Thermal properties of bilayer graphene influenced by interlayer coupling

Moiré is More: Access to New Properties of Two-Dimensional Layered Materials

This paper investigates strain effects on the electronic properties of single-layer and bilayer graphene using a first-principles method. The deformation significantly alters energy dispersion, band overlap, band gap, and the band edges of graphenes. Fermi velocity behaves both linearly and nonlinearly with the strains, depending on the types of deformation and the direction of the Fermi velocity. In bilayer graphene, the uniaxial strain enhances the band overlap by 2 orders of magnitude. A semimetal–insulator transition occurs when bilayer graphene is under a compressive uniaxial strain along the zigzag chain direction. These strain-dependent results are useful for acquiring the intralayer and interlayer atomic relations or Slonczewski–Weiss–McClure parameters. The intralayer coupling γ0 under the H-strain and interlayer couplings γ1, γ3, and γ4 under the P-strain decrease dramatically as the strain increases. Nevertheless, interlayer couplings vary more slowly with the H-strain than the P-strain.

Many of the intriguing properties of bilayer graphene (BLG) are related to interlayer electronic coupling. Since this coupling is sensitive to an applied electric field perpendicular to the layers, we develop a strategy for determining interlayer coupling by decomposing the total electric dipole polarizability, which measures the response of electrons to applied fields, into site-specific contributions and consequently the intralayer and interlayer components. The interlayer polarizability is evaluated from field-induced electron density variations computed with a first-principles approach for twisted BLG quantum dots (QDs). Changes in interlayer polarizability dominate the polarizability variation with twist angle. In addition to the well-recognized strong coupling in the Bernal stackings, enhanced coupling is revealed for the structures at small and size-dependent twist angles when AB stacking first appears in the outermost shell of the QD. The values of these magic angles depend on the QD size. This paper not only provides an approach for measuring interlayer coupling strength but also indicates the existence of strong interlayer coupling even at small twist angles, which could be important for understanding the properties of twisted BLG.

Bilayer graphene can exhibit deformations such that the two graphene sheets are locally detached from each other resulting in a structure consisting of domains with different van der Waals inter-layer coupling. Here we investigate how the presence of these domains affects the transport properties of bilayer graphene. We derive analytical expressions for the transmission probability, and the corresponding conductance, across walls separating different inter-layer coupling domains. We find that the transmission can exhibit a valley-dependent layer asymmetry and that the domain walls have a considerable effect on the chiral tunnelling properties of the charge carriers. We show that transport measurements allow one to obtain the strength with which the two layers are coupled. We perform numerical calculations for systems with two domain walls and find that the availability of multiple transport channels in bilayer graphene significantly modifies the conductance dependence on inter-layer potential asymmetry.

The present work deals with the analysis of the quasi-particle spectrum and the density of states of monolayer and bilayer (AB- and AA-stacked) graphene. The tight binding Hamiltonian containing nearest-neighbor and next-nearest neighbor hopping and onsite Coulomb interaction within two triangular sub-lattice approach for monolayer graphene, along-with the interlayer coupling parameter for bilayer graphene has been employed. The expressions of quasi-particle energies and the density of states (DOS) are obtained within mean-field Green’s function equations of motion approach. It is found that next-nearest-neighbour intralayer hopping introduce asymmetry in the electronic states above and below the zero point energy in monolayer and bilayer (AA- and AB-stacked) graphene. The behavior of electronic states in monolayer and bilayer graphene is different and highly influenced by interlayer coupling and Coulomb interaction. It has been pointed out that the interlayer coupling splits the quasi-particle peak in density of states while the Coulomb interaction suppresses the bilayer splitting and generates a gap at Fermi level in both AA- and AB-stacked bilayer graphene. The theoretically obtained quasi-particle energies and density of states in monolayer and bilayer (AA- and AB-stacked) graphene has been viewed in terms of recent ARPES and STM data on these systems.

The single-particle and many-body properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, particularly when the two layers are rotated relative to each other by a small angle (θ ≈ 1°), owing to the moiré potential induced by the twist. Here we probe the collective excitations of TBG with a spatial resolution of 20 nm, by applying mid-infrared near-field optical microscopy. We find a propagating plasmon mode in charge-neutral TBG for θ = 1.1−1.7°, which is different from the intraband plasmon in single-layer graphene. We interpret it as an interband plasmon associated with the optical transitions between minibands originating from the moiré superlattice. The details of the plasmon dispersion are directly related to the motion of electrons in the moiré superlattice and offer an insight into the physical properties of TBG, such as band nesting between the flat band and remote band, local interlayer coupling, and losses. We find a strongly reduced interlayer coupling in the regions with AA stacking, pointing at screening due to electron–electron interactions. Optical nano-imaging of TBG allows the spatial probing of interaction effects at the nanoscale and potentially elucidates the contribution of collective excitations to many-body ground states. Moiré potentials substantially alter the electronic properties of twisted bilayer graphene at a magic twist angle. A propagating plasmon mode, which can be observed with optical nano-imaging, is associated with transitions between the moiré minibands.

Two-dimensional materials have recently been the focus of extensive research. Graphene-based vertical van der Waals heterostructures are expected to design and fabricate novel electronic and optoelectronic devices. Monolayer gallium telluride is a graphene-like nanosheet synthesized in experiment. Here, the electronic properties of GaTe/graphene heterostructures are investigated under the interlayer coupling and the applied perpendicular electric field. The results show that the electronic properties of GaTe and graphene are preserved, and the energy bandgap of graphene is opened to 13.5 meV in the GaTe/graphene heterostructure. It is found that the n-type Schottky contact is formed in the GaTe/graphene heterostructure, which can be tuned by the interlayer coupling, and the applied electric field. Moreover, a transformation from n-type to p-type Schottky contact is observed when the interlayer distance is smaller than 3.15 Å or the applied electric field is larger than 0.05 V Å−1. These properties are fundamental to the design of new Schottky nanodevices based on the GaTe/graphene heterostructure.

Lifshitz transition and modulation of electronic and transport properties of bilayer graphene by sliding and applied normal compressive strain

The phonon dispersions of monolayer and few-layer graphene ($AB$ bilayer, and $ABA$ and $ABC$ trilayers) are investigated using the density-functional perturbation theory. Compared with the monolayer, the optical phonon ${E}_{2g}$ mode at $\ensuremath{\Gamma}$ splits into two and three doubly degenerate branches for bilayer and trilayer graphene, respectively, due to the weak interlayer coupling. These modes are of various symmetries and exhibit different sensitivities to either Raman or infrared measurements (or both). The splitting is found to be $5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ for bilayer and $2--5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ for trilayer graphene. The interlayer coupling is estimated to be about $2\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. We found that the highest optical modes at $K$ move up by about $12\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ for bilayer and $18\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ for trilayer relative to monolayer graphene. The atomic displacements of these optical eigenmodes are analyzed.

A generic tight-binding model for 2p z electrons in bilayer graphene (BLG) systems is used to derive the expression of effective Hamiltonians for low-energy states around the K-points of hexagonal Brillouin zone. The obtained effective Hamiltonians are validated for two kinds of AA-like and AB-like slid bilayer graphene (SBG). It is shown that, for the former case, the electronic structure is characterized by a gauge vector field which couples to the sliding vector to deform the band structure of the AA-stacked configuration as a perturbation. For the latter case, since the A–B interlayer coupling is the most dominant, it allows separating the energy bands and lowering the 4 × 4 Hamiltonian into a 2 × 2 effective model. A gauge vector field also appears, but different from the AA-like SBGs, it plays the role similar to an in-plane magnetic field.

Bilayer graphene samples may exhibit regions where the two layers are locally delaminated forming a so-called quantum blister in the graphene sheet. Electron and hole states can be confined in this graphene quantum blisters (GQB) by applying a global electrostatic bias. We scrutinize the electronic properties of these confined states under the variation of interlayer bias, coupling, and blister’s size. The spectra display strong anti-crossings due to the coupling of the confined states on upper and lower layers inside the blister. These spectra are layer localized where the respective confined states reside on either layer or equally distributed. For finite angular momentum, this layer localization can be at the edge of the blister and corresponds to degenerate modes of opposite momenta. Furthermore, the energy levels in GQB exhibit electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we demonstrate that confinement in GQB persists even in the presence of a variation in the inter-layer coupling.

Among the graphene family, bilayer graphene (BLG) exhibits more diverse electronic structures and higher tunability than monolayer graphene due to its unique interlayer coupling effect, emerging as a crucial branch in functionalization research. By utilizing its interlayer as an embedding channel, BLG avoids impairing graphene's intrinsic conductivity-a common issue with surface modification. Furthermore, the interlayer coupling allows for synergistic engineering of its electronic structure, yielding performance superior to that of monolayer graphene. Therefore, the interface of BLG represents a potential functionalization site. Based on the aforementioned research status and issues, all calculations in this study are performed using density functional theory (DFT) via the Vienna Ab-initio Simulation Package (VASP). To accurately describe the van der Waals (vdW) interactions (π-π stacking) between the layers of AB-stacked BLG, the DFT-D3 method is employed for vdW correction to investigate the influence of functional groups on BLG electrical properties. This study focuses on four functional groups (-OH, -CO, -CHO, and -COOH), whose contained O and H atoms can readily form chemical bonds with the carbon atoms in BLG. Through interlayer modification, the interactions between these functional groups and the carbon atoms are analyzed to realize the regulation of interlayer coupling and electronic structure characteristics of BLG. The insertion of -OH and -CHO into the interlayer of BLG results in higher stability and lower interfacial binding energy, whereas the insertion of -CO and -COOH leads to reduced stability. The Fermi level of BLG shifts to varying degrees upon the insertion of functional groups. Specifically, the insertion of -OH or -COOH causes the Fermi level to shift toward lower energy levels, reducing the highest occupied energy level. In contrast, the insertion of -CO or -CHO shifts the Fermi level toward higher energy levels, exciting more electrons to higher energy states and resulting in electron filling at elevated energy levels. The band structure of BLG undergoes significant modifications due to the insertion of functional groups. The original parabolic band dispersion is disrupted, and the band distribution becomes more complex, with altered line trajectories and crossing characteristics. Partial density of states (PDOS) and charge density difference calculations reveal orbital hybridization and charge transfer between the functional groups and BLG. All four functional groups form covalent bonds with the carbon atoms of BLG, exhibiting characteristics of chemical adsorption. Moreover, the extent of charge transfer and the perturbation of charge density vary significantly among the different functional groups. This study aims to elucidate the regulatory mechanisms and underlying principles of functional groups, providing a theoretical basis for designing BLG-based electronic materials with specific functionalities, while also enriching the research framework of interlayer functionalization in two-dimensional layered materials.

Graphene is a fascinating new nanocarbon possessing, single-, bi- or few- (≤ ten) layers of carbon atoms forming six-membered rings. Different types of graphene have been investigated by X-ray diffraction, atomic force microscopy, transmission electron microscopy, scanning tunneling microscopy and Raman spectroscopy. The extraordinary electronic properties of single-and bi-layer graphenes are indeed most unique and unexpected. Other properties of graphene such as gas adsorption characteristics, magnetic and electrochemical properties and the effects of doping by electrons and holes are equally noteworthy. Interestingly, molecular charge-transfer also markedly affects the electronic structure and properties of graphene. Many aspects of graphene are yet to be explored, including synthetic strategies which can yield sufficient quantities of graphene with the desired number of layers.

Influence of interlayer coupling and intra-layer Coulomb interaction on electronic transport in bilayer graphene

It is fundamentally important to understand how the interlayer interaction of neighboring graphene sheets is influenced by chemical doping. Here we investigate the interlayer coupling of multilayer graphene doped with controlled boron content via the Raman-active in-plane shear mode. The experimental results reveal a remarkable decline in the interlayer shear modulus as boron content increases, which is a direct consequence of the enlarged interlayer spacing, further supported by the molecular dynamic (MD) simulations. Nanoindentation tests were conducted to clarify the influence of interlayer coupling behaviors on nanomechanical behaviors of boron-doped bilayer graphene. As the interlayer slippage is induced under shear deformations, the weakened shear resistance would lead to the reduced energy dissipation during sliding process. Our results provide valuable insight into fundamental mechanical properties of boron-doped graphene and its interfaces and potentially allows tailoring of interlayer coupling f...