ABA-stacked Trilayer Graphene Research Articles

Nontrivial effect of out-of-plane acoustic phonon mode on limiting room temperature conductivity of ABA-stacked trilayer graphene

The ABA-stacked trilayer graphene (TLG) has a parabolic dispersion band spanning the Fermi level, apart from the linear dispersion band which is almost a duplicate of that in monolayer graphene (MLG). Such a band structure implies that the TLG is a metal and seemingly has a larger conductivity than MLG due to the additional contributions of the parabolic bands when the linear dispersion bands in TLG and MLG host the same number of carriers. However, our numerical calculations indicate that the conductivity of TLG is smaller than that in MLG roughly by 20% when a moderate carrier doping drives the Fermi energy away from the Dirac point by at least 50 meV. To explain such a disagreement between the band structure and the conductivity, we find that the out-of-plane atomic vibration, i.e., the so-called $ZA$ phonon mode in the long-wavelength region, plays a critical role in limiting the conductivity of TLG due to the strong interband scattering. In contrast to MLG, such a $ZA$ phonon mode is completely decoupled from the electron-phonon scattering due to the symmetry incompatibility.

Subband-resolved momentum-conserved resonant tunneling in monolayer graphene/h-BN/ABA-trilayer graphene small-twist-angle tunneling device

We demonstrate twist-controlled resonant tunneling in a monolayer graphene (MLG)/hexagonal boron nitride (h-BN)/ABA-stacked trilayer graphene (TLG) van der Waals (vdW) junction, in which MLG and TLG flakes are aligned with a small twist angle θ of ∼1.05° between their crystallographic orientations through a thin h-BN barrier. Owing to the small interlayer twist, resonant tunneling attributed to the conservation of momentum and energy was observed between the single linear band of MLG and multiple subbands of TLG. We show that different subbands of TLG—bilayer-graphene-like subbands and a MLG-like subband—exhibit distinctly different resonant tunneling behaviors. Therefore, we demonstrate subband-resolved resonant tunneling. This technique provides a method to determine band parameters (Slonczewski–Weiss–McClure parameters) and probes the band dispersion of different two-dimensional materials by utilizing a MLG electrode.

Designing few-layer graphene Schottky contact solar cells: Theoretical efficiency limits and parametric optimization

We theoretically study the efficiency limits and performance characteristics of few-layer graphene–semiconductor solar cells (FGSCs) based on a Schottky contact device structure. We model and compare the power conversion efficiency (PCE) of various configurations by explicitly considering the non-Richardson thermionic emission across few-layer graphene/semiconductor Schottky heterostructures. The calculations reveal that ABA-stacked trilayer graphene–silicon solar cell exhibits a maximal conversion efficiency exceeding 26% due to a lower reversed saturation current when compared to that of the ABC-stacking configuration. The thermal coefficients of PCE for ABA and ABC stacking FGSCs are –0.061%/K and –0.048%/K, respectively. Our work offers insights into optimal designs of graphene-based solar cells, thus paving a route toward the design of high-performance FGSC for future nanoscale energy converters.

Substrate-Dependent Band Structures in Trilayer Graphene/h-BN Heterostructures.

The tight-binding model has been spectacularly successful in elucidating the electronic and optical properties of a vast number of materials. Within the tight-binding model, the hopping parameters that determine much of the band structure are often taken as constants. Here, using ABA-stacked trilayer graphene as the model system, we show that, contrary to conventional wisdom, the hopping parameters and therefore band structures are not constants, but are systematically variable depending on their relative alignment angle between h-BN. Moreover, the addition or removal of the h-BN substrate results in an inversion of the K and K^{'} valley in trilayer graphene's lowest Landau level. Our work illustrates the oft-ignored and rather surprising impact of the substrates on band structures of 2D materials.

Gully quantum Hall ferromagnetism in biased trilayer graphene

Multilayer graphene lattices allow for an additional tunability of the band structure by the strong perpendicular electric field. In particular, the emergence of the new multiple Dirac points in ABA stacked trilayer graphene subject to strong transverse electric fields was proposed theoretically and confirmed experimentally. These new Dirac points dubbed ``gullies'' emerge from the interplay between strong electric field and trigonal warping. In this work we first characterize the properties of new emergent Dirac points and show that the electric field can be used to tune the distance between gullies in the momentum space. We demonstrate that the band structure has multiple Lifshitz transitions and higher-order singularity of ``monkey saddle'' type. Following the characterization of the band structure, we consider the spectrum of Landau levels and structure of their wave functions. In the limit of strong electric fields when gullies are well separated in momentum space, they give rise to triply degenerate Landau levels. In the second part of this work, we investigate how degeneracy between three gully Landau levels is lifted in presence of interactions. Within the Hartree-Fock approximation we show that the symmetry breaking state interpolates between fully gully polarized state that breaks $C_3$ symmetry at high displacement field, and the gully symmetric state when the electric field is decreased. The discontinuous transition between these two states is driven by enhanced inter-gully tunneling and exchange. We conclude by outlining specific experimental predictions for the existence of such a symmetry-breaking state.

Large-area single-crystal AB-bilayer and ABA-trilayer graphene grown on a Cu/Ni(111) foil.

High-quality AB-stacked bilayer or multilayer graphene larger than a centimetre has not been reported. Here, we report the fabrication and use of single-crystal Cu/Ni(111) alloy foils with controllable concentrations of Ni for the growth of large-area, high-quality AB-stacked bilayer and ABA-stacked trilayer graphene films by chemical vapour deposition. The stacking order, coverage and uniformity of the graphene films were evaluated by Raman spectroscopy and transmission electron microscopy including selected area electron diffraction and atomic resolution imaging. Electrical transport (carrier mobility and band-gap tunability) and thermal conductivity (the bilayer graphene has a thermal conductivity value of about 2,300 W m-1 K-1) measurements indicated the superior quality of the films. The tensile loading response of centimetre-scale bilayer graphene films supported by a 260-nm thick polycarbonate film was measured and the average values of the Young's modulus (478 GPa) and fracture strength (3.31 GPa) were obtained.

Electrical Control of Cyclotron Resonance in Dual-Gated Trilayer Graphene.

Landau levels (LLs) of ABA-stacked trilayer graphene (TLG) are described as the combination of monolayer graphene-like LLs and bilayer graphene-like LLs. They are extremely sensitive to the applied perpendicular electric displacement field D. Here, we demonstrate the electrical control of cyclotron resonance (CR) in a dual-gated ABA-stacked TLG. Under the irradiation of mid-infrared light, we observed the photovoltage induced by the CR absorption through the photothermoelectric effect. The resonant magnetic field in CR is changed by applying D while keeping the carrier density constant. Numerical simulations based on the tight-binding model complement the experimental observations. We believe that the present study provides a boost to graphene-based photodetectors and photoemitters with an electrically tunable wavelength in mid-infrared to terahertz spectral ranges.

Interlayer epitaxy of wafer-scale high-quality uniform AB-stacked bilayer graphene films on liquid Pt3Si/solid Pt

Large-area high-quality AB-stacked bilayer graphene films are highly desired for the applications in electronics, photonics and spintronics. However, the existing growth methods can only produce discontinuous bilayer graphene with variable stacking orders because of the non-uniform surface and strong potential field of the solid substrates used. Here we report the growth of wafer-scale continuous uniform AB-stacked bilayer graphene films on a liquid Pt3Si/solid Pt substrate by chemical vapor deposition. The films show quality, mechanical and electrical properties comparable to the mechanically exfoliated samples. Growth mechanism studies show that the second layer is grown underneath the first layer by precipitation of carbon atoms from the solid Pt, and the small energy requirements for the movements of graphene nucleus on the liquid Pt3Si enables the interlayer epitaxy to form energy-favorable AB stacking. This interlayer epitaxy also allows the growth of ABA-stacked trilayer graphene and is applicable to other liquid/solid substrates.

Energy Levels of Quantum Ring in ABA-Stacked Trilayer Graphene

We present the solutions of the energy spectrum of charge carriers confined in a 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. Moreover, the applied potential shifts the energy spectrum vertically while the applied magnetic field breaks all symmetries. We compare our results with those of the ideal quantum ring in monolayer and bilayer graphenes.

Gate-Controlled Conductance in ABA-Stacked Trilayer Graphene

In this work, we theoretically consider the electron transport across a junction on monolayer, Bernal-stacked AB bilayer and ABA trilayer graphene. The electronic transmissions through the electrostatic barrier in trilayer and bilayer graphene are computed within the scattering matrix using Landauer–Buttiker formula. We theoretically evaluate the total conductance. We study the effect of gate potential on the band structures. Our findings show that the effect of the gate potential could open an energy gap and the charge current can be controlled by tuning the gate potential in the middle region that acts as a barrier. Trilayer graphene is chosen as better appropriate candidate for industrial applications. Our findings show that the charge current can be controlled by tuning the gate potential in the middle region trilayer graphene that acts as a barrier.

Quantum parity Hall effect in Bernal-stacked trilayer graphene

The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system's mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance [Formula: see text] is first quantized to [Formula: see text] at a small perpendicular magnetic field [Formula: see text], establishing the presence of four edge channels. As [Formula: see text] increases, [Formula: see text] first decreases to [Formula: see text], indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong [Formula: see text] limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

Landau Level Diagram and the Continuous Rotational Symmetry Breaking in Trilayer Graphene.

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 nonuniform 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 nonuniformity 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 continuous rotational to C_{3} symmetry by the trigonal warping.

High-resolution tunneling spectroscopy of ABA-stacked trilayer graphene

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-level (LL) crossings of the massless and massive Dirac fermions, and effective mass renormalization of the massive Dirac fermions were observed, indicating strong electron-electron interactions in the ABA TLG. Most unexpectedly, we observed unconventional splittings of the lowest LLs for both the massless and massive Dirac fermions in high perpendicular magnetic fields. These splittings of the LLs, which are beyond the description of tight-binding calculations, reveal unexplored broken-symmetry quantum Hall states in the ABA TLG induced by many-body effects.

Tunable Symmetries of Integer and Fractional Quantum Hall Phases in Heterostructures with Multiple Dirac Bands.

The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated ABA-stacked trilayer graphene as a function charge density n, magnetic field B, and interlayer displacement field D, and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable insitu. At D=0, we observe fractional quantum Hall (FQH) states at filling factors 2/3 and -11/3. Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands.

Density functional theory calculations of the electric-field-induced Dirac cones and quantum valley Hall state in ABA-stacked trilayer graphene

We have investigated ABA-stacked trilayer graphene under a perpendicular electric field by using the density functional theory (DFT) calculations, which may contribute to the resolution of the discrepancies between experimental and theoretical results on the electric-field-induced band gap and topological phase transition. We found that the electric field opens a band gap at a low field and closes the gap at a high field, supporting one of the experimental results. While the seven electric-field-induced Dirac cones with mass gaps predicted in recent tight-binding (TB) models are confirmed, our DFT calculations demonstrate a phase transition from a quantum valley Hall insulator to a semimetal, contrasting to the TB model prediction of a topological phase transition between topologically nontrivial insulators at a high electric field.

Magnetic oscillation of optical phonon in ABA- and ABC-stacked trilayer graphene

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 properties. The drastically different coupling behaviour between the electronic excitations and the E2g phonons in ABA- and ABC-stacked TLG reflects their different electronic band structures and the electronic Landau level transitions and thus can be another way to determine the stacking orders and to probe the stacking-order-dependent electronic structures. In addition, the sensitivity of the magneto-Raman scattering to the particular stacking order in few layers graphene highlights the important role of interlayer coupling in modifying the optical response properties in van der Waals layered materials.

Optical bistability of graphene in the terahertz range

We use an exact solution of the relaxation-time Boltzmann equation in a uniform AC electric field to describe the nonlinear optical response of graphene in the terahertz (THz). The cases of monolayer, bilayer and ABA-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of monolayer graphene shows an optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also computed.

Quasi-particle spectrum in trilayer graphene: Role of onsite coulomb interaction and interlayer coupling

Stacking dependent quasi-particle spectrum and density of states (DOS) in trilayer (ABC-, ABA- and AAA-stacked) graphene are analyzed using mean-field Green׳s function equations of motion method. Interlayer coupling (t1) is found to be responsible for the splitting of quasi-particle peaks in each stacking order. Coulomb interaction suppresses the trilayer splitting and generates a finite gap at Fermi level in ABC- while a tiny gap in ABA-stacked trilayer graphene. Influence of t⊥ is prominent for AAA-stacking as compared to ABC- and ABA-stacking orders. The theoretically obtained quasi-particle energies and DOS has been viewed in terms of recent angle resolved photoemission spectroscopic (ARPES) and scanning tunneling microscopic (STM) data available on these systems.

Trilayer Graphene Nanoribbon Field Effect Transistor Analytical Model

The approaching scaling of Field Effect Transistors (FETs) in nanometer scale assures the smaller dimension, low-power consumption, low energy delay production, and high density as well as high speed in processor. Trilayer graphene nanoribbon with different stacking arrangements (ABA and ABC) indicates different electrical properties. Based on this theory, ABA-stacked trilayer graphene nanoribbon application as a field effect transistor channel is investigated in this study. The energy band structure of ABA-stacked trilayer graphene nanoribbon in the presence of a perpendicular electric field using a tight-binding model is presented, and the effect of applied voltage on the curvature of the E-K graph is analytically studied. Moreover, an analytical model of carrier statistics for ABA-stacked trilayer graphene nanoribbon in corporation with a numerical solution is presented and current-voltage characteristic of trilayer graphene nanoribbon FET as a one-dimensional device is explored. In fact, the proposed model can be applied as a useful tool to optimize the nanoscale FET based device performance. DOI : http://dx.doi.org/10.11591/telkomnika.v12i4.4698

Disorder effect on the integer quantum Hall effect in trilayer graphene

We numerically investigate the disorder effect on the integer quantum Hall effect in a trilayer graphene (TLG) system by use of the Kubo formula. For a clean sample, both Bernal (ABA) and rhombohedral (ABC) stacked TLGs display the same quantum rule with abnormal quantized Hall plateaus σxy = νe2/h (ν =± 6, ± 10, ± 14,…) in the band center and normal quantized Hall plateaus at the band edges. In the presence of disorder, the Hall plateaus become obscure and the higher plateaus disappear first with the increase of the disorder; however, the Hall plateaus of the ABA-stacked TLG are destroyed more readily in comparison with the ABC-stacked one. The longitudinal conductance minimums of the system corresponding to the Hall plateaus become narrower and thinner with disorder, and those of the ABC-stacked TLG are comparatively more stable than those of the ABA structure. The findings indicate that the l = 3 chiral quasiparticles with cubic energy dispersion in ABC-stacked TLG have comparatively stronger immunity to the disorder than the l = 1 and 2 chiral quasiparticles in the ABA counterpart.