment demonstrates that both structures are stable in the TBG around the magic angle. By using a STM tip, we show that the two structures can be changed to each other and a triangular network of chiral one-dimensional states hosted by domain boundaries can be switched on and off. Consequently, the bandwidth of the flat band, which plays a vital role in the emergent strongly correlated states in the magic angle TBG, is tuned. This provides an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle. [ABSTRACT FROM AUTHOR]

Berry phase, the geometric phase accumulated over a closed loop in parameter space during an adiabatic cyclic evolution, has been demonstrated to play an important role in many quantum systems since its discovery. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2π, which offers a unique opportunity to explore the tunable Berry phase on physical phenomena. Here, we report experimental observation of Berry-phase-induced valley splitting and crossing in movable bilayer-graphene p-n junction resonators. In our experiment, the resonators are generated by combining the electric field of a scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2π continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer-graphene resonators can be used to manipulate the valley degree of freedom in valleytronics. [ABSTRACT FROM AUTHOR]

ABC-stacked trilayer graphene (TLG) was predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat bands near the charge neutrality point. Here, using high-magnetic-field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG on graphite. We observe an approximately linear magnetic-field scaling of valley splitting and spin splitting in the ABC-stacked TLG. Our experiment indicates that the spin splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the spin splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlated effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields. [ABSTRACT FROM AUTHOR]

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) with two different small twist angles between adjacent layers. Two sets of VHSs, originating from the two twist angles, were observed in the TTG, indicating that the TTG could be simply regarded as a combination of two different twisted bilayers of graphene. By using high-resolution STS, we observed a split of the VHSs and directly imaged the spatial symmetry breaking of electronic states around the VHSs. These results suggest that electron-electron interactions play an important role in affecting the electronic properties of graphene systems with low-energy VHSs. [ABSTRACT FROM AUTHOR]

Finite-size twisted bilayer graphene (TBG, where here the TBG is of nanoscale size) is quite unstable and will change its structure to a Bernal (or AB-stacking) bilayer with a much lower energy. Therefore, the lack of finite-size TBG makes its electronic properties difficult to access in experiments. In this paper, 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 to 0 nm. By using scanning tunneling microscopy, we study carefully the structure and the electronic properties of finite-size TBG. Our results indicate that the low-energy electronic properties, including twist-induced Van Hove singularities (VHSs) and spatial modulation of the local density of states, are strongly affected by the translational symmetry breaking of the finite-size TBG. However, the electronic properties above the energy of the VHSs are almost not influenced by quantum confinement even when the width of the TBG is reduced to only a single moiré spot. [ABSTRACT FROM AUTHOR]

Considerable efforts have been made to trap massless Dirac fermions in a graphene monolayer, but only quasibound states have been realized in continuous graphene sheets up to now. Here, we demonstrate the realization of bound states in nanoscale graphene quantum dots (GQDs) in a continuous graphene sheet. The GQDs are electronically isolated from the surrounding continuous graphene sheet by circular boundaries, which are generated by strong coupling between graphene and the substrate. By using scanning tunneling microscopy (STM), we observe single-electron charging states of the GQDs, seen as Coulomb oscillations in the tunneling conductance. The evolution of single-electron tunneling of the GQDs between the Coulomb blockade regime and the Coulomb staircase regime is observed by tuning the STM tip-sample distances. Spatial maps of the local electronic densities reveal concentric rings inside the GQDs with each ring corresponding to a single Coulomb oscillation of the tunneling spectra. These results indicate explicitly that the electrons are completely trapped inside the nanoscale GQDs. [ABSTRACT FROM AUTHOR]

Pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism. Theoretically, the π magnetism induced by the monovacancy in graphene is characteristic of two spin-split density-of-states (DOS) peaks close to the Dirac point. Since its prediction, many experiments have attempted to study this π magnetism in graphene, whereas only a notable resonance peak has been observed around the atomic defects, leaving the π magnetism experimentally elusive. Here, we report direct experimental evidence of π magnetism by using a scanning tunneling microscope. We demonstrate that the localized state of the atomic defects is split into two DOS peaks with energy separations of several tens of meV. Strong magnetic fields further increase the energy separations of the two spin-polarized peaks and lead to a Zeeman-like splitting. Unexpectedly, the effective g factor around the atomic defect is measured to be about 40, which is about 20 times larger than the g factor for electron spins. [ABSTRACT FROM AUTHOR]

To generate a moderate band gap in a graphene monolayer is a very important but rather difficult task. A rare working solution of this problem is to cut it into one-dimensional (1D) nanometer-wide ribbons. Here we show that, instead of cutting the graphene monolayer, a wide band gap can be created in a unique 1D strained structure, i.e., a wrinkled graphene-nanoribbon-like (GNR-like) structure, of a continuous graphene sheet via strong hybridization between the graphene and the metal substrate. The wrinkled GNR-like structures with widths of only a few nanometers are observed in a continuous graphene sheet grown on a Rh foil by using thermal strain engineering. Spatially resolved scanning tunneling spectroscopy revealed a band-gap opening of a few hundred meV in the GNR-like structure in an otherwise continuous metallic graphene sheet, directly demonstrating the realization of a metallic-semiconducting-metallic junction entirely in a graphene monolayer. [ABSTRACT FROM AUTHOR]

The wave function of Dirac fermions is a two-component spinor. In graphene, a one-atom-thick film showing two-dimensional Dirac-like electronic excitations, the two-component representation, reflects the amplitude of the electron wave function on the A and B sublattices. This unique property provides unprecedented opportunities to image the two components of Dirac fermions spatially. Here, we report atomic resolution imaging of two-component Dirac-Landau levels in gapped graphene monolayers by scanning tunneling microscopy and spectroscopy. A gap of about 20 meV, driven by inversion symmetry breaking by the substrate potential, is observed in the graphene sheets on both SiC and graphite substrates. Such a gap splits the n=0 Landau level (LL) into two levels, 0+ and 0-. We demonstrate that the amplitude of the wave function of the 0+ LL is mainly on the A sites and that of the 0- LL is mainly on the B sites of graphene, characterizing the internal structure of the spinor of the n=0 LL. This provides direct evidence of the two-component nature of Dirac fermions. [ABSTRACT FROM AUTHOR]