Influence of the Diagonal and Off-Diagonal Electron–Phonon Interactions on the Formation of Local Polarons and Their Band Structure in Materials with Strong Electron Correlations

For systems with strong electron correlations and strong electron–phonon interaction, we analyze the electron–phonon interaction in local variables. The effects of the mutual influence of electron–electron and electron–phonon interactions that determine the structure of local Hubbard polarons are described. Using a system containing copper–oxygen layers as an example, we consider the competition between the diagonal and off-diagonal interactions of electrons with the breathing mode as the polaron band structure is formed within a corrected formulation of the polaron version of the generalized tight-binding method. The band structure of Hubbard polarons is shown to depend strongly on the temperature due to the excitation of Franck–Condon resonances. For an undoped La₂CuO₄ compound we have described the evolution of the band structure and the spectral function from the hole dispersion in an antiferromagnetic insulator at low temperatures with the valence band maximum at point (π/2, π/2) to the spectrum with the maximum at point (π, π) typical for the paramagnetic phase. The polaron line width at the valence band top and its temperature dependence agree qualitatively with angle-resolved photoemission spectroscopy for undoped cuprates.     

Possible polaron formation of zigzag graphene nano-ribbon in the presence of Rashba spin–orbit coupling

In this article we study the role of Rashba spin–orbit coupling and electron–phonon interaction on the electronic structure of zigzag graphene nanoribbon with different width. The total Hamiltonian of nanoribbon is written in the tight binding form and the electron–electron interaction is modeled in the Hubbard term. We used a unitary transformation to reach an effective Hamiltonian for nano ribbon in the presence of electron–phonon interaction. Our results show that small Rashba spin orbit coupling annihilates the anti-ferromagnetic phase in the zigzag edges of ribbon and the electron–phonon interaction yields small polaron formation in graphene nano ribbon. Furthermore, Rashba type spin–orbit coupling increases (decreases) the polaron formation energy for up (down) spin state.     

Two-dimensional phonon transport in graphene

Properties of phonons-quanta of the crystal lattice vibrations-in graphene have recently attracted significant attention from the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature, while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in a quasi-two-dimensional system such as graphene compared to the basal planes in graphite or three-dimensional bulk crystals. The unique nature of two-dimensional phonon transport translates into unusual heat conduction in graphene and related materials. In this review, we outline different theoretical approaches developed for phonon transport in graphene, discuss contributions of the in-plane and cross-plane phonon modes, and provide comparison with available experimental thermal conductivity data. Particular attention is given to analysis of recent results for the phonon thermal conductivity of single-layer graphene and few-layer graphene, and the effects of the strain, defects, and isotopes on phonon transport in these systems.     

Phonon dispersion of quasi-freestanding graphene on Pt(111)

High-resolution electron energy loss spectroscopy has been used to probe phonon dispersion in quasi-freestanding graphene epitaxially grown on Pt(111). Loss spectra clearly show different dispersing features related to both acoustic and optical phonons. The present results have been compared with graphene systems which strongly interact with the substrate, i.e. the nearly-flat monolayer graphene (MLG)/Ni(111) and the corrugated MLG/Ru(0001). We found that the phonon dispersion of graphene/Pt(111) reproduces well the behavior of pristine graphite. This could be taken as an indication of the negligible interaction between the graphene sheet and the underlying Pt substrate. The softening of out-of-plane modes observed for interacting graphene/metal interfaces does not occur for the nearly-free-standing graphene/Pt(111).     

单壁碳纳米扶手椅、锯齿管声子色散关系的计算

引用石墨经验力常数计算碳纳米管声子色散关系时，必须处理由二维平面卷曲形成三维实体纳米管所引入的问题. 报道对一系列扶手椅和锯齿单壁碳纳米管计及卷曲效应的声子色散关系的计算结果. 基于实际的数值计算结果，以及对单壁碳纳米扶手椅、锯齿管结构的对称性分析，讨论了Brillouin区中心Γ点晶格振动模的分类. 关键词： 碳纳米管 声子色散关系     

Thermal properties of transition-metal dichalcogenide

Beyond graphene, the layered transition metal dichalcogenides(TMDs) have gained considerable attention due to their unique properties. Herein, we review the lattice dynamic and thermal properties of monolayer TMDs, including their phonon dispersion, relaxation time, mean free path(MFP), and thermal conductivities. In particular, the experimental and theoretical studies reveal that the TMDs have relatively low thermal conductivities due to the short phonon group velocity and MFP, which poses a significant challenge for efficient thermal management of TMDs-based devices. Importantly,recent studies have shown that this issue could be largely addressed by connecting TMDs and other materials(such as metal electrode and graphene) with chemical bonds, and a relatively high interfacial thermal conductance(ITC) could be achieved at the covalent bonded interface. The ITC of MoS_2/Au interface with chemical edge contact is more than 10 times higher than that with physical side contact. In this article, we review recent advances in the study of TMD-related ITC.The effects of temperature, interfacial vacancy, contact orientation, and phonon modes on the edge-contacted interface are briefly discussed.     

势能模型对石墨烯导热性质分子动力学模拟的影响

针对常用的Tersoff势、Rebo势和Airebo势,系统性地分析势能模型对分子动力学模拟计算石墨烯色散关系、声子态密度、群速度和热导率的影响. 结果表明：Rebo势和Airebo势描述的声子色散关系接近实验值,Airebo势对应的声子态密度与第一性原理计算的结果较为符合,Rebo势和Airebo势计算的Γ点处声子群速度高于Tersoff势. 采用Airebo势得到石墨烯热导率约为1 150 W·（m·K）^-1,与实验值相近. 综合各种影响,相比于Tersoff势和Rebo势,Airebo势能模型更适合计算石墨烯的导热性质.     

Thermal transport in graphene

The recent advances in graphene isolation and synthesis methods have enabled potential applications of graphene in nanoelectronics and thermal management, and have offered a unique opportunity for investigation of phonon transport in two-dimensional materials. In this review, current understanding of phonon transport in graphene is discussed along with associated experimental and theoretical investigation techniques. Several theories and experiments have suggested that the absence of interlayer phonon scattering in suspended monolayer graphene can result in higher intrinsic basal plane thermal conductivity than that for graphite. However, accurate experimental thermal conductivity data of clean suspended graphene at different temperatures are still lacking. It is now known that contact of graphene with an amorphous solid or organic matrix can suppress phonon transport in graphene, although further efforts are needed to better quantify the relative roles of interface roughness scattering and phonon leakage across the interface and to examine the effects of other support materials. Moreover, opportunities remain to verify competing theories regarding mode specific scattering mechanisms and contributions to the total thermal conductivity of suspended and supported graphene, especially regarding the contribution from the flexural phonons. Several measurements have yielded consistent interface thermal conductance values between graphene and different dielectrics and metals. A challenge has remained in establishing a comprehensive theoretical model of coupled phonon and electron transport across the highly anisotropic and dissimilar interface.     

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials. The phonon dispersion relation, as well as the vibrational density of states, is also often used as an indicator of variation of lattice thermal conductivity with the external stress, defects, etc. In this study, a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package. The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present. The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell. Then, the phonon dispersions corresponding to several potentials or force fields, which are commonly used in the LAMMPS package to modeling the graphene, are obtained to compare with that from the DFT calculation. They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation. The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell, which predicts the phonon band gaps along the cross-plane direction. Since the phonon dispersion relation plays an important role in the physical properties of condensed matter, the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.     

The linewidth of infrared light transitions between the Landau levels in graphene

We theoretically propose a structure that the population inversion between the Landau levels (LLs) of the graphene can be achieved by the electrical injection. This structure may be used for the Landau level-laser and related infrared and terahertz emitters. We mainly study the linewidth of the optical transitions between LLs in graphene due to the electron–acoustic phonon scattering. Within the Huang–Rhysʼs lattice relaxation model, we improve the effective single-phonon mode (ESM) for the acoustic phonon to calculate the linewidth of the optical transition and compare the obtained results with that of in the low and high-temperature limit. We find that the ESM provides a very good approximation for the temperature dependence of linewidth, which covers the dominating features of the low and high-temperature limit.     

Thickness and stacking geometry effects on high frequency overtone and combination Raman modes of graphene

We investigate two high frequency Raman overtone and combination modes of graphene named 2D' and 2D + G bands, and located at ~3240 and ~ 4260 cm^–1, respectively. The graphene thickness and stacking geometry effects for these two modes are systematically studied. The features of the 2D' band, which arises from intravalley double resonance, are not sensitive to the variation of thickness with single Lorentzian peak and fixed linewidth. We explain it theoretically by calculating the phonon dispersion mode in k‐space and find that the flat band region of longitudinal optical phonon near Γ point is the mechanism leading to the 2D' band nonsplit. With the thickness increasing, the band position exhibits blueshift and the linewidth increases for the 2D + G band. With changing thickness and stacking geometry of graphene, the intensities of these two high‐frequency bands show obvious different evolution compared with that of G band. Copyright © 2012 John Wiley & Sons, Ltd.     

Formation of quasi-free graphene on the Ni(111) surface with intercalated Cu,Ag, and Au layers

This paper reports on a study by angle-resolved photoelectron and low-energy electron energy loss spectroscopy of graphene monolayers, which are produced by propylene cracking on the Ni(111) surface, followed by intercalation of Cu, Ag, and Au atoms between the graphene monolayer and the substrate, for various thicknesses of deposited metal layers and annealing temperatures. It has been shown that the spectra of valence-band π states and of phonon vibrational modes measured after intercalation become similar to those characteristic of single-crystal graphite with weak interlayer coupling. Despite the strong coupling of the graphene monolayer to the substrate becoming suppressed by intercalation of Cu and Ag atoms, the π state branch does not reach at the K point of the Brillouin zone the Fermi level, with the graphene coating itself breaking up partially to form graphene domains. At the same time after intercalation of Au atoms, the electronic band structure approaches the closest to that of isolated graphene, with linear π-state dispersion near the K point of the Brillouin zone, and the point of crossing of the filled, (π), with empty, (π*), states lying in the region of the Fermi level, which makes this system a promising experimental model of the quasi-free graphene monolayer.     

Phonon dispersion in graphene

Taking into account the constraints imposed by the lattice symmetry, we calculate the phonon dispersion for graphene with interactions between the first and second nearest neighbors. We show that only five force constants give a very good fitting to the elastic constants and phonon frequencies observed in graphite. The text was submitted by the author in English.     

Theory of superconductivity for Dirac electrons in graphene

Phonon-exchange-induced superconducting pairing of effectively ultrarelativistic electrons in graphene is investigated. The Eliashberg equation obtained for describing pairing in the Cooper channel with allowance for delayed interaction are matrix equations with indices corresponding to the valence and conduction bands. The equations are solved in the high doping limit, in which pairing is effectively a single-band process, and in the vicinity of a critical quantum point of underdoped graphene for a value of the coupling constant for which pairing is an essentially multiband process. For such cases, analytic estimates are obtained for the superconducting transition temperature of the system. It is shown that the inclusion of dynamic effects makes it possible to determine the superconducting transition temperature, as well as the critical coupling constant for underdoped graphene, more accurately than in the static approximation of the BCS type. Estimates of the constants of electron interaction with the scalar optical phonon mode in graphene indicate that an appreciable superconducting transition temperature can be attained under a high chemical doping level of graphene.     

Interlayer transport of an electron in bilayer graphene with phonon-induced lattice distortion in the presence of biased potential

The interlayer transport of an electron in bilayer graphene influenced by a phonon in the presence of a biased potential is investigated using the tight-binding approach. The in-plane optical mode E2g and out-of-plane optical mode B1g associated with the applied biased potential are considered to compute and discuss the interlayer transport probability of an electron initially localized on the bottom layer at the Dirac point in the Brillouin zone. Without the biased potential, the interlayer transport probability is equal to 0.5 regardless of the phonon displacement except for a few special cases. Applying a biased potential to the layers, we find that in different phonon modes the function of the transport probability with respect to the applied biased potential and phonon displacement is complex and various, but on the whole the transport probability decreases with the increase in the absolute value of the applied biased potential. These phenomena are discussed in detail in this paper.     

Interlayer transport of electron in bilayer graphene with phonon-induced lattice distortion in the presence of biased potential

The interlayer transport of electron in bilayer graphene influenced by phonon in the presence of biased potential is investigated using the tight-binding approach. The in-plane optical mode E_2g and out-of-plane optical mode B_1g associated with the applied biased potential are considered to compute and discuss the interlayer transport probability of an electron initially localized on the bottom layer at the Dirac point in the Brillouin zone. Without the biased potential, the interlayer transport probability is equal to 0.5 regardless of the phonon displacement except for a few special cases. Applying a biased potential to the layers, we find that in different phonon mode the function of the transport probability with respect to applied biased potential and phonon displacement is complex and various, but on the whole the transport probability decreases with the increase in the absolute value of the applied biased potential. These phenomena are discussed in detail in this paper.     

Observation of low‐wavenumber out‐of‐plane optical phonon in few‐layer graphene

Few‐layer graphene grown by chemical vapor deposition has been studied by Raman and ultrafast laser spectroscopy. A low‐wavenumber Raman peak of ~120 cm⁻¹ and a phonon‐induced oscillation in the kinetic curve of electron–phonon relaxation process have been observed, respectively. The Raman peak is assigned to the low‐wavenumber out‐of‐plane optical mode in the few‐layer graphene. The phonon band shows an asymmetric shape, a consequence of so‐called Breit‐Wigner‐Fano resonance, resulting from the coupling between the low‐wavenumber phonon and electron transitions. The obtained oscillation wavenumber from the kinetic curve is consistent with the detected low‐wavenumber phonon by Raman scattering. The origin of this oscillation is attributed to the generation of coherent phonons and their interactions with photoinduced electrons. Copyright © 2012 John Wiley & Sons, Ltd.     

Phonon dispersion in Xe

The predictions of the Mie-Lennard-Jones potentials for phonon dispersion in solid Xe at 10°K and at 77°K are compared with the results of recent measurements. The dynamics of the crystal are described by the first order self-consistent phonon theory for the imaginary part of the one phonon Green's function. The fit obtained is quite poor though we point out that no conclusion can be drawn about the size of three-body forces. We conclude that improved potentials are needed to account for the experimental data.     

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.     

Analytical model of transverse oscillations of graphene

A simple analytical model of transverse oscillations of graphene is constructed. The model is applicable to both free and stretched graphene monolayers. The dispersion relation for transverse oscillations of graphene and the corresponding phonon state density are determined.