Using infrared spectroscopy, we investigate bottom gated ABA-stacked trilayer graphene subject to an additional environment-induced p-type doping. We find that the Slonczewski-Weiss-McClure tight-binding model and the Kubo formula reproduce the gate voltage-modulated reflectivity spectra very accurately. This allows us to determine the charge densities and the potentials of the π-band electrons on all graphene layers separately and to extract the interlayer permittivity due to higher energy bands.
In a magnetic field graphene trilayers support a special multiplet of 12 zero(-energy)-mode Landau levels with a threefold degeneracy in Landau orbitals. A close look is made into such zero-mode levels in ABA-stacked trilayers, with the Coulomb interaction taken into account. It turns out that the zero-mode Landau levels of ABA trilayers are greatly afflicted with electron-hole and valley asymmetries, which come from general hopping parameters and which are enhanced by the Coulomb interaction and the associated vacuum effect, the orbital Lamb shift, that lifts the zero-mode degeneracy. These a…
The electronic structure of multilayer graphenes depends strongly on the number of layers as well as the stacking order. Here we explore the electronic transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect device configuration. We find that both the zero-magnetic-field transport and the quantum Hall effect at high magnetic fields are distinctly different from the monolayer and bilayer graphenes, and that they show electron-hole asymmetries that are strongly suggestive of a semimetallic band overlap. When the ABA trilayers are subjected to an electric field perpendicul…
For the first time, we have observed the obvious triple G peak splitting of ABA stacked trilayer graphene. The G peak splitting can be quantatively understood through the different electron-phonon coupling strength of Ea', Eb' and Ea" modes. In addition, the fluctuation of G peak position at different sample locations can also be understood from the view of the varied interaction strength among graphene layers of TLG, which is induced by nonuniform hole doping at the microscopic level.
Layer stacking and crystal lattice symmetry play important roles in the band structure and the Landau levels of multilayer graphene. ABA-stacked trilayer graphene possesses mirror-symmetry-protected monolayer-like and bilayer-like band structures. Broken mirror symmetry by a perpendicular electric field therefore induces hybridization between these bands and various quantum Hall phases emerge. We experimentally explore the evolution of Landau levels in ABA-stacked trilayer graphene under electric field. We observe a variety of valley and orbital dependent Landau level evolutions. These evoluti…
The band structure and the optical conductivity of an ABA (Bernal-type) stacked graphene trilayer are calculated. It is shown that, under appropriate doping, a strong resonant peak develops in the optical conductivity, located at the frequency corresponding to approximately 1.4 times the interlayer hopping energy and caused by the 'nesting' of two nearly parabolic bands in the electronic spectrum. The intensity of this resonant absorption can be controlled by adjusting the gate voltage. The effect is robust with respect to increasing temperature.
We present the solutions of the energy spectrum of charge carriers confined in quantum ring in ABA-stacked trilayer graphene subjected to a perpendicular magnetic field. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e. freezing out the carrier radial motion. We show that the obtained energy spectrum exhibits different symmetries with respect to the magnetic field and other parameters. The application of a potential shift the energy spectrum vertically while the application of a magnetic field breaks all sym…
We report markedly different transport properties of ABA- and ABC-stacked trilayer graphenes. Our experiments in double-gated trilayer devices provide evidence that a perpendicular electric field opens an energy gap in the ABC trilayer, while it causes the increase of a band overlap in the ABA trilayer. In a perpendicular magnetic field, the ABA trilayer develops quantum Hall plateaus at filling factors of ν= 2, 4, 6... with a step of Δν= 2, whereas the inversion symmetric ABC trilayer exhibits plateaus at ν= 6 and 10 with 4-fold spin and valley degeneracy.
We investigate the proximity spin-orbit and exchange couplings in ABA and ABC trilayer graphene encapsulated within monolayers of semiconducting transition-metal dichalcogenides and the ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$. Employing first-principles calculations we obtain the electronic structures of the multilayer stacks and extract the relevant proximity-induced orbital and spin interaction parameters by fitting the low-energy bands to model Hamiltonians. We also demonstrate the tunability of the proximity effects by a transverse electric field. Using the model Hamiltonians we als…
We calculate the electronic band structure of ABA-stacked trilayer graphene in the presence of external gates, using a self-consistent Hartree approximation to take account of screening. In the absence of a gate potential, there are separate pairs of linear and parabolic bands at low energy. A gate field perpendicular to the layers breaks mirror reflection symmetry with respect to the central layer and hybridizes the linear and parabolic low-energy bands, leaving a chiral Hamiltonian essentially different from that of monolayer or bilayer graphene. Using the self-consistent Born approximation,…
The tight-binding model is closely associated with the modified random-phase approximation to thoroughly explore the electron-electron interactions in trilayer AB-stacked graphene. The intralayer and interlayer atomic/Coulomb interactions dominate the collective and electron-hole excitations. The unusual energy bands are directly reflected in the diverse transferred momentum-frequency phase diagrams. There exist three kinds of plasmon modes during the variation of the doping level, being accompanied with the complicated intraband and interband single-particle excitations. The excitation behavi…
We obtain an analytical expression for the Hall conductivity in AAA-stacked trilayer graphene (TLG) within the linear response Kubo formalism. Interestingly, we find that the quantization of the Hall conductivity is severely dependent on the value of the chemical potential and the magnetic field. The origin of this unusual quantization, attributed to the Landau level spectrum of AAA-stacked TLG, is explained in detail. We show that is a characteristic of the multilayer graphene structures with AA stacking order.
Crystal symmetry plays a central role in governing a wide range of fundamental physical phenomena. One example is the nonlinear optical second harmonic generation (SHG), which requires inversion symmetry breaking. Here we report a unique stacking-induced SHG in trilayer graphene, whose individual monolayer sheet is centrosymmetric. Depending on layer stacking sequence, we observe a strong optical SHG in Bernal (ABA) stacked non-centrosymmetric trilayer, while it vanishes in rhombohedral (ABC) stacked one which preserves inversion symmetry. This highly contrasting SHG due to the distinct stacki…
In a magnetic field graphene trilayers support a characteristic multiplet of 12 zero(-energy)-mode Landau levels with a threefold degeneracy in Landau orbitals. It was earlier noted for bilayer graphene that Coulombic vacuum fluctuations, specific to graphene, lift the orbital degeneracy of such zero-energy modes and that these Lamb-shfted" orbital modes, with filling, get mixed via the Coulomb interaction. It is pointed out that analogous orbital Lamb shift and mixing of zero-mode levels can also take place, with an enriched symmetry content, in ABC-stacked trilayer graphene; and its conseque…
We study the electronic transport through np and npn junctions for AAA-stacked trilayer graphene. Two kinds of gates are considered where the first is a single gate and the second is a double gate. After obtaining the solutions for the energy spectrum, we use the transfer matrix method to determine the three transmission probabilities for each individual cone $τ=0, \pm 1$. We show that the quasiparticles in AAA-stacked trilayer graphene are not only chiral but also labeled by an additional cone index $τ$. The obtained bands are composed of three Dirac cones that depend on the chirality indexes…
We obtain the quasiparticle band structure of ABA and ABC-stacked graphene trilayers through ab initio density functional theory (DFT) and many-body quasiparticle calculations within the GW approximation. To interpret our results, we fit the DFT and GW $π$ bands to a low energy tight-binding model, which is found to reproduce very well the observed features near the K point. The values of the extracted hopping parameters are reported and compared with available theoretical and experimental data. For both stackings, the self energy corrections lead to a renormalization of the Fermi velocity, an…
Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. In the absence of a magnetic field, multiple Lifshitz transi…
We present a combined group-theoretical and tight-binding approach to calculate the intrinsic spin-orbit coupling (SOC) in ABC stacked trilayer graphene. We find that compared to monolayer graphene, a larger set of d orbitals (in particular the d_{z^2} orbital) needs to be taken into account. We also consider the intrinsic SOC in bilayer graphene, because the comparison between our tight-binding bilayer results and the density functional computations of Ref.[40] allows us to estimate the values of the trilayer SOC parameters as well. We also discuss the situation when a substrate or adatoms in…
We observed distinct interlayer shear mode Raman spectra for trilayer graphene with ABA and ABC stacking order. There are two rigid-plane shear-mode phonon branches in trilayer graphene. We found that ABA trilayers exhibit pronounced Raman response from the high-frequency shear branch, without any noticeable response from the low-frequency branch. In contrast, ABC trilayers exhibit no response from the high-frequency shear branch, but significant Raman response from the low-frequency branch. Such complementary behaviors of Raman shear modes can be explained by the distinct symmetry of the two …
The sequence of the zeroth Landau levels (LLs) between filling factors $ν$=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the non-uniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the non-uniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the cont…
We report on the transport properties of ABC and ABA stacked trilayer graphene using dual, locally gated field effect devices. The high efficiency and large breakdown voltage of the HfO2 top and bottom gates enables independent tuning of the perpendicular electric field and the Fermi level over an unprecedentedly large range. We observe a resistance change of six orders of magnitude in the ABC trilayer, which demonstrates the opening of a band gap. Our data suggest that the gap saturates at a large displacement field of D ~ 3 V/nm, in agreement with self-consistent Hartree calculations. In con…
ABC-stacked trilayer graphene has exhibited a variety of correlated phenomena owing to its relatively flat bands and gate-tunable bandgap. However, convenient methods are still lacking for identifying ABC graphene with nanometer-scale resolution. Here we demonstrate that the scanning near-field optical microscope (SNOM) working in ambient conditions can provide quick recognition of ABC trilayer graphene with no ambiguity and excellent resolution (~20 nm). The recognition is based on the difference in their near-field infrared (IR) responses between the ABA and ABC trilayers. We show that in mo…
Graphene flakes are prepared on freshly cleaved mica by exfoliation and studied by scanning tunneling microscopy in ultra high vacuum. On few-layer graphene, a triangular network of partial dislocations separating ABC stacked and ABA stacked graphene was found similar to the networks occasionally visible on freshly cleaved HOPG. We found differences in the electronic structure of ABC and ABA stacked areas by scanning tunneling spectroscopy, i.e., a pronounced peak at 0.25 eV above the Fermi level exclusively in the ABA areas, which is shown to be responsible for the different apparent heights …
We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, th…
We calculate the static polarization of AAA-stacked trilayer graphene (TLG) and study its screening properties within the random phase approximation (RPA) in all undoped, doped and biased regimes. We find that the static polarization of undoped AAA-stacked TLG is a combination of the doped and undoped single layer graphene static polarization. This leads to an enhancement of the dielectric background constant along a Thomas-Fermi screening with the Thomas-Fermi wave vector which is independent of carrier concentrations and a 1/r^3 power law decay for the long-distance behavior of the screened …
We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene. We derive analytic low energy expressions for the spectrum, the validity of which is confirmed by comparison to a π-band tight-binding calculation of the density of states on the honeycomb lattice. We further study the effect of a perpendicular electric field on the spectrum, where a zero-energy plateau appears for ABC stacking order, due to the opening of a gap at the Dirac point, while the ABA-stacked trilayer graphene remains metallic. We discuss our results in the context of recent electronic transport experiment…
ABA-stacked trilayer graphene (TLG), the simplest system consisting of both massless and massive Dirac fermions, is expected to exhibit many interesting broken-symmetry quantum Hall states and interaction-induced phenomena. However, difficulties in microscopically identifying the stacking order of the TLG and limited spectroscopic resolution have stymied experimental probes of these interesting states and phenomena in scanning tunneling microscopy (STM) studies. Here we studied the detailed features of the electronic structure in the ABA TLG by using high-resolution STM measurements. Landau-le…
We present low temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν=-8, -2, 2, 6, and 10, in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau levels (LL). Under an out-of-plane electric field E, we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E selectively breaks the LL degen…
The interaction between electrons and plasmons in trilayer graphene is investigated within the Overhauser approach resulting in the 'plasmaron' quasi-particle. This interaction is cast into a field theoretical problem, nd its effect on the energy spectrum is calculated using improved Wigner-Brillouin perturbation theory. The plasmaron spectrum is shifted with respect to the bare electron spectrum by $ΔE(\mathbf{k})\sim 50\div200\,{\rm meV}$ for ABC stacked trilayer graphene and for ABA trilayer graphene by $ΔE(\mathbf{k})\sim 30\div150\,{\rm meV}$ ($ΔE(\mathbf{k})\sim 1\div5\,{\rm meV}$) for t…
We present a comparative measurement of the G-peak oscillations of phonon frequency, Raman intensity and linewidth in the Magneto-Raman scattering of optical E2g phonons in mechanically exfoliated ABA- and ABC-stacked trilayer graphene (TLG). Whereas in ABA-stacked TLG, we observe magnetophonon oscillations consistent with single-bilayer chiral band doublets, the features are flat for ABC-stacked TLG up to magnetic fields of 9 T. This suppression can be attributed to the enhancement of band chirality that compactifies the spectrum of Landau levels and modifies the magnetophonon resonance prope…
Trilayer graphene in both ABA (Bernal) and ABC (rhombohedral) stacking sequences is shown to exhibit intense infrared absorption from in-plane optical phonons. The feature, lying at ~1580 cm-1, changes strongly with electrostatic gating. For ABC-stacked graphene trilayers, we observed a large enhancement in phonon absorption amplitude, as well as softening of the phonon mode, as the Fermi level is tuned away from charge neutrality. A similar, but substantially weaker effect is seen in samples with the more common ABA stacking order. The strong infrared response of the optical phonons and the p…
The stacking order degree of freedom in trilayer graphene plays a critical role in determining the existence of an electric field tunable band gap. We present spatially-resolved tunneling spectroscopy measurements of dual gated Bernal (ABA) and rhombohedral (ABC) stacked trilayer graphene devices. We demonstrate that while ABA trilayer graphene remains metallic, ABC trilayer graphene exhibits a widely tunable band gap as a function of electric field. However, we find that charged impurities in the underlying substrate cause substantial spatial fluctuation of the gap size. Our work elucidates t…
The magneto-optical spectra of ABC-stacked trilayer graphene are enriched by the electric field. A lot of prominent absorption peaks, which arise from the inter- Lnadau-level transitions, gradually change from the twin-peak structures into the double-peak ones with the increasing electric-field strength. This comes from the de- struction in mirror symmetry of xy-plane and the non-equivalence for two sublattices with the identical projections. Specially, a single threshold peak becomes a double- peak structure, owing to the Fermi-Dirac distribution. The absorption frequencies continuously grow …
Magneto-transport experiments on ABC-stacked suspended trilayer graphene reveal a complete splitting of the twelve-fold degenerated lowest Landau level, and, in particular, the opening of an exchange-driven gap at the charge neutrality point. A quantitative analysis of distinctness of the quantum Hall plateaus as a function of field yields a hierarchy of the filling factors: ν=6, 4, and 0 are the most pronounced, followed by ν=3, and finally ν=1, 2 and 5. Apart from the appearance of a ν=4 state, which is probably caused by a layer asymmetry, this sequence is in agreement with Hund's rules for…
The electronic tunneling properties of the two stable forms of trilayer graphene (TLG), rhombohedral ABC and Bernal ABA, are examined for pn and pnp junctions as realized by using a single gate (SG) or a double gate (DG). For the rhombohedral form, due to the chirality of the electrons, the Klein paradox is found at normal incidence for SG devices while at high energy interband scattering between additional propagation modes can occur. The electrons in Bernal ABA TLG can have a monolayer- or bilayer-like character when incident on a SG device. Using a DG however both propagation modes will cou…
ABC-stacked trilayer graphene (TLG) are predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat-band structures near the charge neutrality point (CNP). Here, using high magnetic field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG. We observe an approximately linear magnetic-field-scaling of the valley splitting and orbital splitting in the ABC-stacked TLG. Our experiment indicates that the valley splitting decreases dramatically with increasing the LL index. When the lowest LL is p…
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only for trilayer graphene, although the bilayer has a gapless parabolic band component. Our model rigorously exhibits basic facts from tight-binding calculations, effective two-dimensional models and a $π$-orbital continuum model with nearest-neighbour tunneling that have been discussed in the physics literature.
The electronic spectrum of three coupled graphene layers (graphene trilayers) is investigated in the presence of an external magnetic field. We obtain analytical expressions for the Landau level spectrum for both the ABA and ABC - type of stacking, which exhibit very different dependence on the magnetic field. The effect of layer asymmetry and of external gate voltages can strongly influence the properties of the system.
There is an increasing interest in the electronic properties of few layer graphene as it offers a platform to study electronic interactions because the dispersion of bands can be tuned with number and stacking of layers in combination with electric field. However, electronic interaction becomes important only in very clean devices and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism (QHF) seen in ABA trilayer graphene (ABA-TLG). Due to high mobility $\sim$5…
The dependence of the Raman spectrum on the excitation energy has been investigated for ABA-and ABC- stacked few-layer graphene in order to establish the fingerprint of the stacking order and the number of layers, which affect the transport and optical properties of few-layer graphene. Five different excitation sources with energies of 1.96, 2.33, 2.41, 2.54 and 2.81 eV were used. The position and the line shape of the Raman 2D, G*, N, M, and other combination modes show dependence on the excitation energy as well as the stacking order and the thickness. One can unambiguously determine the sta…
In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains additional quantum numbers associated with the LL orbital index $% n=0,1,2$. Remote inter-layer hopping terms and external potential difference $Δ_{B}$ between the layers lead to LL splitting by introducing a gap $% Δ_{LL}$ between the degenerate zero-energy triplet LL orbitals. Assuming that the spin and valley degrees of freedom are frozen, we study the phase diag…
The band structures and optical properties of AAB-stacked trilayer graphenes (AAB-TLG) are calculated by the tight-binding model and gradient approximation. Three pairs of the energy bands exhibit very different energy dispersions at low energy and saddle points at the middle energy. At zero electric field, $3$$^2$ excitation channels exist in both the low and middle frequencies, and cause the very rich joint density of states (JDOS). However, the structures in the JDOS do not appear in the absorption spectra completely. Due to the different contributions from the velocity metric elements, som…
We report a nano-infrared (IR) imaging study of trilayer graphene (TLG) with both ABA (Bernal) and ABC (rhombohedral) stacking orders using the scattering-type scanning near-field optical microscope (s-SNOM). With s-SNOM operating in the mid-IR region, we mapped in real space the surface plasmon polaritons (SPPs) of ABA-TLG and ABC-TLG, which are tunable with electrical gating. Through quantitative modeling of the plasmonic imaging data, we found that the plasmon wavelength of ABA-TLG is significantly larger than that of ABC-TLG, resulting in a sizable impedance mismatch and hence a strong pla…
The layer-based random-phase approximation is further developed to investigate electronic excitations in tri-layer ABC-stacked graphene. All the layer-dependent atomic interactions and Coulomb interactions are included in the dynamic charge screening. There exist rich and unique (momentum, frequency)-excitation phase diagrams, in which the complex single-particle excitations and five kinds of plasmon modes, are dominated by the unusual energy bands and doping carrier densities. The latter frequently experience the significant Landau damping due to the former, leading to the coexistence/destruc…
We developed the generalized tight-binding model to study the magneto-electronic properties of AAB-stacked trilayer graphene. Three groups of Landau levels (LLs) are characterized by the dominating subenvelope function on distinct sublattices. Each LL group could be further divided into two sub-groups in which the wavefunctions are, respectively, localized at 2/6 (5/6) and 4/6 (1/6) of the total length of the enlarged unit cell. The unoccupied conduction and the occupied valence LLs in each sub-group behave similarly. For the first group, there exist certain important differences between the t…
The few-layer graphene quantum dot provides a promising platform for quantum computing with both spin and valley degrees of freedom. Gate-defined quantum dots in particular can avoid noise from edge disorders. In connection with the recent experimental efforts [Y. Song et al., Nano Lett. 16, 6245 (2016)], we investigate the bound state properties of trilayer graphene (TLG) quantum dots (QDs) through numerical simulations. We show that the valley degeneracy can be lifted by breaking the time reversal symmetry through the application of a perpendicular magnetic field. The spectrum under such a p…
Small-twist-angle bilayer graphene supports strongly correlated insulating states and superconductivity. Twisted few-layer graphene systems are likely to open up new directions for strong correlation physics in moiré superlattices. We derive and study moiré band models that describe the electronic structure of graphene trilayers in which one of the three layers is twisted by a small angle relative to perfect AAA, ABA, or ABC stacking arrangements. We find that the electronic structure depends very strongly on the starting stackings arrangement and on which layer is twisted. We identify ABA sta…
Optical Hall conductivity, as directly related to Faraday rotation, is theoretically studied for bilayer and trilayer graphene. In bilayer graphene, the trigonal warping of the band dispersion greatly affects the resonance structures in Faraday rotation not only in the low-energy region where small Dirac cones emerge, but also in the higher-energy parabolic bands as a sequence of satellite resonances. In ABA-stacked trilayer, the resonance spectrum is a superposition of effective monolayer and bilayer contributions with band gaps, while ABC trilayer exhibits a distinct spectrum peculiar to the…
In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electron-electron interaction g and doping level n, we determine whether the total energy is minimized for a paramagnetic or ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in…
Ballistic transport was studied in a multiple-band system consisting of an antidot lattice of AB-stacked trilayer graphene. The low temperature magnetoresistance showed commensurability peaks arising from matching of the antidot lattice period and radius of cyclotron orbits for each mono- and bilayer-like band in AB stacked trilayer graphene. The commensurability peak of the monolayer-like band appeared at a lower magnetic field than that of the bilayer-like band, which reflects the fact that the Fermi surface of the bilayer-like band is larger than that of monolayer-like band. Rotation of the…
The ABC-stacked N-layer-graphene family of two-dimensional electron systems is described at low energies by two remarkably flat bands with Bloch states that have strongly momentum-dependent phase differences between carbon pi-orbital amplitudes on different layers, and large associated momentum space Berry phases. These properties are most easily understood using a simplified model with only nearest-neighbor inter-layer hopping which leads to gapless semiconductor electronic structure, with p^N dispersion in both conduction and valence bands. We report on a study of the electronic band structu…
We perform an optical spectroscopy study to investigate the properties of different artificial MoS$_2$ bi- and trilayer stacks created from individual monolayers by a deterministic transfer process. These twisted bi- and trilayers differ from the common 2H stacking in mineral MoS$_2$ in the relative stacking angle of adjacent layers and the interlayer distance. The combination of Raman spectroscopy, second-harmonic-generation microscopy and photoluminescence measurements allows us to determine the degree of interlayer coupling in our samples. We find that even for electronically decoupled arti…
We propose use of disorder to produce a field effect transistor (FET) in biased bilayer and trilayer graphene. Modulation of the bias voltage can produce large variations in the conductance when the disorder's effects are confined to only one of the graphene layers. This effect is based on the bias voltage's ability to select which of the graphene layers carries current, and is not tied to the presence of a gap in the density of states. In particular, we demonstrate this effect in models of gapless ABA-stacked trilayer graphene, gapped ABC-stacked trilayer graphene, and gapped bilayer graphene…
We use a self-consistent Hartree-Fock approximation with realistic Coulomb interactions for $π$-band electrons to explore the possibility of broken symmetry states in weakly disordered ABC stacked trilayer graphene. The competition between gapped and gapless broken symmetry states, and normal states is studied by comparing total energies. We find that gapped states are favored and that, unlike the bilayer case, gapless nematic broken symmetry states are not metastable. Among the gapped states the layer antiferromagnetic state is favored over anomalous and spin Hall states.
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 th…
