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The stacked two layered materials with a lattice constant mismatch and/or with twist angle relative to each other can create a moir\'e pattern, modulating the electronic properties of the pristine materials. Here, we combine scanning tunneling microscopy/spectroscopy and density functional theory calculations to investigate the moir\'e potential induced bandgap tuning in InSe/CuSe vertical heterostructure synthesized by a two-step of molecular beam epitaxy. Scanning tunneling microscopy measurements demonstrate the heterostructure with a superlattice periodicity of ~3.48nm and a twist angle of about 11{\deg} between the monolayers. Scanning tunneling spectroscopy record on the different stacking sites of the heterostructure reveals the bandgap of the InSe is location-dependent and a variation of 400 meV is observed. Density functional theory calculations reveal that the moir\'e-induce electric dipole in the monolayer InSe is the key factor for tuning the bandgap. Besides, charge transfer between CuSe and InSe also contributes to the bandgap variation due to its stacking related. We also show that the moir\'e potential not only can tune the bandgap of InSe but also can vanish the Dirac nodal line of CuSe in some stackings. Our explorations provide valuable information in understanding the electronic properties of the twodimensional moir\'e materials., Comment: Accepted for publication in Appl. Phys. Lett

Monolayer PbSe has been predicted to be a two-dimensional (2D) topological crystalline insulator (TCI) with crystalline symmetry-protected Dirac-cone-like edge states. Recently, few-layered epitaxial PbSe has been grown on the SrTiO

As a two-dimensional semiconductor with many physical properties, including, notably, layer-controlled electronic bandgap and coupled spin-valley degree of freedom, monolayer MoSe2 is a strong candidate material for next-generation opto- and valley-electronic devices. However, due to substrate effects such as lattice mismatch and dielectric screening, preserving the monolayer's intrinsic properties remains challenging. This issue is generally significant for metallic substrates whose active surfaces are commonly utilized to achieve direct chemical or physical vapor growth of the monolayer films. Here, we demonstrate high-temperature-annealed Au foil with well-defined (100) facets as a weakly interacting substrate for atmospheric pressure chemical vapor deposition of highly crystalline monolayer MoSe2. Low-temperature scanning tunneling microscopy/spectroscopy measurements reveal a honeycomb structure of MoSe2 with a quasi-particle bandgap of 1.96 eV, a value comparable with other weakly interacting systems such as MoSe2/graphite. Density functional theory calculations indicate that the Au(100) surface exhibits the preferred energetics to electronically decouple from MoSe2, compared with the (110) and (111) crystal planes. This weak coupling is critical for the easy transfer of monolayers to another host substrate. Our study demonstrates a practical means to produce high-quality monolayers of transition-metal dichalcogenides, viable for both fundamental and application studies.

Low-energy moir\'e flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moir\'e flat bands of tBG are based on the extended structures, i.e., the moir\'e patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moir\'e patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of a magic-angle tBG near the sample terminated edge and report a direct observation of breakdown of the moir\'e flat bands. We show that the moir\'e electronic structures, including the low-energy flat bands, can sufficiently exist in a complete moir\'e spot, i.e., a moir\'e supercell, right at the edge even the translational symmetry of the moir\'e patterns is broken in one direction. However, the flat-band characteristic is obviously absent in the incomplete moir\'e spots that are partly terminated by the edge. Our results indicate that a whole moir\'e spot is sufficient and indispensable for the generation of the effective moir\'e flat bands in tBG., Comment: 14 pages, 3 figures

Flat electronic bands with tunable structures offer opportunities for the exploitation and manipulation of exotic interacting quantum states. Here, we present a controllable route to construct easily tunable flat bands in folded graphene, by nano origami-controlled strain engineering, and discover correlated states in this system. Via tearing and folding graphene monolayer at arbitrary step edges with scanning tunneling microscope manipulation, we create strain-induced pseudo-magnetic fields as well as resulting flat electronic bands in the curved edges of folded graphene. We show that the intensity of the pseudo-magnetic field can be readily tuned by changing the width of the folding edge due to the edge-width-dependent lattice deformation, leading to the well adjustability of the geometry of flat bands in folded graphene. Furthermore, by creating expected dispersionless flat bands using this technique, the correlation-induced splits of flat bands are successfully observed in the density of states when these bands are partially filled. Our experiment provides a feasible and effective pathway to engineer the system with tunable flat band structures, and establishes a new platform that can be used to realize devisable strain and interaction induced quantum phases., 18 pages, 4 figures

The transition metal dichalcogenide (TMD)-metal interfaces constitute an active part of TMD-based electronic devices with optimized performances. Despite their decisive role, current strategies for nanoscale electronic tuning remain limited. Here, we demonstrate electronic tuning in the WSe

Graphene nanostructures with specified edge terminations has attracted considerable attention owing to their unique electronic properties induced by the edges. However, an efficient way to controllably fabricate such nanostructures is still highly desired. Here, we show that graphene nanostructures with zigzag edge terminations can be easily and efficiently constructed at room-temperature by tip manipulation of a scanning tunneling microscope (STM). Though intentionally increasing the tip-graphene interaction, we controllably tear and fold graphene sheets against step edges and successfully fabricate nanoscale graphene islands such as quantum dots and nanoribbon-like structures on graphite. Interestingly, the tearing directions are found to mainly along the zigzag orientations of graphene hexagonal lattice, leading to the generated graphene nanostructures possessing the same specified edges with well zigzag terminations. Theoretical modelling demonstrates that the enhanced tip-graphene repulsive force can account for the tearing and folding processes, whereas the preferential zigzag-tearing is attributed to the predicted lowest bond-breaking energy of the zigzag orientation in graphene. Our experiment provides a simple and controllable method for fabrication of graphene nanostructures with precise zigzag edge terminations. The obtained zigzag-edge-terminated graphene nanostructures also provide a platform for engineering novel quantum properties.

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Two-dimensional (2D) semiconductors, such as lead selenide (PbSe), locate at the key position of next-generation devices. However, the ultrathin PbSe is still rarely reported experimentally, particularly on metal substrates. Here, we report the ultrathin PbSe synthesized via sequential molecular beam epitaxy on Ag(111). The scanning tunneling microscopy is used to resolve the atomic structure and confirms the selective formation of ultrathin PbSe through the reaction between Ag5Se2 and Pb, as further evidenced by the theoretical calculation. It is also found that the increased accumulation of Pb leads to the improved quality of PbSe with larger and more uniform films. The detailed analysis demonstrates the bilayer structure of synthesized PbSe, which could be deemed to achieve the 2D limit. The differential conductance spectrum reveals a metallic feature of the PbSe film, indicating a certain interaction between PbSe and Ag(111). Moreover, the moiré pattern originated from the lattice mismatch between PbSe and Ag(111) is observed, and this moiré system provides the opportunity for studying physics under periodical modulation and for device applications. Our work illustrates a pathway to selectively synthesize ultrathin PbSe on metal surfaces and suggests a 2D experimental platform to explore PbSe-based opto-electronic and thermoelectric phenomena.

Germanene has attracted much attention because the material was predicted to host Dirac fermions. However, the synthesis of germanene is still in its infancy; moreover, the predicted tiny bandgap induced by the spin–orbit coupling is far from practical applications for nanoelectronic devices. Herein, quasi-freestanding germanene with linear dispersion relation of the band structure is well grown on a WSe2/Au(100) substrate. Band structure calculations reveal that the interaction of germanene with the substrate destroys the sublattice symmetry. The energy-dependent contribution of σ orbitals responsible for band crossing at the Fermi level around the Γ point induces asymmetric density of states at the Dirac point. Upon annealing in ultra-high vacuum, we observe a bandgap opening in germanene of about ∼0.17 eV, which is attributed to a sublattice symmetry breaking in germanene and the emergence of a net electric field. This work provides an effective method to tune or tailor the electronic properties of germanene, paving the way to germanene-based field-effect applications.

As a two-dimensional semiconductor with many physical properties, including, notably, layer-controlled electronic bandgap and coupled spin-valley degree of freedom, monolayer MoSe

Despite recent transport studies of ABC-stacked multilayer graphene systems revealed various unusual quantum phenomena which arise from the nearly flat electronic bands, their quantum tunneling properties have rarely been addressed. Here we investigate the local tunneling characteristics of a gapped ABC-stacked trilayer graphene (TLG) and report the experimental observation of the nearly flat band induced atomic-site-dependent negative differential conductivity (NDC, characterized by a current drop with increasing voltage) via scanning tunneling spectroscopy (STS) measurements. We show that strong NDC emerges in the gap region next to a sharp STS peak induced by the very flat low-energy dispersion of ABC TLG. The NDC is found to mainly reside on one atomic sublattice of the surface layer due to the strong sublattice and layer localization of the nearly flat bands. The observed NDC behavior is explained by the tunnel-diode mechanism, namely, the coexistence of a sharp flat-dispersion STS peak in which tunneling is strongly enhanced and a subsequent gap region in which tunneling is forbidden. Furthermore, we also find that a local defect could effectively switch off the NDC over a large spatial range. Our result highlights a quantum tunneling effect unique to the graphene-based nearly flat band system and expands the potential application scope of ABC TLG.

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 θ_{c}. Experimentally, the θ_{c} 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.

The grain boundaries (GBs) of a graphene surface were extensively studied because GBs with specific defect configurations result in the formation of new curved structures, which can be treated as new carbon allotropes. We studied the structures and electronic spectra of two periodic GBs in graphene on highly oriented pyrolytic graphite (HOPG) surfaces using scanning tunneling microscopy and spectroscopy (STM/S). Our results demonstrated that a GB consisting of dual parallel periodic dislocation cores of pentagonal-heptagonal (5-7) carbon rings gives rise to an enhanced localized state at 0.45 eV above the Dirac point in graphene surfaces, which is attributed to van Hove singularities (VHSs). Moreover, the energy positions of the localized states are varied between 0.40 and 0.47 eV depending on the site and eventually decayed to 0.36 eV. The variation of the energy positions is induced by two parallel GBs because of the higher electron density at the GB as a defect center and the lower electron away from the GB. Another periodic GB with a symmetric zigzag structural feature induced VHSs at -0.038 and 0.12 eV near the Fermi level. Moreover, intervalley scattering was observed on both these GBs. This means that carrier concentration and thus, the conductance around the periodic GBs can be significantly enhanced by localized density of states. This finding suggests that graphene with a properly embedded ordered GB is promising for improving the performance of graphene-based electronic devices., 21 pages, 4 figures

Bulk group IB transition-metal chalcogenides have been widely explored due to their applications in thermoelectrics. However, a layered two-dimensional form of these materials has been rarely reported. Here, we realize semiconducting Cu2Se by direct selenization of Cu(111). Scanning tunneling microcopy measurements combined with first-principles calculations allow us to determine the structural and electronic properties of the obtained structure. X-ray photoelectron spectroscopy data reveal chemical composition of the sample, which is Cu2Se. The observed moiré pattern indicates a lattice mismatch between Cu2Se and the underlying Cu(111)- 3 × 3 surface. Differential conductivity obtained by scanning tunneling spectroscopy demonstrates that the synthesized Cu2Se exhibits a band gap of 0.78 eV. Furthermore, the calculated density of states and band structure demonstrate that the isolated Cu2Se is a semiconductor with an indirect band gap of ∼ 0.8 eV, which agrees quite well with the experimental results. Our study provides a simple pathway varying toward the synthesis of novel layered 2D transition chalcogenides materials.

Interlayer coupling in layered semiconductors can significantly affect their optoelectronic properties. However, understanding the mechanisms behind the interlayer coupling at the atomic level is not straightforward. Here, we study modulations of the electronic structure induced by the interlayer coupling in the γ-phase of indium selenide (γ-InSe) using scanning probe techniques. We observe a strong dependence of the energy gap on the sample thickness and a small effective mass along the stacking direction, which are attributed to strong interlayer coupling. In addition, the moiré patterns observed in γ-InSe display a small band-gap variation and nearly constant local differential conductivity along the patterns. This suggests that modulation of the electronic structure induced by the moiré potential is smeared out, indicating the presence of a significant interlayer coupling. Our theoretical calculations confirm that the interlayer coupling in γ-InSe is not only of the van der Waals origin, but also exhibits some degree of hybridization between the layers. Strong interlayer coupling might play an important role in the performance of γ-InSe-based devices.

Despite various novel broken symmetry states have been revealed in bilayer graphene (BLG) experimentally, the atomic-scale spectroscopic investigation has been greatly limited. Here, we study high-resolution spectroscopic characteristics of high-quality BLG and observe rich broken-symmetry-induced Landau level (LL) splittings, including valley, spin and orbit, by using ultralow-temperature and high-magnetic-field scanning tunneling microscopy and spectroscopy (STM and STS). Our experiment demonstrates that both the spin and orbital splittings of the lowest n = (0,1) LL depend sensitively on its filling and exhibit an obvious enhancement at partial-filling states. More unexpectedly, the splitting of a fully-filled and valley-polarized LL is also enhanced by partial filling of the LL with the opposite valley. These results reveal significant many-body effects in this system. At half filling of the n = (0,1) LL (filling factor v = 0), a single-particle intermediate v = 0 phase, which is the transition state between canted antiferromagnetic and layer-polarized states in the BLG, is measured and directly visualized at the atomic scale. Our atomic-scale STS measurement gives direct evidence that this intermediate v = 0 state is the predicted orbital-polarized phase.

A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the ``relativistic'' zero Landau level (LL) of the graphene monolayer. However, identification of these high-field broken-symmetry states has mostly relied on macroscopic transport techniques, which lack spatial resolution. Here, we demonstrate a direct approach by imaging the QHIFM states at atomic scale with a scanning tunneling microscope. At half filling of the zero LL ($\ensuremath{\nu}=0$), the system is in a spin unpolarized state and we observe a linear magnetic-field-scaling of valley splitting. The wave functions of the QHIFM states at $\ensuremath{\nu}=0$ are directly imaged at the atomic scale and we observe an interaction-driven density wave featuring a Kekul\'e distortion, which is responsible for the large gap in high magnetic fields. Moreover, our experiment demonstrates that both the valley and spin splittings depend on the filling factor. For example, the spin splitting in the zero LL is dramatically enhanced (in excess of about 200% at maximum) when the Fermi level lies inside spin-polarized states (at $\ensuremath{\nu}=1$ or \ensuremath{-}1), accounting for strong many-body effects.

Very recently, twisted graphene bilayers (TGBs) around the first magic angle $\ensuremath{\theta}\ensuremath{\approx}1.{1}^{\ensuremath{\circ}}$ have attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately study a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicates that a moderate heterostrain enables the structural evolution from the small-angle TGB (\ensuremath{\theta} \ensuremath{\sim} 1.5\ifmmode^\circ\else\textdegree\fi{}) to the strained magic-angle TGB (\ensuremath{\theta} \ensuremath{\sim} 1.1\ifmmode^\circ\else\textdegree\fi{}), exhibiting the characteristic low-energy flat bands. The heterostrain can even drive the system into highly strained tiny-angle TGBs (\ensuremath{\theta}$\ensuremath{\ll}1.1$\ifmmode^\circ\else\textdegree\fi{}) with large deformed tetragonal superlattices, where a unique network of topological helical edge states emerges. Furthermore, the predicted domain wall modes, which are strongly localized and result in a hexagon-triangle-mixed frustrated lattice derived from the Kagome lattice, are observed in the strained tiny-angle TGBs.

A unique design of a hexagonal boron nitride (h-BN)/HfO2 dielectric heterostructure stack is demonstrated, with few-layer h-BN to alleviate the surface optical phonon scattering, followed by high-κ HfO2 deposition to suppress Coulombic impurity scattering so that high-performance top-gated two-dimensional semiconductor transistors are achieved. Furthermore, this dielectric stack can also be extended to GaN-based transistors to enhance their performance.

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.

Even after a decade of research, a fundamental controversy persists concerning the electronic structure of a suspended graphene monolayer, as revealed by scanning tunneling spectroscopy (STS). Is the spectrum truly gapped, or V-shaped? This study systematically shows that substrate interaction can affect the STS spectrum of graphene crucially, by suppressing out-of-plane phonons and thus eliminating any gap. Switching the tunneling spectrum of graphene with voltage pulses through the probe's tip is also demonstrated. This sort of clear understanding is needed for successful engineering of related graphene devices.

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 bilayer graphene. By using high-resolution STS, we observed split of the VHSs and directly imaged 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., 4 Figures in main text

When electrons are confined in a two-dimensional (2D) system, typical quantum–mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum–mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.

Pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism. Theoretically, the $\ensuremath{\pi}$ 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 $\ensuremath{\pi}$ magnetism in graphene, whereas only a notable resonance peak has been observed around the atomic defects, leaving the $\ensuremath{\pi}$ magnetism experimentally elusive. Here, we report direct experimental evidence of $\ensuremath{\pi}$ 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.

Trilayer graphene (TLG) exhibits rich novel electronic properties and extraordinary quantum Hall phenomena owning to enhanced electronic interactions and tunable chirality of its quasiparticles. Here, we report direct observation of chirality transition of quasiparticles at stacking solitons of TLG via spatial-resolved Landau level spectroscopy. The one-dimensional stacking solitons with width of the order of 10 nm separate adjacent Bernal-stacked TLG and rhombohedral-stacked TLG. By using high field tunneling spectra of scanning tunneling microscopy, we measured Landau quantization in both the Bernal-stacked TLG and the rhombohedral-stacked TLG and, importantly, we observed evolution of quasiparticles between the chiral degree l = 1&2 and l = 3 across the stacking domain wall solitons. Our experiment indicates that such a chirality transition occurs smoothly, accompanying the transition of the stacking orders of TLG, around the domain wall solitons. This result demonstrates the important and hitherto neglected relationship between the crystallographic stacking order and the chirality of quasiparticles in graphene systems., 4 Figures

The AB–BA domain wall in gapped graphene bilayers is a rare naked structure hosting topological electronic states. Although it has been extensively studied in theory, a direct imaging of its topological edge states is still missing. Here we image the topological edge states at the graphene bilayer domain wall by using scanning tunnelling 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 further demonstrates that the one-dimensional topological states are quite robust even in the presence of high magnetic fields. The result reported here may raise hopes of graphene-based electronics with ultra-low dissipation., Domain wall between gapped graphene bilayers is believed to host one-dimensional topological states, which is yet waiting for direct evidences. Here, Yin et al. report images of the AB-BA stacked bilayer graphene domain wall, providing direct evidence for topological edge states in such system.

In strained graphene, lattice deformation can create pseudomagnetic fields affecting the behavior of massless Dirac fermions and result in zero-field Landau level-like quantization. In the presence of an external magnetic field, valley-polarized Landau levels are predicted to be observed because the strain-induced pseudomagnetic fields are of opposite directions in the $K$ and ${K}^{\ensuremath{'}}$ valleys of graphene. However, an experimental verification of such a unique valley-polarized Landau quantization has not been reported so far. Here, we present experimental spectroscopic measurements in strained graphene on Rh foil by scanning tunneling microscopy. We directly observed the splitting of the Landau level in the quantum Hall regime and we interpreted the experimental result as the valley-polarized Landau level induced by the coexistence of the pseudomagnetic fields and external magnetic fields. The observed result paves the way to exploit novel electronic properties in graphene through the combination of the spatially varying strain (or the pseudomagnetic fields) and the external magnetic fields.

We use the tip of a scanning tunneling microscope (STM) to manipulate single weakly bound nanometer-sized sheets on a highly oriented pyrolytic graphite (HOPG) surface through artificially increasing the tip and sample interaction by pretreatment of the surface using a liquid thiol molecule. By this means it is possible to tear apart a graphite sheet against a step and fold this part onto the HOPG surface and thus generate graphene superlattices with hexagonal symmetry. The tip and sample surface interactions, including the van der Waals force, electrostatic force and capillary attraction force originating from the Laplace pressure due to the formation of a highly curved fluid meniscus connecting the tip and sample, are discussed quantitatively to understand the formation mechanism of a graphene superlattice induced by the STM tip. The capillary force plays a key role in manipulating the graphite surface sheet under humid conditions. Our approach provides a simple and feasible route to prepare controllable superlattices and graphene nanoribbons and also to better understand the process of generation of a graphene superlattice on the surface of HOPG with the tip.

The electron-hole symmetry in graphene monolayer, which is analogous to the inherent symmetric structure between electrons and positrons of the Universe, plays a crucial role in the chirality and chiral tunnelling of massless Dirac fermions. Here we demonstrate that both strain and charged-defect scattering could break this symmetry dramatically in graphene monolayer. In our experiment, the Fermi velocities of electrons and holes are measured directly through Landau level spectroscopy. In strained graphene with lattice deformation and curvature, the and are measured as 1.2 x 106 m/s and 1.02 x106 m/s, respectively. This giant asymmetry originates from enhanced next-nearest-neighbor hopping in the strained region. Around positively charged-defect, we observe opposite electron-hole asymmetry, and the and are measured to be 0.86x 106 m/s and 1.14 x106 m/s, respectively. Such a large asymmetry is attributed to the fact that the massless Dirac fermions in graphene monolayer are scattered more strongly when they are attracted to the charged-defect than when they are repelled from it., 4 Figures in main text

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 VHSs, the observed Landau quantization in the twisted bilayers is identical to that of massless Dirac fermions in graphene monolayer, which allows us to measure the Fermi velocity directly. Our result indicates that the Fermi velocity of the twisted bilayers depends remarkably on both the twisted angles and the interlayer coupling strengths. This removes the discrepancy about the Fermi velocity renormalization in the twisted bilayers and provides a consistent interpretation of all current data., 4 Figures in main text

Recently, the 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. Here, we demonstrate that it is possible to probe the stacking order and electronic spectrum of the r-TLG directly with a 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 meV and 23 meV, respectively. The observed features are well reproduced by a low-energy effective Hamiltonian., 3 Figures

Electronic properties of surface areas decoupled from graphite are studied using scanning tunnelling microscopy and spectroscopy. We show that it is possible to identify decoupled graphene monolayer, Bernal bilayer, and Bernal trilayer on graphite surface according to their tunnelling spectra in 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 trilayer. Our result demonstrates that the surface of graphite provides a natural ideal platform to probe the electronic spectra of graphene layers., Comment: 5 figures

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 is a direct evidence for the evolution of Landau levels into the quantum Hall edge states in graphene bilayers. Our experiment indicates that it is possible to explore rich quantum Hall physics in graphene systems using STM and STS., Comment: 4 Figures in main text and 4 Figures in SI

The wavefunction of massless 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 wavefunction on the A and B sublattices. This unique property provides unprecedented opportunities to image the two components of massless Dirac fermions spatially. Here we report atomic resolution imaging of the two-component Dirac-Landau levels in a gapped graphene monolayer by scanning tunnelling microscopy and spectroscopy. A gap of about 20 meV, driven by inversion symmetry breaking by the substrate potential, is observed in the graphene 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 wavefunction of the 0- LL is mainly at the A sites and that of the 0+ LL is mainly at 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 massless Dirac fermions., Comment: 4 Figures in main text and 4 Figures in SI

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 density of states due to the action of the non-Abelian gauge fields4,6-8. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunnelling peaks with energy spacing detal E ~ vF/D ~ 70 meV (here vF is the Fermi velocity of graphene and D is the period of the Moire patterns). Our results direct demonstrate 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 Moire patterns., Comment: 4 figure in main text

Despite the 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 (Moir\'e 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 Moir\'e spot., Comment: 4 figures in main text and 8 figures in SI