ABA Stacking Research Articles

Uniaxial Strain-Induced Stacking Order Change in Trilayer Graphene.

The layer stacking order in two-dimensional heterostructures, like graphene, affects their physical properties and potential applications. Trilayer graphene, specifically ABC-trilayer graphene, has captured significant interest due to its potential for correlated electronic states. However, achieving a stable ABC arrangement is challenging due to its lower thermodynamic stability compared to the more stable ABA stacking. Despite recent advancements in obtaining ABC graphene through external perturbations, such as strain, the stacking transition mechanism remains insufficiently explored. In this study, we unveil a universal mechanism to achieve ABC stacking, applicable for understanding ABA to ABC stacking changes induced by any mechanical perturbations. Our approach is based on a novel strain engineering technique that induces interlayer slippage and results in the formation of stable ABC domains. We investigate the underlying interfacial mechanisms of this stacking change through computational simulations and experiments. Our findings demonstrate a highly anisotropic and significant transformation of ABA stacking to large and stable ABC domains facilitated by interlayer slippage. Through atomistic simulations and local energy analysis, we systematically demonstrate the mechanism for this stacking transition, that is dependent on specific loading orientation. Understanding such a mechanism allows this material system to be engineered by design compatible with industrial techniques on a device-by-device level. We conduct Raman studies to validate and characterize the formed ABC stacking, highlighting its distinct features compared to the ABA region. Our results contribute to a clearer understanding of the stacking change mechanism and provide a robust and controllable method for achieving stable ABC domains, facilitating their use in developing advanced optoelectronic devices.

Revealing large room-temperature Nernst coefficients in 2D materials by first-principles modeling.

Two-dimensional (2D) materials have attracted significant attention owing to their distinctive electronic, thermal, and mechanical characteristics. Recent advancements in both theoretical understanding and experimental methods have greatly contributed to the understanding of thermoelectric properties in 2D materials. However, thermomagnetic properties of 2D materials have not yet received the same amount of attention. In this work, we select promising 2D materials guided by the physics of the Nernst effect and present a thorough first-principles study of their electronic structures, carrier mobilities, and Nernst coefficients as a function of carrier concentration. Specifically, we reveal that trilayer graphene with an ABA stacking exhibits an exceptionally large Nernst coefficient of 112 μV (KT)-1 at room temperature. We further demonstrate that monolayer graphene, ABC-stacked trilayer graphene, and trilayer phosphorene (AAA stacking) have large Nernst coefficients at room temperature. This study establishes an ab initio framework for the quantitative study of the thermomagnetic effects in 2D materials and demonstrates high fidelity with previous experimental data.

Halogenated graphene derivatives as an absorber layer for solar cell applications : A DFT study with vdw correction

Due to the flexible nature and high transparency of Graphene (G) in the ultraviolet to infrared spectrum, it is ideal for thin-film solar cell applications. To use graphene for such a purpose, there is a need to tune its band gap at Fermi level, and the most convenient method is chemical functionalization. So, in this study, we will investigate electronic and mechanical properties, along with the structure and stability analysis of halogenated (X) bilayer and trilayer graphene B(T)LG using density functional theory with van der Waals correction (vdw-GGA). These halogenated B(T)LGs are designed by adsorbing the top and bottom surfaces with fluorine (F) and chlorine (Cl) at the maximum possible separation. BLGs are designed as X/graphene/graphene/X with bernal (AB) and non-bernal (AA) stacking. TLGs are designed as X/graphene/graphene/graphene/X as AAA, ABA, and ABC stacking with 50% X termination at the top and 50% on the bottom side. Chlorination results in weak physisorption while fluorination results in chemisorption. Binding energies Eb found quite higher for fluorinated bilayer graphene derivatives. Halogenation of TLG disturbs Dirac cones at Fermi level in case of fluorine adsorption while remaining unaffected under chlorination. Due to repositioning of some states above EF, provide an additional path for intraband transition, made systems more conductive except for fluorinated bilayer graphenes F-BLGs. A small band gap of 0.2 meV and 0.04 eV appeared at Fermi level of fluorinated non-bernal and bernal configuration, respectively. An E-field applied normal to the plane of F-BLGs can further tune the band gap. Due to underestimation of Band gap using GGA, hybrid functionals HSE06 were used for better estimation.

Study on the mechanically exfoliated graphene saturable absorption dependence on the number of layers and its influence on passive mode-locking erbium-doped fiber laser dynamics

We experimentally investigated the saturable absorption influence of graphene layers with natural stacking order in an erbium-doped fiber laser passive mode-locking. Mechanically exfoliated graphene saturable absorber (MEGSA) samples, ranging from 1 to 6 layers, were fabricated preserving their natural ABA stacking order and precisely characterized by 2D band profile from Raman spectroscopy. By incorporating the samples as saturable absorbers (SA) in the fiber laser, mode-locking performances with pulse duration from 670–780 fs and bandwidth from 3.8–4.6 nm could be generated. Also, we identified a transition in the mode-locking activation mechanism from non-self-starting, for monolayer and bilayer graphene, to self-starting, for trilayer and few-layer graphene, which is a strong indicative of fast-to-slow saturable absorption response dependence on the number of graphene layers.

Spintronic phase transition of graphene/BN/graphene van de Waals heterostructures

Based on a single-orbital tight-binding (TB) Hubbard model under mean-field approximation, we study band structure and half-metallicity of zigzag graphene/boron nitride/graphene (Z-G/BN/G) trilayer nanoribbon systems. Under different Coulomb repulsion and local potentials, the system will exhibit metallic, half-metallic and semiconductor phases, and the corresponding phase transition regions are also different. For the three stacking sequences, a large local potential on the top layer can destroy its half-metallicity. For AAA and ABA stacking, half-metallicity can occur in top or bottom layer, whereas half-metallicity occurs in bottom layer for ABC stacking. This indicates that the stacking sequence can be a new degree of freedom to tune the half-metallicity.

Direct Visualization and Manipulation of Stacking Orders in Few-Layer Graphene by Dynamic Atomic Force Microscopy.

Stacking order plays a central role in governing a wide range of properties in layered two-dimensional materials. In the case of few-layer graphene, there are two common stacking configurations: ABA and ABC stacking, which have been proven to exhibit dramatically different electronic properties. However, the controllable characterization and manipulation between them remain a great challenge. Here, we report that ABA- and ABC-stacked domains can be directly visualized in phase imaging by tapping-mode atomic force microscopy with much higher spatial resolution than conventional optical spectroscopy. The contrasting phase is caused by the different energy dissipation by the tip-sample interaction. We further demonstrate controllable manipulation on the ABA/ABC domain walls by means of propagating stress transverse waves generated by the tapping of tip. Our results offer a reliable strategy for direct imaging and precise control of the atomic structures in few-layer graphene, which can be extended to other two-dimensional materials.

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.

Real-time tracking of the self-assembled growth of a 3D Ge quantum dot lattice in an alumina matrix

A laboratory in situ grazing-incidence small-angle X-ray scattering (GISAXS) tracking of the self-assembled growth of a regular 3D Ge quantum dot (QD) structure in an amorphous Al2O3 matrix during the ion beam sputter deposition of a periodic Ge/Al2O3 multilayer on silicon is reported. A 573 K substrate temperature proved to be necessary to achieve the self-assembly effect. Relying on a fast repeated acquisition of GISAXS patterns, the temporal evolution of the growing 3D Ge QD structure was analyzed bilayer by bilayer to determine its type, lateral and vertical correlation lengths, and inter-QD distance. The QD structure was found to have body-centered tetragonal lattice type with ABA stacking, with the lattice parameters refined by fitting the final GISAXS pattern relying on a paracrystal model. A single set of paracrystal parameters enables one to simulate the temporal evolution of the in situ GISAXS patterns throughout the deposition process, suggesting that the Ge QD self-assembly is driven from the very beginning solely by the growing surface morphology. Ex situ GISAXS and X-ray reflectivity measurements along with a cross-section high-resolution transmission electron microscopy analysis complete the study.

Giant perpendicular magnetic anisotropy in Ir/Co/Pt multilayers

We have studied the magnetic properties of multilayers composed of ferromagnetic metal Co and heavy metals with strong spin orbit coupling (Pt and Ir). Multilayers with symmetric (ABA stacking) and asymmetric (ABC stacking) structures are grown to study the effect of broken structural inversion symmetry. We compare the perpendicular magnetic anisotropy (PMA) energy of symmetric Pt/Co/Pt, Ir/Co/Ir multilayers and asymmetric Pt/Co/Ir, Ir/Co/Pt multilayers. First, the interface contribution to the PMA is studied using the Co layer thickness dependence of the effective PMA energy. Comparison of the interfacial PMA between the Ir/Co/Pt, Pt/Co/Ir asymmetric structures and Pt/Co/Pt, Ir/Co/Ir symmetric structures indicate that the broken structural inversion symmetry induced PMA is small compared to the overall interfacial PMA. Second, we find the magnetic anisotropy field is significantly increased in multilayers when the ferromagnetic layers are antiferromagnetically coupled via interlayer exchange coupling (IEC). Macrospin model calculations can qualitatively account for the relation between the anisotropy field and the IEC. Among the structures studied, the IEC is the largest for the asymmetric Ir/Co/Pt multilayers: the exchange coupling field exceeds 3 T and consequently, the anisotropy field approaches 10 T. Third, comparing the asymmetric Ir/Co/Pt and Pt/Co/Ir structures, we find the IEC and, to some extent, the interface PMA are stronger for the former than the latter. X-ray magnetic circular dichroism (XMCD) studies suggest that the proximity-induced magnetization in Pt is larger for the Ir/Co/Pt multilayers than the inverted structure (Pt/Co/Ir), which may partly account for the difference in the magnetic properties. These results show the intricate relation between PMA, IEC, and the proximity-induced magnetization that can be exploited to design artificial structures with unique magnetic characteristics.

Computational Modeling of Tensile Stress Effects on the Structure and Stability of Prototypical Covalent and Layered Materials.

Understanding the stability limit of crystalline materials under variable tensile stress conditions is of capital interest for technological applications. In this study, we present results from first-principles density functional theory calculations that quantitatively account for the response of selected covalent and layered materials to general stress conditions. In particular, we have evaluated the ideal strength along the main crystallographic directions of 3C and 2H polytypes of SiC, hexagonal ABA stacking of graphite and 2H-MoS. Transverse superimposed stress on the tensile stress was taken into account in order to evaluate how the critical strength is affected by these multi-load conditions. In general, increasing transverse stress from negative to positive values leads to the expected decreasing of the critical strength. Few exceptions found in the compressive stress region correlate with the trends in the density of bonds along the directions with the unexpected behavior. In addition, we propose a modified spinodal equation of state able to accurately describe the calculated stress–strain curves. This analytical function is of general use and can also be applied to experimental data anticipating critical strengths and strain values, and for providing information on the energy stored in tensile stress processes.

Stacking control in graphene-based materials: A promising method for fascinating physical properties

Graphene, defined as a single atomic plane of graphite, is a semimetal with small overlap between the valence and the conduction bands. The stacking of graphene up to several atomic layers can produce diverse physical properties, depending on the stacking way. The bilayer graphene is also a semimetal, adopting the AB-stacked (or Bernal-stacked) structure or the rare AA-stacked structure. The trilayer or a few layer graphene (FLG) can be semimetal or semiconductor, depending on whether it takes Bernal (ABA) stacking or rhombohedral (ABC) stacking. We will give a perspective on the recent two mild approaches to control the stacking via local transition from ABC stacking into ABA stacking. It is believed that with the rapid development of graphene-based materials, these techniques for stacking control can be used for more complex structure to fulfill fascinating properties and devices.

Stacking transition in rhombohedral graphite

Few layer graphene (FLG) has been recently intensively investigated for its variable electronic properties defined by a local atomic arrangement. While the most natural layers arrangement in FLG is ABA (Bernal) stacking, a metastable ABC (rhombohedral) stacking characterized by a relatively high energy barrier can also occur. When both stacking occur in the same FLG device this results in in-plane heterostructure with a domain wall (DW). We show that ABC stacking in FLG can be controllably and locally turned into ABA stacking by two following approaches. In the first approach, Joule heating was introduced and the transition was characterized by 2D-peak Raman spectra at a submicron spatial resolution. The observed transition was initiated at a small region and then the DW controllably shifted until the entire device became ABA stacked. In the second approach, the transition was achieved by illuminating the ABC region with a train of laser pulses of 790 nm wavelength, while the transition was visualized by transmission electron microscopy in both diffraction and dark field modes. Also, with this approach, a DW was visualized in the dark-field imaging mode, at a nanoscale spatial resolution.

Using a multi-layer graphene-based emitter to improve the performance of a concentrated solar thermionic converter

A new model of the concentrated solar thermionic converter (CSTIC) with a multi-layer graphene (MLG)-based emitter is established. Based on the formulas of the thermionic emission from the MLG with ABA and ABC stacking orders, the power output and the efficiency of the CSTIC are derived. The performance characteristics of the CSTIC are discussed. It is revealed that the maximum efficiency of the CSTIC with the MLG-based emitter is higher than that with the single layer graphene (SLG)-based emitter, and the operating temperature of the MLG-based cathode is lower than that of the SLG-based cathode. It is important to find that the performances of the CSTIC with the ABA stacked graphene are better than those with the ABC stacked graphene. The optimum surface work function of the MLG-based cathode at the maximum efficiency is larger than the work function of the SLG-based cathode so that the CSTIC with the MLG-based emitter can be experimentally implemented more easily than the CSTIC with the SLG-based emitter.

Selective fabrication of free-standing ABA and ABC trilayer graphene with/without Dirac-cone energy bands

Graphene is a single-layer carbon sheet with a honeycomb structure, and bilayer graphene consists of two graphene sheets with AB stacking. In trilayer graphene, the third graphene sheet has two possible stacking sequences, A or C, when it is overlaid on bilayer graphene. It has been theoretically predicted that trilayer graphene exhibits a variety of novel electronic properties with/without a Dirac-cone band, depending on the stacking sequence. In this regard, trilayer graphene has a high potential for widening the capability of graphene-based electronic devices. However, the difficulty of selective fabrication has hindered the progress of research. Here, we report the first success in the selective fabrication of quasi-free-standing trilayer graphene with ABA or ABC stacking grown epitaxially on hydrogen-terminated silicon carbide. Angle-resolved photoemission spectroscopy (ARPES) clearly demonstrated that our trilayer graphene with ABA stacking has a massless Dirac-like band near the Fermi level, while that with ABC stacking shows a parabolic non-Dirac-like band dispersion.

Efficient utilization of multilayer graphene towards thermionic convertors

In this paper a comprehensive model to investigate the thermionic emission from few layer graphene (FLG) structures operating at finite temperature (T) and its feasibility towards thermionic energy conversion scheme as cathode, has been proposed. Taking into account the stacking dependent energy dispersion for the evaluation of density of states of Fermionic electrons and Fowler's treatment of the electron emission, the analytical expressions for the thermionic flux from ABA/ABC stacked FLG surfaces have been derived and shown to be an increasing function of number of constituent layers (N). In contrast to the usual RD law (∝T2) thermionic flux-temperature scaling, ABA and ABC stacked FLG have been identified to display ∝T3 and ∝T1+2/N temperature scaling. Utilizing the competence of FLGs to deliver substantial thermionic flux in fabricating the FLG based cathodes, an appropriate operating regime for the constituent parameters of the thermionic convertors (TCs) describing efficient energy conversion, has been specified. As a remarkable feature, FLG based cathodes provide flexibility to operate TC at low cathode (and high anode) temperature, with a sustained optimum efficacy (equal to the monolayer graphene). As an illustrative case, a TC configured with FLG based cathode (N = 10, ABA stacking, ∼900 K) and low work function (Cesium coated) metallic anode (2.0 V, 400 K) has been identified to display ∼55% of the conversion efficiency (equivalent to ∼82% of the Carnot efficiency). On the basis of analytical formulation, appropriately tuned FLG based cathode operating at low temperature, is proposed as a promising contrivance in achieving efficient energy conversion of heat into electrical power.

Synthesis of large size uniform single-crystalline trilayer graphene on premelting copper

Single-crystalline trilayer graphene (TLG) has attracted intensive interest due to rich optical and electronic properties. However, precise synthesis of large-size uniform single-crystalline TLG with ABA stacking still remains enormous challenge. Herein, an atmospheric pressure chemical vapor deposition (APCVD) process was developed to fabricate the uniform single-crystalline TLG on premelting copper at 1080 °C, which is slightly lower than copper melting temperature. As the results, ∼80 μm uniform single-crystalline TLG with ABA stacking was achieved on a premelting copper layer. Raman mapping and selected area electron diffraction of individual isolated domains reveals they are uniform single-crystalline with ABA stacking. The growth mechanism of the TLG was explored by studying the influence of varied growth temperature, which is subsequently shown that the 2nd and 3rd layer graphene grow simultaneously from external to internal with a twist angle of 20 ± 5°.

First-principles studies of electric field effects on the electronic structure of trilayer graphene

A gate electric field is a powerful way to manipulate the physical properties of nanojunctions made of two-dimensional crystals. To simulate field effects on the electronic structure of trilayer graphene, we used density functional theory in combination with the effective screening medium method, which enables us to understand the field-dependent layer-layer interactions and the fundamental physics underlying band gap variations and the resulting band modifications. Two different graphene stacking orders, Bernal (or ABC) and rhombohedral (or ABA), were considered. In addition to confirming the experimentally observed band gap opening in ABC-stacked and the band overlap in ABA-stacked trilayer systems, our results reveal rich physics in these fascinating systems, where layer-layer couplings are present but some characteristics features of single-layer graphene are partially preserved. For ABC stacking, the electric-field-induced band gap size can be tuned by charge doping, while for ABA band the tunable quantity is the band overlap. Our calculations show that the electronic structures of the two stacking orders respond very differently to charge doping. We find that in the ABA stacking hole doping can reopen a band gap in the band-overlapping region, a phenomenon distinctly different from electron doping. The physical origins of the observed behaviors were fully analyzed, and we conclude that the dual-gate configuration greatly enhances the tunability of the trilayer systems.

Atomic and electronic structure of trilayer graphene/SiC(0001): Evidence of Strong Dependence on Stacking Sequence and charge transfer.

The transport properties of few-layer graphene are the directly result of a peculiar band structure near the Dirac point. Here, for epitaxial graphene grown on SiC, we determine the effect of charge transfer from the SiC substrate on the local density of states (LDOS) of trilayer graphene using scaning tunneling microscopy/spectroscopy and angle resolved photoemission spectroscopy (ARPES). Different spectra are observed and are attributed to the existence of two stable polytypes of trilayer: Bernal (ABA) and rhomboedreal (ABC) staking. Their electronic properties strongly depend on the charge transfer from the substrate. We show that the LDOS of ABC stacking shows an additional peak located above the Dirac point in comparison with the LDOS of ABA stacking. The observed LDOS features, reflecting the underlying symmetry of the two polytypes, were reproduced by explicit calculations within density functional theory (DFT) including the charge transfer from the substrate. These findings demonstrate the pronounced effect of stacking order and charge transfer on the electronic structure of trilayer or few layer graphene. Our approach represents a significant step toward understand the electronic properties of graphene layer under electrical field.

Rhombohedral Multilayer Graphene: A Magneto-Raman Scattering Study.

Graphene layers are known to stack in two stable configurations, namely, ABA or ABC stacking, with drastically distinct electronic properties. Unlike the ABA stacking, little has been done to experimentally investigate the electronic properties of ABC graphene multilayers. Here, we report on the first magneto optical study of a large ABC domain in a graphene multilayer flake, with ABC sequences exceeding 17 graphene sheets. ABC-stacked multilayers can be fingerprinted with a characteristic electronic Raman scattering response, which persists even at room temperatures. Tracing the magnetic field evolution of the inter Landau level excitations from this domain gives strong evidence for the existence of a dispersionless electronic band near the Fermi level, characteristic of such stacking. Our findings present a simple yet powerful approach to probe ABC stacking in graphene multilayer flakes, where this highly degenerated band appears as an appealing candidate to host strongly correlated states.

Anharmonicity effects in the frictionlike mode of graphite

Graphite is a prototypical solid lubricant demanding a thorough understanding of its low-friction behavior. The ${E}_{2g}$(1) Raman active vibrational mode of graphite is associated with the rigid-layer relative movement of its graphene sheets. Thus, this mode can provide a good means of exploring the low resistance of graphene layers to slip with respect to each other. To take advantage of this fact, the anharmonicity of the ${E}_{2g}$(1) mode has to be carefully characterized and evaluated since the atomic arrangement of carbon atoms in the ambient condition ABA stacking of graphite evidences potential asymmetry. The calculated one-dimensional energetic profile of the ${E}_{2g}$(1) mode reveals this local anisotropy around the energy minima and can be microscopically interpreted in terms of electron density interactions. Morse-type potentials accurately fit the energetic profiles at different interlayer separations, and provide simple analytical expressions for evaluating harmonic and anharmonic contributions to the $\mathrm{\ensuremath{\Gamma}}$-point ${E}_{2g}$(1) frequency ${\ensuremath{\omega}}_{{E}_{2g}(1)}$ under a perturbative algebraic treatment. We quantify how the anharmonic contribution increases with the available energy ($E$) at zero pressure, and how this contribution decreases as hydrostatic pressure ($p$) or uniaxial stress is applied for a given available energy. The calculated ${\ensuremath{\omega}}_{{E}_{2g}(1)}\ensuremath{-}p$ and ${\ensuremath{\omega}}_{{E}_{2g}(1)}\ensuremath{-}E$ trends indicate an increasing (decreasing) of frictional forces in graphite with pressure (temperature). Our conclusions are supported by the good agreement of the calculated frequencies with existing Raman experiments under hydrostatic pressure conditions.