We propose a harmonic linear response (HLR) method to calculate the phonon dispersion relations of two-dimensional (2D) layers from equilibrium simulations at finite temperature. This HLR approach is based on the linear response of the system, as derived from the analysis of its centroid density in equilibrium path integral simulations. In the classical limit, this approach is closely related to those methods that study vibrational properties by the diagonalization of the covariance matrix of atomic fluctuations. The validity of the method is tested in the calculation of the phonon dispersion relations of a graphene monolayer, a graphene bilayer, and graphane. Anharmonic effects in the phonon dispersion relations of graphene are demonstrated by the calculation of the temperature dependence of the following observables: the kinetic energy of the carbon atoms, the vibrational frequency of the optical $E_{2g}$ mode, and the elastic moduli of the layer.
We present Phonon Unfolding, a Fortran90 program for unfolding phonon dispersions. It unfolds phonon dispersions by using a generalized projection algorithm, which can be used to any kind of atomic systems in principle. Thus our present program provides a very useful tool for the phonon dispersion and vibration mode analysis of surface reconstructions, atomic point defects, alloys and glasses.
Direct measurement of local phonon dispersion in individual nanostructures can greatly advance our understanding of their electrical, thermal, and mechanical properties. However, such experimental measurements require extremely high detection sensitivity and combined spatial, energy and momentum resolutions, thus has been elusive. Here, we develop a four-dimensional electron energy loss spectroscopy (4D-EELS) technique based a monochromated scanning transmission electron microscope (STEM), and present the position-dependent phonon dispersion measurement in individual boron nitride nanotubes (B…
The phonon dispersion unfolding method is useful for obtaining hidden Bloch symmetries and comparing theoretical results with experiment spectrums (e.g., inelastic neutron scattering, inelastic X-ray scattering, Raman). In this paper, we propose a method to unfold phonon dispersions. The main advantage of this method is the ability to handle systems with heavy breaking of spatial translational symmetry. Its validity is tested by pure diamond, diamond with Si substitution, and diamond with C vacancies.
Phonon dispersions in <100> silicon nanowires (SiNW) are modeled using a Modified Valence Force Field (MVFF) method based on atomistic force constants. The model replicates the bulk Si phonon dispersion very well. In SiNWs, apart from four acoustic like branches, a lot of flat branches appear indicating strong phonon confinement in these nanowires and strongly affecting their lattice properties. The sound velocity (Vsnd) and the lattice thermal conductance (kl) decrease as the wire cross-section size is reduced whereas the specific heat (Cv) increases due to increased phonon confinement and su…
Atomic undercoordination, charge injection, mechanical and thermal activation mediate the properties of a material intrinsically by bond relaxation from one equilibrium to another while the phonon spectrometrics probes the ever-unexpected information of the binding energy density, atomic cohesive energy, single bond force constant, crystal elastic modulus, Debye temperature and the abundance-length-stiffness transition of bonds under perturbation.
he correct estimation of thermal properties of ultra-scaled CMOS and thermoelectric semiconductor devices demands for accurate phonon modeling in such structures. This work provides a detailed description of the modified valence force field (MVFF) method to obtain the phonon dispersion in zinc-blende semiconductors. The model is extended from bulk to nanowires after incorporating proper boundary conditions. The computational demands by the phonon calculation increase rapidly as the wire cross-section size increases. It is shown that the nanowire phonon spectrum differ considerably from the bul…
We compute electron-phonon coupling (EPC) of selected phonon modes in graphene and graphite using various ab-initio methods. The inclusion of non-local exchange-correlation effects within the GW approach strongly renormalizes the square EPC of the A$'_1$ {\bf K} mode by almost 80$%$ with respect to density functional theory in the LDA and GGA approximations. Within GW, the phonon slope of the A$'_1$ {\bf K} mode is almost two times larger than in GGA and LDA, in agreement with phonon dispersions from inelastic x-ray scattering and Raman spectroscopy. The hybrid B3LYP functional overestimates t…
Recently, first principle-based prediction of lattice thermal conductivity $κ$ from the perturbation theory has achieved significant success. However, it only includes three-phonon scattering due to the assumption that four-phonon and higher-order processes are generally unimportant. Also, directly evaluating the scattering rates of four-phonon and higher-order processes has been a long-standing challenge. In this work, however, we have developed a formalism to explicitly determine quantum mechanical scattering probability matrices for four-phonon scattering in the full Brillouin Zone, and by …
Weyl semimetals display unusual electronic transport properties when placed under magnetic fields. Here, we investigate how magnetic fields alter the dynamics of long wavelength lattice vibrations in these materials. To that end, we develop a theory for the phonon dispersion, which incorporates contributions from chiral and nonchiral Landau levels, electron-phonon interactions, electron-electron interactions, and disorder. We predict (i) a magnetic-field-induced hybridization between optical phonons and plasmons, (ii) avoided crossings between pseudoscalar optical phonons and electronic excita…
We report results of Brillouin - Mandelstam spectroscopy of transparent alumina crystals with Nd dopants. The ionic radius and atomic mass of Nd atoms are distinctively different from those of the host Al atoms. Our results show that even a small concentration of Nd atoms incorporated into the alumina samples produces a profound change in the acoustic phonon spectrum. The velocity of the transverse acoustic phonons decreases by ~600 m/s at the Nd density of only ~0.1 %. Interestingly, the decrease in the phonon frequency and velocity with the doping concentration is non-monotonic. The obtained…
We report the dispersion measurements, using angle-resolved reflection electron-energy-loss-spectroscopy (AREELS), on two-dimensional (2D) plasmons in single and multilayer graphene which couple strongly to surface optical phonon (FK phonon) modes of silicon carbide substrate. The coupled modes show discrete dispersion behaviors in the single and bilayer graphene. With increasing graphene layers on SiC(0001), a transition from plasmon-like dispersion to phonon-like dispersion is observed. For plasmon-like modes, the dispersion is strongly damped by electron-hole pair excitations at entering si…
Taking into account the constraints imposed by the lattice symmetry, we calculate the phonon dispersion for graphene with interactions between the first, second, and third nearest neighbors in the framework of the Born--von Karman model. Analytical expressions obtained for the dispersion of the out-of-plane (bending) modes give the nonzero sound velocity. The dispersion of four in-plane modes is determined by coupled equations. Values of the force constants are found in fitting with frequencies at critical points and with elastic constants measured on graphite.
High-harmonic spectroscopy has become an essential ingredient in probing various ultrafast electronic processes in solids with sub-cycle temporal resolution. Despite its immense importance, sensitivity of high-harmonic spectroscopy to phonon dynamics in solids is not well known. This work addresses this critical question and demonstrates the potential of high-harmonic spectroscopy in probing intertwined phonon-electron dynamics in solids. A pump pulse excites in-plane optical phonon modes in monolayer graphene and a circularly polarised pulse is employed to probe the excited phonon dynamics th…
The phonon dispersion of chiral single wall carbon nanotubes has been obtained from $6\times 6$ dyanimic matrix. The present manuscript is the extension of G. D. Mahan and Gun Sang Jeon's work on armchair and zigzag nanotubes. [see P. R. B., {\bf 70}, 075405 (2004)]. We use spring and mass model with the proper phonon potential suggested by \cite{M2}. We can calculate the dispersion of single wall carbon nanotubes near $Γ$ point with arbitrary chirality. The results are compatible with Mahan et. al's results for armchair and zigzag SWNTs.
Interfaces play an essential role in phonon-mediated heat conduction in solids, impacting applications ranging from thermoelectric waste heat recovery to heat dissipation in electronics. From a microscopic perspective, interfacial phonon transport is described by transmission and reflection coefficients, analogous to the well-known Fresnel coefficients for light. However, these coefficients have never been directly measured, and thermal transport processes at interfaces remain poorly understood despite considerable effort. Here, we report the first measurements of the Fresnel transmission coef…
We reveal that the periodic radius modulation peculiar to one-dimensional (1D) peanut-shaped fullerene (C$_{60}$) polymers exerts a strong influence on their low-frequency phonon states and their interactions with mobile electrons. The continuum approximation is employed to show the zone-folding of phonon dispersion curves, which leads to fast relaxation of a radial breathing mode in the 1D C$_{60}$ polymers. We also formulate the electron-phonon interaction along the deformation potential theory, demonstrating that only a few set of electron and phonon modes yields a significant magnitude of …
The natural transition from the radiative regime to the conductive regime of heat transfer between two identical isotropic dielectric solid materials, is questioned by investigating the possibility of induced phonon transfer in vacuum. We describe the process in a general way assuming a certain phonon coupling mechanism between the two identical solids, then we particularly illustrate the case of coupling through Casimir force. We analyze how this mechanism of heat transfer compares and competes with the near field thermal radiation using a local model of the dielectric function. We show that …
Interfaces play an essential role in phonon-mediated heat conduction in solids, impacting applications ranging from thermoelectric waste heat recovery to heat dissipation in electronics. From the microscopic perspective, interfacial phonon transport is described by transmission coefficients that link vibrational modes in the materials composing the interface. However, direct experimental determination of these coefficients is challenging because most experiments provide a mode-averaged interface conductance that obscures the microscopic detail. Here, we report a metrology to extract thermal ph…
Bi-layer graphene with a twist angle θ between the layers generates a superlattice structure known as Moiré pattern. This superlattice provides a θ-dependent q wavevector that activates phonons in the interior of the Brillouin zone. Here we show that this superlattice-induced Raman scattering can be used to probe the phonon dispersion in twisted bi-layer graphene (tBLG). The effect reported here is different from the broadly studied double-resonance in graphene-related materials in many aspects, and despite the absence of stacking order in tBLG, layer breathing vibrations (namely ZO' phonons) …
Taking into account the constraints imposed by the lattice symmetry, the phonon dispersion is calculated for graphene with interactions between the first and second nearest neighbors in the framework of the Born-von Karman model. Analytical expressions are obtained for the out-of-plane (bending) modes determined only by two force constants as well as for the in-plane modes with four force constants. Values of the force constants are found in fitting to elastic constants and Raman frequencies observed in graphite.
Weyl semimetals exhibitinging the topologically nontrivial touching points in electronic band dispersion of solids pave the wave way to novel electronic devices and functionalities. Here, we demonstrate the signature of topologically nontrivial Weyl points (WPs) in phonon dispersion of solids through a first-principles investigations. ofT noncentrosymmetric wurtzite CuI (cuprous iodide at high temperature). These type-II phononic WP in phonon dispersion of wurtzite CuI is manifested in noncentrosymmetric wurtzite CuI by six pairs of the nontrivial touching points in the k_z=0.0 plane. The idea…
Spectral correlations in the optical phonon spectrum of a solid with a complex unit cell are analysed using the Wigner-Dyson statistical approach. Despite the fact that all force constants are real, we find that the statistics are predominantly of the GUE type depending on the location within the Brillouin zone of a crystal and the unit cell symmetry. Analytic and numerical results for the crossover from GOE to GUE statistics are presented.
In atoms and molecules, the electrons screen the nucleus from the external electric field. However, if the frequency of the electric field reaches the energy of atomic or molecular transition, the electric field at the nucleus may be resonantly enhanced by many orders in magnitude. In this paper, we study the mechanisms of screening or enhancement of electric field acting on the nuclei in solid states. We show that in dielectric crystals the phonon oscillations of the lattice play crucial role for determining the electric field on nuclei in the MHz-THz region. As an application, we propose an …
We report the changes in dispersion relations of hypersonic acoustic phonons in free-standing silicon membranes as thin as \sim 8 nm. We observe a reduction of the phase and group velocities of the fundamental flexural mode by more than one order of magnitude compared to bulk values. The modification of the dispersion relation in nanostructures has important consequences for noise control in nano and micro-electromechanical systems (MEMS/NEMS) as well as opto-mechanical devices.
In recent years, the fundamental physics of spin-thermal (i.e., magnon-phonon) interaction has attracted significant experimental and theoretical interests given its potential paradigm-shifting impacts in areas like spin-thermoelectrics, spin-caloritronics and spintronics. Modelling studies of the transport of magnons and phonons in magnetic crystals are very rare. In this paper, we use spin-lattice dynamics (SLD) simulations to model ferromagnetic crystalline iron, where the spin and lattice systems are coupled through the atomic position-dependent exchange function, and thus the interaction …
Solid-state emitters are excellent candidates for developing integrated sources of single photons. Yet, phonons degrade the photon indistinguishability both through pure dephasing of the zero-phonon line and through phonon-assisted emission. Here, we study theoretically and experimentally the indistinguishability of photons emitted by a semiconductor quantum dot in a microcavity as a function of temperature. We show that a large coupling to a high quality factor cavity can simultaneously reduce the effect of both phonon-induced sources of decoherence. It first limits the effect of pure dephasi…
Scattering of phonons at boundaries of a crystal (grains, surfaces, or solid/solid interfaces) is characterized by the phonon wavelength, the angle of incidence, and the interface roughness, as historically evaluated using a specularity parameter p formulated by Ziman [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. This parameter was initially defined to determine the probability of a phonon specularly reflecting or diffusely scattering from the rough surface of a material. The validity of Ziman's theory as extended to solid/solid interfaces has not been previously valida…
A simple model for flexural phonons in graphite (and graphene, corresponding to the limiting case of infinite distance between carbon planes) is proposed, in which the local dipolar moment is assumed to be proportional to the curvature of the carbon sheets. Explicit expressions for dispersion curves with full account for the long-range dipolar interaction forces are given and fitted to the experimental data using a single adjustable parameter of the theory. This parameter is expected to depend on the ground state configuration of molecular $π$-orbitals, the same both for graphite and for graph…
We report finite-volume simulations of the phonon Boltzmann transport equation (BTE) for heat conduction across the heterogeneous interfaces in SiGe superlattices. The diffuse mismatch model incorporating phonon dispersion and polarization is implemented over a wide range of Knudsen numbers. The results indicate that the thermal conductivity of a Si/Ge superlattice is much lower than that of the constitutive bulk materials for superlattice periods in the submicron regime. We report results for effective thermal conductivity of various material volume fractions and superlattice periods. Details…
Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum. In the quantum limit the spin lifetime is determined by phononic vacuum fluctuations. However, this limit was not observed in previous studies due to thermal phonon contributions or phonon-bottleneck processes. Here we use a dispersive detection scheme based on cavity quantum electrodynamics (cQED) to observe this quantum limit of spin rela…
Electron-electron thermalization and electron-phonon relaxation processes in laser-excited solids are often assumed to occur on different timescales. This is true for the majority of the conduction band electrons in a metal. However, electron-phonon interactions can influence the thermalization process of the excited electrons. We study the interplay of the underlying scattering mechanisms for the case of a noble metal with help of a set of complete Boltzmann collision integrals. We trace the transient electron distribution in copper and its deviations from a Fermi-Dirac distribution due to th…
Dirac fermions exist in many solid state systems including graphene, silicene and other two dimensional membranes such as are found in group VI dichalcogenides, as well as on the surface of some insulators where such states are protected by topology. Coupling of those fermions to phonons introduces new structures in their dispersion curves and, in the case of massive Dirac fermions, can shift and modify the gap. We show how these changes present in angular-resolved photoemission spectroscopy of the dressed charge carrier dispersion curves and scanning tunneling microscopy measurements of their…
We investigate a semiconductor quantum dot as a microscopic analog of a basic optomechanical setup. We show, that optomechanical features can be reproduced by the solid-state platform, arising from parallels of the underlying interaction processes, which in the optomechanical case is the radiation pressure coupling and in the semiconductor case the electron-phonon coupling. In optomechanics, phonons are typically induced via confined photons, acting on a movable mirror, while in the semiconductor system the phonons are emitted by the laser-driven electronic system. There are analogous effects …
Phonon-driven decoherence of high-harmonic generation in the solid-state
Joint Attosecond Science Laboratory, National Research Council of Canada and University of Ottawa（加拿大国家研究委员会与渥太华大学联合阿秒科学实验室）；Advanced Laser Light Source (ALLS), Institut National de la Recherche Scientifique, Centre Énergie Matériaux Télécommunications（国家科学研究研究所能源材料通信中心先进激光光源（ALLS））；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Department of Physics, University of Windsor（温莎大学物理系）
This article discusses quantum fluctuation properties of a crystal lattice, and in particular, phonon squeezed states. Squeezed states of phonons allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. Here we discuss our studies of both continuous-wave and impulsive second-order Raman scattering mechanisms. The later approach was used to experimentally suppress (by one part in a million only, which might be noise) fluctuations in phonons (and it has not been clearly reproduced by other experimental groups…
The implementation of quantum entangling gates between qubits is essential to achieve scalable quantum computation. Here, we propose a robust scheme to realize an entangling gate for distant solid-state spins via a mechanical oscillator in its thermal equilibrium state. By appropriate Hamiltonian engineering and usage of a protected subspace, we show that the proposed scheme is able to significantly reduce the thermal effect of the mechanical oscillator on the spins. In particular, we demonstrate that a high entangling gate fidelity can be achieved even for a relatively high thermal occupation…
Compared to nanoscale friction of translational motion, the mechanisms of rotational friction have received less attention. Such motion becomes an important issue for the miniaturization of mechanical machineries which often involve rotating gears. In this study, molecular dynamics simulations are performed to explore rotational friction for solid-state gears rotating on top of different substrates. In each case, viscous damping of the rotational motion is observed and found to be induced by the pure van-der-Waals interaction between gear and substrate. The influence of different gear sizes an…
