Anisotropy of long-wavelength optical phonons in GaAs/AlAs superlattices

The angular anisotropy of optical phonons in GaAs/AlAs (001) superlattices is investigated by Raman scattering spectroscopy. Scattering configurations allowed for phonons with wave vectors oriented along the superlattice layers and normally to them are used. For phonons localized in GaAs layers, the theoretically predicted mixing of the LO1 longitudinal modes with TO1 transverse modes in which atomic displacements occur along the normal to the superlattice is observed experimentally. These modes possess noticeable angular anisotropy. For transverse modes in which atoms move in the plane of the superlattice, the angular anisotropy is small.     

Acoustic phonon damping in cubic metals

Electron-phonon-induced linewidths of phonons are discussed in terms of near neighbor tight-binding parameters. Predictions are made of the anisotropy of the linewidth, and some selection rules are given for long-wavelength acoustic phonons.     

Effect of dispersion on the phonon focusing and anisotropy of thermal conductivity of silicon single crystals in the boundary scattering regime

The effect of dispersion on the focusing of thermal phonons and on the thermal conductivity of silicon single crystals in the boundary scattering regime has been investigated. Analysis of the spectra of acoustic modes obtained for silicon single crystals from inelastic neutron scattering data has demonstrated that, upon transition from long-wavelength phonons to short-wavelength phonons, the directions of their focusing change. With an increase in temperature, this leads to a change in the anisotropy of thermal conductivity of phonons with different polarizations and, consequently, to a change in the anisotropy of the total thermal conductivity. Analysis of the temperature dependence of the thermal conductivity has revealed that the presence of extended flattened sections in the spectrum of short-wavelength transverse phonons indicates anomalously low values of the group velocity and, accordingly, a significant decrease in the contribution from these phonons to the thermal conductivity with increasing temperature. The contribution from longitudinal phonons to the thermal conductivity also significantly increases even at temperatures higher than 110 K and becomes dominant.     

Anharmonic processes of scattering and relaxation of slow quasi-transverse phonons in cubic crystals

Relaxation of slow quasi-transverse phonons in anharmonic processes of scattering in cubic crystals with positive (Ge, Si, diamond) and negative (KCl, NaCl) anisotropies of the second-order elastic moduli has been considered. The dependences of the relaxation rates on the direction of the wave vector of phonons in scattering processes with the participation of three quasi-transverse phonons (the TTT relaxation mechanisms) are analyzed within the anisotropic continuum model. It is shown that the TTT relaxation mechanisms in crystals are associated with their cubic anisotropy, which is responsible for the interaction between noncollinear phonons. The dominant contribution to the phonon relaxation comes from large-angle scattering. For crystals with significant anisotropy of the elastic energy (Ge, Si, KCl, NaCl), the total contribution of the TTT relaxation mechanisms to the total relaxation rate exceeds the contribution of the Landau-Rumer mechanism either by several factors or by one to two orders of magnitude depending on the direction. The dominant role of the TTT relaxation mechanisms as compared to the Landau-Rumer mechanism is governed, to a considerable extent, by the second-order elastic moduli. The total relaxation rates of slow quasi-transverse phonons are determined. It is demonstrated that, when the anharmonic processes of scattering play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the mechanisms of relaxation of the slow quasi-transverse mode by two slow or two fast modes) is insufficient for describing the anisotropy of the total relaxation rates in cubic crystals.     

Low-temperature phonoemissive tunneling rates in single molecule magnets

Tunneling between the two lowest energy levels of single molecule magnets with Ising type anisotropy, accompanied by the emission or absorption of phonons, is considered. Quantitatively accurate calculations of the rates for such tunneling are performed for a model Hamiltonian especially relevant to the best studied example, Fe₈. Two different methods are used: high-order perturbation theory in the spin–phonon interaction and the non-Ising-symmetric parts of the spin Hamiltonian, and a novel semiclassical approach based on spin-coherent-state-path-integral instantons. The methods are found to be in good quantitative agreement with other, and consistent with previous approaches to the problem. The implications of these results for magnetization of molecular solids of these molecules are discussed briefly.     

Nonlinear elasticities of octagonal and dodecagonal quasicrystals

The nonlinear elasticities are analyzed for octagonal and dodecagonal quasicrystals. All the third-order elastic constants are determined. According to Hermann's theorem, quasicrystal anisotropy may be revealed by the nonlinear elasticities due to the coupling between phonons and phasons. The summary on isotropy or anisotropy of all quasicrystal elasticities is given.     

Anisotropy of the mean free paths of phonons in single-crystal films of germanium,silicon, and diamond at low temperatures

The physical aspects of the influence of the elastic energy anisotropy of crystals on the anisotropy of the mean free paths of phonons in single-crystal films of germanium, silicon, and diamond in the diffuse scattering of phonons at the boundaries of the samples have been considered. It has been shown that, for sufficiently wide films of germanium, silicon, and diamond with the {100} and {111} orientations and the lengths of less than or equal to their width, the phonon mean free paths are isotropic (independent of the direction of the temperature gradient in the plane of the film). The anisotropy of the phonon mean free paths depends primarily on the orientation of the film plane and is determined by the focusing and defocusing of phonon modes. For single-crystal films of germanium, silicon, and diamond with the {100} and {111} orientations and lengths much larger than their width, the phonon mean free paths are anisotropic.     

Manifestation of LO-LA phonons in Raman scattering in graphene

We analyze the spectral density of Raman scattering in graphene accompanied by the emission of a pair of LO or LA phonons from the corner of the Brillouin zone. Using a minimal tight-binding model approach, we find that the lineshape of the corresponding Raman signal consists of two peaks with a strongly non-Lorentzian (almost triangular) form with their width and the splitting between the peaks being strongly dependent on the energy of the incoming photon. The asymmetric lineshape is determined by the kinematics of the fully-resonant two-phonon process, and it reflects a strong anisotropy of LO-LA phonons’ dispersion around the Brillouin zone corners.     

Thermal conductivity of polycrystalline zinc selenide

The thermal conductivity of optically transparent zinc selenide polycrystals fabricated by vapor deposition was experimentally studied in the temperature range 80–400 K in the as-deposited state and after deformation along the crystal growth direction followed by recrystallization. In the low-temperature range, textured ZnSe samples exhibit anisotropy of the thermal conductivity, which also persisted after their deformation and recrystallization. The anisotropy of the thermal conductivity is caused by phonon scattering by dislocations oriented along the crystal growth direction. The thermal conductivity of ZnSe at T>270 K is shown to be limited by the scattering of acoustic phonons by optical phonons.     

Phonon emission spectra of superconducting tunnel junctions

Resonant scattering of phonons by the stress split acceptor ground state in Si:B has been used to investigate the phonon emission spectra of superconducting tunnel junctions. Symmetric Sn, Pb and PbBi alloy junctions have been studied in the single particle tunneling regime. The spectra show many features as expected from relaxation and recombination of quasiparticles via one-phonon emission. The results are compared with the steady state solutions of the kinetic equations for quasiparticles and phonons. Spatially homogeneous distribution functions are assumed. This approach describes the spectra of tin junctions fairly well. However, there are marked deviations for Pb and PbBi junctions which are attributed to a decay of transverse phonons within the junction.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

金属/介质薄膜中声子热辐射的空间和各向异性研究

基于理论、实验和仿真相结合的方式,着重研究了金属/介质(MD)薄膜中声子热辐射的空间特性和各向异性。声子是由于晶格振动产生的元激发,是物质的内在属性。尽管声子不易调控,但是声子与其他光学激发的耦合会产生奇异的光学现象。特别是红外到太赫兹范围内的光子与极性介质中的声子强耦合产生表面声子激元（SPhP）。SPhP具有强局域、低损耗等特点,与等离子体（plasmon polaritons）形成互补,使得深亚波长光学成为可能。为了进一步了解声子吸收的内在理论基础,首先通过黄昆方程和超晶格连续介电模型在理论上分析了声子吸收。实验上,主要以SiO₂声子作为研究对象,利用等离子体增强化学气相沉积(PECVD)方法,分别在Si/Al（150 nm）薄膜和Si衬底上制备出500 nm厚的SiO₂薄膜。基于傅里叶红外光谱仪(FTIR),在垂直入射下得到热辐射光谱,通过热辐射光谱分析,并结合由时域有限差分算法（finite-difference time-domain,FDTD）计算得出的仿真光谱图,对比了MD薄膜结构和非MD薄膜结构中声子的热辐射,发现MD薄膜结构更能够有利于声子和SPhP的激发。根据Berreman效应,纵光学波（LO）声子只在倾斜入射时产生。光谱线没有呈现洛伦兹线型,因此,虽然LO声子在垂直入射时测得的热辐射图中不辐射,但同样影响横光学波（TO）声子辐射谱的线型。另外,利用FTIR对金属（Si/Al）/介质（SiO₂薄膜）进行热辐射转角测试,对热辐射转角图分析证明,Si/Al/SiO₂薄膜中SiO₂声子遵循LST(lyddano-sachs-teller)关系,纵横声子成对出现,且两种声子的空间辐射特性不同。改变偏振,发现在S偏振和P偏振下,声子热辐射呈现不同的模式, 体现出声子的空间各向异性。并且,声子与光子耦合可以激发SPhP,反过来,SPhP可以增强声子的吸收。基于MD结构,能够激发并调控SPhP和声子辐射行为,为红外器件的实现奠定了基础。     

Theorie des stimulierten Raman-Effekts

We consider stimulated Raman emission in solids, placed in a plane laser beam external to the cavity. The Hamiltonian of the system of phonons, electrons and electromagnetic fields is derived within the framework of a generalized adiabatic approximation for electrons and nuclei. It contains terms due to nonlinear interactions between electrons and phonons. Because the usual time-dependent perturbation theory cannot describe coherence effects properly we turn toHeisenberg's equations of motion for the operators of photons, phonons and electron excitations. In order to solve these equations in the steady state we apply an iteration procedure. We start with the light waves which give rise to electron transitions. The electrons such excited create phonons which then react on the electrons. Finally the electrons are coupled again to the lightfield. This procedure yields besides the usual wellknown Raman process two main processes occurring in stimulated Raman emission: a coupled two step Raman process and a parametric process. In the first one two phonons are involved. If the linewidth of phonons is comparable to the phonon frequencies the non-resonant parts of the above processes also become important. In solving the set of coupled equations for the light amplitudes, obtained from the iteration procedure, we only consider terms due to the first Stokes, the first anti-Stokes and the laser line. We then find frequency shifts of these lines due to the stimulated emission which are of the order of the linewidth of photons if this linewidth is very much smaller than that of phonons as it is the case in solids. This means that the coupled two step Raman process is dominant, in good agreement with measurements ofChiao andStoicheff in calcite.     

High-temperature slow relaxation of the magnetization in Ni10 magnetic molecules

We investigate a family of molecular crystals containing noninteracting Ni10 magnetic molecules. We find slow relaxation of the magnetization below a temperature as high as 17 K and we show that this behavior is not associated with an anisotropy energy barrier. Ni10 has a characteristic magnetic energy spectrum structured in dense bands, the lowest of which makes the crystal opaque to phonons of energy below about 1 meV. We ascribe the nonequilibrium behavior to the resulting resonant trapping of these low-energy phonons. Trapping breaks up spin relaxation paths leading to a novel kind of slow magnetic dynamics which occurs in the lack of anisotropy, magnetic interactions and quenched disorder.     

The effect of phonon focusing on the electron-phonon relaxation and electron transport in potassium crystals

The influence of anisotropy of elastic energy on electron-phonon relaxation and the role of shear waves in the electrical resistance of potassium crystals are investigated. It is shown that, at temperatures much lower than the Debye temperature (T<< θ_D), the contribution of slow quasi-transverse phonons to the electrical resistance of potassium crystals exceeds that of longitudinal phonons by an order of magnitude. Earlier, the Bloch-Grüneisen theory left aside this component under the above conditions. At the same time, at high temperatures(T>>θ_D), the contribution of longitudinal phonons to the electrical resistance turns out to be 4 times greater than the total contribution of electron relaxation by fast and slow transverse modes. The role of shear waves in the electrical resistance of potassium crystals is analyzed. It is shown that, at low temperatures, this mechanism provides 32% of the total electrical resistance. It is 4 times higher than the contribution of longitudinal phonons to the electrical resistance and should be taken into account when analyzing the electrical resistance of alkali metals. The distribution function of the most effective phonons for electrical resistance is defined, and the inelasticity of electron-phonon scattering is analyzed. It is shown that the calculated results of the electrical resistance of potassium in the temperature range from 40 to 400 K, taking into account the anisotropy of elastic energy, are in good agreement with the experimental data without the use of fitting parameters.     

Relaxation times and mean free paths of phonons in the boundary scattering regime for silicon single crystals

The phonon focusing in cubic dielectric crystals and its influence on the heat transfer in the boundary phonon scattering regime at low temperatures have been investigated. The mean free paths of phonons of different polarizations in samples of infinite and finite lengths with circular and square cross sections have been calculated in the anisotropic continuum model. For samples of infinite length with circular and square cross sections in the case of the equality of the cross-sectional areas, the angular dependences of the mean free paths normalized by the Casimir length almost completely coincide. It has been shown that the anisotropy of the mean free paths decreases significantly upon changing over from infinite samples to samples of finite length. For silicon crystals, the anisotropy of the phonon mean free paths has been analyzed for each of the branches of the phonon spectrum. It has been found that the mean free paths for phonons of each vibrational mode reach maximum values in the directions of focusing, and, in these directions, they exceed the mean free paths for phonons of the other vibrational modes.     

Acoustic phonon emission from a weakly coupled superlattice under vertical electron transport: observation of phonon resonance

We report measurements of acoustic phonon emission from a weakly coupled AlAs/GaAs superlattice (SL) under vertical electron transport. The phonons were detected using superconducting bolometers. A peak (resonance) was observed in emission parallel to the SL growth axis when the electrical energy drop per SL period matched the energy of the first SL mini-Brillouin zone-center phonon mode. This peak was mirrored by an increase of the differential conductance of the SL. These results are evidence for stimulated emission of terahertz phonons as previously predicted theoretically and suggest that such a SL may form the basis of a SASER (sound amplification by stimulated emission of radiation) device.     

Phonon focusing of elastically scattered phonons in GaAs

The propagation of high-frequency phonons through crystals at low temperatures is characterized by both ballistic and diffusive processes. Ballistic propagation of heat pulses is highly anisotropic due to phonon focusing, while diffusive propagation is expected to be nearly isotropic in cubic crystals. By using phonon imaging techniques, we have attempted to identify the heat flux from ballistic and scattered phonons in GaAs. Comparison of this data to Monte Carlo calculations which incorporate elastic scattering shows that the flux from phonons scattered a few times in the bulk retains a significant degree of anisotropy. In particular, a sharp feature discovered by Stock, Ulbrich, and Fieseler and attributed to ballistic propagation of phonons with frequencies up to 1.5 THz is now identified with the scattering of sub-THz phonons. Our analysis provides insights into the evolution of heat propagation from the ballistic to diffusive regimes.     

Absorption and electroabsorption near the indirect edge of GaSe

Absorption and electroabsorption spectra have been measured near the indirect edge of the layer semiconductor GaSe. The experimental structures observed at 1.5 K are ascribed to the indirect excitonic transition with emission of different phonons. The determination of the threshold energy of the no-phonon indirect absorption process affords the energies of the phonons involved in the indirect transition to be derived.     

Quantum statistics of phonon radiations in optomechanical systems

We study the correlation statistics of phonon radiations in a weakly driven optomechanical system. Three dominated scattering processes are identified by the scattering theory analytically and the master equation numerically, whose interplay determines the phonon statistical properties. Our results show that for the large detuning, the driving field off-resonant with the system induces a small emission rate of two anti-bunched phonons. For the resonant driving field, there is a relatively large emission rate of two bunched phonons.