利用密度泛函微扰理论研究了单层和少层石墨烯（AB双层、ABA和ABC三层）的声子色散。与单层相比，由于层间耦合较弱，双层和三层石墨烯的光学声子$E_{2g}$模在$Γ$处分别分裂为两个和三个双简并分支.这些模式具有不同的对称性，并且对拉曼或红外（IR）测量（或两者）表现出不同的灵敏度。发现双层石墨烯的分裂为5 cm $^{-1}$，三层石墨烯的分裂为2至5 cm $^{-1}$。层间耦合估计为约2 cm $^{-1}$。我们发现，在K的最高光学模式移动约12厘米$^{-1}$的双层和18厘米$^{-1}$的三层相对于单层石墨烯。分析了这些光学本征模的原子位移。
英文摘要：
The phonon dispersions of monolayer and few-layer graphene (AB bilayer, ABA and ABC trilayers) are investigated using the density-functional perturbation theory (DFPT). Compared with the monolayer, the optical phonon $E_{2g}$ mode at $Γ$ 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 symmetry and exhibit different sensitivity to either Raman or infrared (IR) measurements (or both). The splitting is found to be 5 cm$^{-1}$ for bilayer and 2 to 5 cm$^{-1}$ for trilayer graphene. The interlayer coupling is estimated to be about 2 cm$^{-1}$. We found that the highest optical modes at K move up by about 12 cm$^{-1}$ for bilayer and 18 cm$^{-1}$ for trilayer relative to monolayer graphene. The atomic displacements of these optical eigenmodes are analyzed.
Manipulating electronic interlayer coupling in layered van der Waals (vdW) materials is essential for designing opto-electronic devices. Here, we control vibrational and electronic interlayer coupling in bi- and trilayer 2H-MoS$_2$ using large external electric fields in a micro-capacitor device. The electric field lifts Raman selection rules and activates phonon modes in excellent agreement with ab-initio calculations. Through polarization resolved photoluminescence spectroscopy in the same device, we observe a strongly tunable valley dichroism with maximum circular polarization degree of $\s…
Due to the absence of interlayer coupling and inversion symmetry, transition metal dichalcogenide (MX$_2$) semiconductor monolayers exhibit novel properties that are distinctly different from their bulk crystals such as direct optical band gaps, large band spin splittings, spin-valley coupling, piezoelectric and nonlinear optical responses, and thus have promising applications in, e.g., opto-electronic and spintronic devices. Here we have performed a systematic first-principles study of the second-order nonlinear optical properties of MX$_2$ (M = Mo, W; X = S, Se) monolayers and trilayers with…
Among the most common few-layers transition metal dichalcogenides (TMDs), WSe2 is the most challenging material from the lattice dynamics point of view. Indeed, for a long time the main two phonon modes (A1g and E12g) have been wrongly assigned. In the last few years, these two modes have been properly interpreted, and their quasi-degeneracy in the monolayer has been used for its identification. In this work, we show that this approach has a limited validity and we propose an alternative, more general approach, based on multi-phonon bands. Moreover, we show and interpret all the peaks (about 4…
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…
In this work, we have presented a first principle simulation study on the electronic properties of MoS2/MX2/MoS2 (M=Mo or W; X=S or Se) trilayer heterostrcuture. We have investigated the effect of stacking configuration, bi-axial compressive and tensile strain on the electronic properties of the trilayer heterostructures. In our study, it is found that, under relaxed condition all the trilayer heterostructures at different stacking configurations show semiconducting nature. The nature of the bandgap however depends on the inserted TMDC monolayer between the top and bottom MoS2 layers and their…
Assessing quantitative phase reliability in electron ptychography using a twisted trilayer WS2 thickness staircase
University of Science and Technology of China（中国科学技术大学）；Yanshan University（燕山大学）；Zhejiang University of Technology（浙江工业大学）；University of Chinese Academy of Sciences（中国科学院大学）
First-principles studies of two-dimensional transition metal dichalcogenides have contributed considerably to the understanding of their dielectric, optical, elastic, and vibrational properties. The majority of works to date focus on a single material or physical property. Here we use a single first-principles methodology on the whole family of systems, to investigate in depth the relationships between different physical properties, the underlying symmetry and the composition of these materials, and observe trends. We compare to bulk counterparts to show strong interlayer effects in triclinic …
Starting with twisted bilayer graphene, graphene-based moiré materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic-angle of 1.16$^\circ$. When monolayer graphene is twisted on ABA trilayer graphene, the flat bands are not isolated, but are intersected by a Dirac cone with a large Fermi velocity. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap …
The mechanical response of embedded ABA trilayer graphene flakes loaded in tension and compression on polymer beams is monitored by simultaneous Raman measurements through the strain sensitivity of the G or 2D peaks. A characteristic peculiarity of the investigated flake is that it contains a trilayer and bilayer part. The Bernal stacked bilayer was used as a strain sensor aiming to assess the efficiency of the load transfer from the polymer matrix through shear to the individual graphene layers. For the trilayer graphene in tension, both peaks are redshifted and splitting of the G peak is rep…
Remote Moiré Modulation of Decoupled Dirac Subsystems in Twisted Trilayer Graphene
Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；National Institute for Materials Science（国立材料研究所）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究院）
We report ab-initio calculations of the phonon dispersion relation on the bulk and single layer of SnO and PbO. We identify Raman active modes and infrared active modes at the zone center Γ point. In agreement with experimental observations of Raman spectroscopy measurement, we find that A1g mode is higher in frequency than that of Eg mode. Moreover, the reason behind the shift of A2u mode to higher frequency for monolayer of both SnO and PbO is revealed from our calculations. We also find that long-range Coulomb interaction enhances the dielectric constant and Born effective charges in bulk S…
We present a comprehensive first-principles analysis of the non-adiabatic effects due to the electron-phonon interaction on the vibrational spectrum of the electron-doped monolayer MoS$_{2}$. Deep changes in the Fermi surface upon doping cause the linewidth broadening of the normal modes governing the spin-conserving inter-valley electronic scattering, which become unstable with the population of all the spin-split conduction valleys. We find that the non-adiabatic spectral effects modify dramatically the adiabatic dispersion of the long-wavelength optical phonon modes, responsible for intra-v…
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monola…
Lattice structure and symmetry of two-dimensional (2D) layered materials are of key importance to their fundamental mechanical, thermal, electronic and optical properties. Raman spectroscopy, as a convenient and nondestructive tool, however has its limitations on identifying all symmetry allowing Raman modes and determining the corresponding crystal structure of 2D layered materials with high symmetry like graphene and MoS2. Due to lower structural symmetry and extraordinary weak interlayer coupling of ReS2, we successfully identified all 18 first-order Raman active modes for bulk and monolaye…
The evolution of titanyl-phthalocyanine (TiOPc) thin films on Ag(111) has been investigated using IRAS, SPA-LEED and STM. In the (sub)monolayer regime various phases are observed that can be assigned to a 2D gas, a commensurate and a point-on-line phase. In all three phases the non-planar TiOPc molecule is adsorbed on Ag(111) in an oxygen-up configuration with the molecular pi-conjugated backbone oriented parallel to the surface. The commensurate phase reveals a high packing density, containing two molecules at inequivalent adsorption sites within the unit cell. Both molecules assume different…
We report diffusion quantum Monte Carlo (DMC) and many-body $GW$ calculations of the electronic band gaps of monolayer and bulk hexagonal boron nitride (hBN). We find the monolayer band gap to be indirect. $GW$ predicts much smaller quasiparticle gaps at both the single-shot $G_0W_0$ and the partially self-consistent $GW_0$ levels. In contrast, solving the Bethe-Salpeter equation on top of the $GW_0$ calculation yields an exciton binding energy for the direct exciton at the $K$ point in close agreement with the DMC value. Vibrational renormalization of the electronic band gap is found to be si…
From monolayers composed of different atoms, we can build structures with spontaneous vertical polarization by conveniently stacking multiple layers. We have studied, using first-principles methods and based on modern polarization theory, a system composed of three layers of hexagonal Boron-Nitride(h-BN) in all possible stackings. We obtain for each of the configurations how charge transfers between the layers and how it impacts on the polarization of the system. In addition, we studied a system of three layers, one of them rotated, and we found that not only did the magnitude of the polarizat…
The investigation of thermal transport properties of novel two dimensional materials is crucially important in order to assess their potential to be used in future technological applications, such as thermoelectric power generation. In this respect, lattice thermal transport properties of monolayer structures of the group \textrm{VA} elements (P, As, Sb, Bi, PAs, PSb, PBi, AsSb, AsBi, SbBi, P$_{3}$As$_{1}$, P$_{3}$Sb$_{1}$, P$_{1}$As$_{3}$, As$_{3}$Sb$_{1}$) with black phosphorus like puckered structure were systematically investigated by first principles calculations and an iterative solution…
Spin-density-wave transition in monolayer-trilayer La3Ni2O7 single crystals
ShanghaiTech University（上海科技大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；University of Chinese Academy of Sciences（中国科学院大学）；Center for High Pressure Science and Technology Advanced Research（高压科学先进研究发展中心）；Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments (MFree)（极端环境材料前沿研究上海市重点实验室）；Institute for Shanghai Advanced Research in Physical Sciences (SHARPS)（上海高等研究院物理科学研究所）；ShanghaiTech Laboratory for Topological Physics（上海科技大学拓扑物理实验室）；Shanghai Key Laboratory of High-resolution Electron Microscopy（高分辨电子显微学上海市重点实验室）；Department of Physics, Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室物理系）；School of Physical Sciences, Great Bay University（大湾区大学物理科学学院）
Molybdenum disulfide, MoS2, has recently gained considerable attention as a layered material where neighboring layers are only weakly interacting and can easily slide against each other. Therefore, mechanical exfoliation allows the fabrication of single and multi-layers and opens the possibility to generate atomically thin crystals with outstanding properties. In contrast to graphene, it has an optical gap of 1.9 eV. This makes it a prominent candidate for transistor and opto-electronic applications. Single-layer MoS$_2$ exhibits remarkably different physical properties compared to bulk MoS$_2…
We report on magneto-transport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the twelve-fold degeneracy of the zeroth Landau level. As a function of perpendicular electric field, our data exhibits a sequence of phase transitions between all integer quantum Hall states in the filling factor interval $-8<ν<0$. We develop a theoretical model and argue that, in contrast to monolayer and bilayer graphene, the observed Landau level splittings and quantum Hall phase…
Density functional theory (DFT) is widely used to study defects in monolayer graphene with a view to applications ranging from water filtration to electronics to investigation of radiation damage in graphite moderators. To assess the accuracy of DFT in such applications, we report diffusion quantum Monte Carlo (DMC) calculations of the formation energies of some common and important point defects in monolayer graphene: monovacancies, Stone-Wales defects, and silicon substitutions. We find that standard DFT methods underestimate monovacancy formation energies by around 1 eV. The disagreement be…
We have investigated the effects of number of layers on the structural, vibrational, electronic and optical properties of $α$-PbO using first principles calculations. Our theoretical calculations have shown that four Raman active modes of $α$-PbO tend to red-shift from bulk to monolayer due to decreasing of force constants and increasing of bond lengths. It has been shown that while bulk and multilayer $α$-PbO have an indirect band gap, monolayer form has a direct band gap value of 2.59 eV. Although lead atoms have 5d states, spin-orbit coupling does not significantly affect the band structure…
Finite-temperature properties of graphene monolayers under tensile stress have been studied by path-integral molecular dynamics (PIMD) simulations. This method allows one to consider the quantization of vibrational modes in these crystalline membranes and to analyze the influence of anharmonic effects in the membrane properties. Quantum nuclear effects turn out to be appreciable in structural and thermodynamic properties of graphene at low temperature, and they can even be noticeable at room temperature. Such quantum effects become more relevant as the applied stress is increased, mainly for p…
Orhorhombic $α$-MoO$_3$ is a layered oxide with various applications and with excellent potential to be exfoliated as a 2D ultrathin film or monolayer. In this paper, we present a first-principles computational study of its vibrational properties. Our focus is on the zone center modes which can be measured by a combination of infared and Raman spectroscopy. The polarization dependent spectra are simulated. Calculations are also performed for a monolayer form in which "double layers" of Mo$_2$O$_6$ which are weakly van der Waals bonded in the $α$-structure are isolated. Shift in phonon frequenc…
We present first-principles calculations of the vibrational properties of the transition metal dichalcogenide 1T-TaS$_2$ for various thicknesses in the high-temperature (undistorted) phase and the low-temperature commensurate charge density wave (CDW) phase. We also present measurements of the Raman spectra for bulk, few-layer, and monolayer samples at temperatures well below that of the bulk transition to the commensurate phase. Through our calculations, we identify the low-frequency folded-back acoustic modes as a convenient signature of the commensurate CDW wave structure in vibrational spe…
Using density functional theory calculations, we investigated the properties of few-layer silicene nanosheets, namely bilayers and trilayers, functionalized with group-III or group-V atoms of the periodic table. We considered the Si$_2$X$_2$ bilayers and the Si$_2$X$_4$ trilayers, X = B, N, Al, P. We computed the structural, energetic, dynamic, elastic, and electronic properties of those systems in several stacking configurations, labeled as AA$'$, AB, AA$'$A$''$, and ABC. The results revealed that AA$'$-Si$_2$N$_2$, AB-Si$_2$N$_2$, AA$'$-Si$_2$P$_2$, AB-Si$_2$P$_2$, ABC-Si$_4$B$_2$, ABC-Si$_4…
Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finite-temperature properties were analyzed in the range from 12 to 2000~K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in t…
Nonlinear light-matter interactions in structured materials are the source of exciting properties and enable vanguard applications in photonics. However, the magnitude of nonlinear effects is generally small, thus requiring high optical intensities for their manifestation at the nanoscale. Here, we reveal a large nonlinear response of monolayer hexagonal boron nitride (hBN) in the mid-infrared phonon-polariton region, triggered by the strongly anharmonic potential associated with atomic vibrations in this material. We present robust first-principles theory predicting a threshold light field $\…
Propagating atomic vibrational waves, phonons, rule important thermal, mechanical, optoelectronic and transport characteristics of materials. Thus the knowledge of phonon dispersion, namely the dependence of vibrational energy on momentum is a key ingredient to understand and optimize the material's behavior. However, despite its scientific importance in the last decade, the phonon dispersion of a freestanding monolayer of two dimensional (2D) materials such as graphene and its local variations has still remained elusive because of experimental limitations of vibrational spectroscopy. Even tho…
We have studied the electronic, magnetic and linear phonon dispersion behavior of Phosphorene monolayer using rst principle based ab initio method. Phosphorene monolayer is a semiconducting system with a dimensional dependent variable range of band gap. Vacancy has been done to study the geometry and physical behavior of the monolayer system. Pristine, vacancy induced monolayer and vacancy induced doped monolayer are included in the calculation. Dopant concentration has been well checked via optimization algorithm to maintain the dilute magnetic semiconducting behavior of the monolayer system.…
The effect of femtosecond laser irradiation on bulk and single-layer MoS2 on silicon oxide is studied. Optical, Field Emission Scanning Electron Microscopy (FESEM) and Raman microscopies were used to quantify the damage. The intensity of A1g and E2g1 vibrational modes was recorded as a function of the number of irradiation pulses. The observed behavior was attributed to laser-induced bond breaking and subsequent atoms removal due to electronic excitations. The single-pulse optical damage threshold was determined for the monolayer and bulk under 800nm and 1030nm pulsed laser irradiation and the…
Mott insulator plays a central role in strongly correlated physics, where the repulsive Coulomb interaction dominates over the electron kinetic energy and leads to insulating states with one electron occupying each unit cell. Doped Mott insulator is often described by the Hubbard model3, which can give rise to other correlated phenomena such as unusual magnetism and even high-temperature superconductivity. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott phy…
We report measurements of vibrational mode shapes of mechanical resonators made from ultrathin carbon nanomembranes (CNMs) with a thickness of approximately 1 nm. CNMs are prepared from electron irradiation induced cross-linking of aromatic self-assembled monolayers (SAMs) and the variation of membrane thickness and/or density can be achieved by varying the precursor molecule. Single- and triple-layer freestanding CNMs were made by transferring them onto Si substrates with square/rectangular orifices. The vibration of the membrane was actuated by applying a sinusoidal voltage to a piezoelectri…
Growth, electronic and magnetic properties of $γ'$-Fe$_{4}$N atomic layers on Cu(001) are studied by scanning tunneling microscopy/spectroscopy and x-ray absorption spectroscopy/magnetic circular dichroism. A continuous film of ordered trilayer $γ'$-Fe$_{4}$N is obtained by Fe deposition under N$_{2}$ atmosphere onto monolayer Fe$_{2}$N/Cu(001), while the repetition of a bombardment with 0.5 keV N$^{+}$ ions during growth cycles results in imperfect bilayer $γ'$-Fe$_{4}$N. The increase in the sample thickness causes the change of the surface electronic structure, as well as the enhancement in …
Element-specific ultrafast lattice dynamics in monolayer WSe2
Technical University Berlin（柏林工业大学）；Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）；University of Münster（明斯特大学）；Chinese Academy of Sciences（中国科学院）；Fraunhofer Institute for Electronic Microsystems and Solid State Technologies (EMFT)（弗劳恩霍夫电子微系统和固态技术研究所(EMFT)）；Adam Mickiewicz University（亚当·密茨凯维奇大学）；Freie Universität Berlin（柏林自由大学）
