Phonon Wavenumber Research Articles

Phonon energy dependence of scattering in quasi-two-dimensional electron gases at low temperature

We investigate the scattering of electrons in a quasi-two-dimensional electron gas by acoustic phonons at low temperatures. In contrast to scattering at high temperatures, we find that at low temperatures the average scattering rate is dominated by phonon modes with energies much larger than kT. An analytic calculation of either the energy-loss rate or the mobility depends on approximations which are valid only for small phonon wave numbers. Because of the contribution of high-energy phonons, these approximations remain inappropriate to much lower temperatures than previously supposed. For most cases, we find that the approximate analytic solution differs significantly from a more accurate solution obtained by numerical integration.

Soliton-Phonon Interactions in trans-Polyacetylene

We have studied interactions between a soliton and phonons in trans-polyacetylene. It is found that effect nonlinear in interacting phonon amplitudes gives rise to a shift of the soliton location. When there is a soliton at rest, it was known the linearized equation of motion for optical phonons has four types of independent solutions, translation mode, other two localized modes, and propagating phonons. In the second order approximation, these modes interact. An incoming phonon produces a translation of the soliton, giving rise to its random walk. The magnitude of the translation is calculated as a function of phonon wave number. It is from four to six times as large as that of a φ 4 -soliton.

Temperature dependence of the Raman spectrum of tetraphosphorus triselenide

The Raman spectrum of P 4Se 3 has been measured as a function of temperature in the range 20–370 K, at ambient pressure. The internal and external first-order Raman-active phonons vary smoothly in wave number over the temperature interval 20–350 K, but the crystalline-plastic phase change at 355 K. results in the loss of the external mode manifold from the 370 K Raman spectrum, leaving only a wing to the Raleigh-scattered component. The temperature coefficients of most external phonons are larger than those of the energetically well-separated internal phonons. The lowest wave number rigid layer phonon displays soft behaviour (d ṽ/d T positive) whereas the remaining members of the external mode manifold have negative temperature coefficients which increase in magnitude approximately as the phonon wave number increases. Some of the internal mode Davydov components show near-zero or positive temperature coefficients, a behaviour similar to that observed for other chalcogenide semiconductors.

Momentum Transfer between a Kink and a Phonon in the One-Dimensional φ4System

Higher order collision process between a kink and a phonon is investigated in the one-dimensional φ 4 system. Diagrammatic perturbation method is used, where the amplitude of the phonon is the smallness parameter. It is shown that the phonon transfers the momentum to the kink in the fourth order. The momentum transfer is obtained by the contributions of poles of order two in the integrals over momenta. The final velocity of the kink, derived as a function of the incident phonon wave number, reproduces exactly the result of the previous discussion using conservation laws. The kink, which is not moving at first, begins to move after the collision in the direction of the incident phonon. The effective interaction between them is attractive. Possible mechanisms which determine the viscosity of the kink are pointed out.

Accurate measurement of low-energy phonon dispersion in liquidHe4

This paper presents results of a new and highly accurate technique for measuring low-energy phonon dispersion in liquid $^{4}\mathrm{He}$. The technique is based on the behavior of ultrasonic second-harmonic generation in a lossless, dispersive medium. By using frequencies in the low gigahertz range and measuring second-harmonic intensity as a function of propagation distance, the coherence length for the harmonic generation can be determined. The coherence length is, in turn, related to the phonon dispersion curve in a simple way. The results are interpreted in terms of the series expansion $\ensuremath{\epsilon}(k)={c}_{0}\ensuremath{\hbar}k(1+{\ensuremath{\alpha}}_{1}k+{\ensuremath{\alpha}}_{2}{k}^{2}+{\ensuremath{\alpha}}_{3}{k}^{3}+\ensuremath{\cdots})$, where $\ensuremath{\epsilon}$ and $k$ are phonon energy and wave number, respectively. By using measurements taken at two different fundamental frequencies, we find $|{\ensuremath{\alpha}}_{1}|<{10}^{\ensuremath{-}3}$ \AA{} at saturated vapor pressure (SVP) and 6.3 bars, and ${\ensuremath{\alpha}}_{2}=(1.56\ifmmode\pm\else\textpm\fi{}0.06)$ ${\mathrm{\AA{}}}^{2}$ at SVP. If ${\ensuremath{\alpha}}_{1}$ is assumed to be zero, the ${\ensuremath{\alpha}}_{2}$ can be determined from a measurement at a single frequency, and we find ${\ensuremath{\alpha}}_{2}=(1.55\ifmmode\pm\else\textpm\fi{}0.01)$ ${\mathrm{\AA{}}}^{2}$ at SVP. At higher pressures, ${\ensuremath{\alpha}}_{2}$ decreases. Since the excitation spectrum is probed with such low-momentum phonons ($k<0.011$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$), the analysis is insensitive to assumed values of ${\ensuremath{\alpha}}_{4}$, ${\ensuremath{\alpha}}_{5}$, etc., and is only slightly sensitive to the assumed value of ${\ensuremath{\alpha}}_{3}$.

LO-phonon instability in semiconductors in the presence of two laser radiation fields

The rate of change of the LO-phonon population due to scattering by free carriers in the presence of two laser fields is calculated. It is found that LO-phonon propagating parallel to the direction of polarization of the radiation fields may become unstable over a relatively narrow range of phonon wavenumbers.

Phonon attenuation in heavily doped many-valley semiconductors

An expression for the phonon relaxation rate due to the electron-phonon interaction has been derived for heavily doped many-valley semiconductors by solving the equation of motion for the single-particle density matrix within the relaxation time approximation. Detailed calculations have been performed for longitudinal phonons in n-type Ge at 0K. It is shown that acoustic waves which remove the degeneracy of the conduction-band valleys are strongly attenuated for q<or approximately=2kF where q is the phonon wavenumber and kF the Fermi wavenumber. Comparison with other expressions is also given.

The interaction of polar-optical phonons with a two-dimensional electron gas

The interaction Hamiltonian for a two-dimensional electron gas with optical phonons was obtained, for an electron gas on the interface of a polar semiconductor in a metal-insulator-semiconductor device. We found that the electron-phonon interaction is proportional to the inverse square root of the phonon wave number. The dependence of the electron-phonon coupling constant on the dielectric constant of the insulator is determined.

Quasiselection rules for multiphonon absorption in alkali halides

A quasiselection rule is derived that multiphonon infrared absorption in alkali halides prefers final states containing an odd number of optical phonons. This quasiselection rule explains the recent observation of a well-defined peak in the low-temperature infrared absorption of several alkali halides at a frequency corresponding to the sum of three optical phonons. No corresponding peak occurs at the two- or four-opticalphonon summation-band frequencies. It is shown that the quasiselection rule results from the relative ionic displacements for optical modes being approximately in phase with the individual ion displacements, while the relative ionic displacements for acoustical modes are approximately 90\ifmmode^\circ\else\textdegree\fi{} out of phase. The further realization that, at least for optical modes, the magnitude of the Fourier-transformed relative displacement is nearly independent of the phonon wave number greatly reduces the effort of the calculation. This approximation reduces an extremely tedious momentum-dependent sum to a thermally and frequency weighted density of states in which the phonon branches are kept distinct.

X-Ray Scattering Study of Phonon Amplification inn-GaAs: Plasma Effect

Under conditions of q l >1 and ω p τ>1, acousto-electrically amplified phonons are spectroscopically studied in n -GaAS at 77 K by the X-ray Brillouin scattering, where q is the phonon wave number, l the electron mean free path, ω p the plasma frequency and τ the electron collision time. The observed maximum gain frequencies in weak signal regime are compared with theoretical ones. It is found that the observed value for sample with carrier concentration of ∼10 16 cm -3 deviates from the calculated value based upon the ordinary phonon amplification process. This deviation is qualitatively explained in terms of the plasma enhancement of the phonon amplification. The phonon spectra in strong signal regime and the shape of the phonon-flux domain are also observed.

Observation of Giant Kohn Anomaly in the One-Dimensional ConductorK2Pt(CN)4Br0.3· 3H2O

Longitudinal acoustic phonons have been measured by coherent inelastic neutron scattering in the direction of the platinum chains of a single crystal of the one-dimensional conductor ${\mathrm{K}}_{2}$Pt${(\mathrm{CN})}_{4}$${\mathrm{Br}}_{0.3}$\ifmmode\cdot\else\textperiodcentered\fi{}3${\mathrm{H}}_{2}$O at room temperature. The phonon dispersion curve shows a pronounced anomaly at the phonon wave number ${q}_{0}=0.32$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and is interpreted as the logarithmic Kohn anomaly characteristic of a one-dimensional metal.

Lattice Thermal Conductivity ofp-Type Mercury Telluride

The lattice thermal conductivity between 1.7 and 150 K of $p$-type mercury telluride is reported. For most of this temperature range the thermal-conductivity behavior is similar to that of other valence or ionic crystals, but at the lowest temperatures the thermal conductivity is limited, not by boundary scattering of phonons, but apparently by hole-phonon scattering. The Callaway phenomenological model is used to fit the data and to obtain the magnitudes of the normal-, umklapp-, and Rayleigh-scattering relaxation times. Although the hole concentrations of the samples ranged from 5.0 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ to 4.4 \ifmmode\times\else\texttimes\fi{} ${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, the magnitude of the inverse relaxation time for the scattering of phonons by holes did not vary significantly and was approximately $2.7q$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for the phonon wave number $q$ less than 6 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. This behavior is attributed to the complex shape of the hole Fermi surface. As the hole concentration of HgTe increases, the maximum dimension of the hole Fermi surface increases relatively slowly because of the overlapping valence and conduction bands, and thus the range of wave numbers of phonons which can interact with holes is only weakly dependent upon the density of holes. Measurements of the thermoelectric power also are reported, and the same hole-phonon-scattering relaxation time required to explain the low-temperature thermal conductivity accounts for the phonon-drag contribution to the thermoelectric power.

Optical Absorption Spectra of Chromium-Doped Zinc Sulfide Crystals

We have measured the optical absorption spectra of twinned cubic crystals of chromiumdoped zinc sulfide between 5000 and 29 000 ${\mathrm{cm}}^{\ensuremath{-}1}$ (2-0.34 \ensuremath{\mu}m) at 4.2-500\ifmmode^\circ\else\textdegree\fi{}K. Two broad absorption bands are specific to chromium; at 77\ifmmode^\circ\else\textdegree\fi{}K, one has a maximum at 24 400 ${\mathrm{cm}}^{\ensuremath{-}1}$, the other, at 5700 ${\mathrm{cm}}^{\ensuremath{-}1}$. Weak photoconductivity is observed in the former; but none in the latter. Twelve narrow bands between 5100 and 5250 ${\mathrm{cm}}^{\ensuremath{-}1}$ are identified as zero-phonon transitions in ${\mathrm{Cr}}^{2+}$ (3${\mathrm{d}}^{4}$) substitutional at cation sites, two for the cubic structure, ten for the twin boundaries. The cubic crystal field is determined. Thirteen phonon-assisted transitions are identified and the phonon wave numbers are evaluated. We propose that the 24 400-${\mathrm{cm}}^{\ensuremath{-}1}$ band involves transitions to the conduction band edge.

Effect of Annealing on Low-Temperature Thermal Conductivity of High-Density Polyethylene

Thermal conductivity of high-density polyethylene was measured by the steady-flow method at temperatures from 4.2 to 20°K. Results were analysed assuming two scattering processes of phonons: grain boundary scattering with a mean free path ΛG which is independent of phonon wave number k and intragrain scattering with a mean free path ΛD=A/ak2. It was found that ΛG=0.48 μ and A/a=0.51×1010 cm−1 for the as-received sample, and both increase with annealing. The radius of spherulite which was kept constant with annealing ranged 5 to 10 μ. ΛG is attributed to the extension of lamellar crystallite in the ab-plane. ΛD is assigned to intralamellar sub-boundaries. According to results in literature, the ratio of thermal conductivity K to specific heat C is almost constant from 1 to 3°K, where the grain boundary scattering is predominant. Since at 1°K the contribution of two-dimensional lattice waves (Lamb waves in lamellae) is more appreciable than three-dimensional ones, the above result implies that ΛG is the same for the two types of waves, which is consistent with our conclusion for ΛG.

Ultrasonic Attenuation of Pure Strong-Coupling Superconductors

The low-frequency longitudinal ultrasonic attenuation of strong-coupling superconductors is discussed. The starting point is a formula due to Kadanoff and Falko which expresses the attenuation in terms of various correlation functions. These functions were evaluated in the ladder approximation. The results are valid for all values of $\mathrm{ql}$ ($l$=electron mean free path, $q$=phonon wave number). In the limit $\mathrm{ql}\ensuremath{\gg}1$, the contribution of the density-density correlation function is dominant and we obtain Ambegaokar's result for the reduced attenuation (ratio of attenuation in superconducting to normal states). In the limit $\mathrm{ql}\ensuremath{\ll}1$, all correlation functions are equally important. The reduced attenuation is a function of $q$ and differs from the results of the BCS isotropic model. Numerical calculations for the reduced attenuation in lead were performed for various values of $q$ which satisfy $\mathrm{ql}\ensuremath{\ll}1$. The results are in rough agreement with those of Deaton's experiment.

Generation of Spin Waves in Nonuniform Magnetic Fields. III. Magnetoelastic Interaction

If a spin wave propagates through a region of nonuniform magnetic field in which the effective magnon wavenumber equals the phonon wavenumber, it is partially converted into an elastic wave. The conversion efficiency depends primarily on the field gradient (H′) at the crossover point. Theories have been developed both for the case of weak magnetoelastic coupling and strong magnetoelastic coupling. For weak coupling the magnon-phonon conversion efficiency ηmp is ηmp=H′crit/|H′| (for |H′|&amp;gt;&amp;gt;H′crit), whereas for strong coupling ηmp = 1−π2exp(−H′crit/|H′|) (for |H′|&amp;lt;&amp;lt;H′crit). Here H′crit=πb22 ω/cMμ is a critical field gradient, b2 is one of the magnetoelastic constants, ω/2π the signal frequency, c the velocity of (transverse) sound, M the saturation magnetization, and μ the shear modulus. It has been assumed that the dc magnetic field is applied along a cube edge of a cubic crystal and that the material is elastically isotropic. For yttrium iron garnet (YIG) at room temperature and a signal frequency of 3×109 sec−1, H′crit≃5×104 Oe/cm. The field gradients encountered in practice are usually appreciably smaller. Thus the strong coupling theory applies and the magnon-phonon conversion should be substantially complete. The magnetoelastic interaction also gives rise to a reflected wave which originates in the crossover region. The amplitude of the reflected wave is much smaller than the amplitude of the transmitted wave.

Infrared Lattice Bands in AlSb

Lattice bands in AlSb involving interactions of infrared radiation with one, two, three, and four phonons have been observed between 8 and 38 \ensuremath{\mu}. The multiphonon combination bands (summation or difference) can be explained in terms of four characteristic phonons at or near the zone boundary. The corresponding phonon wave numbers are 316, 297, 132, and 65 ${\mathrm{cm}}^{\ensuremath{-}1}$. The interaction of infrared radiation with the transverse optical phonon at the center of the zone results in a single-phonon absorption band and the Reststrahlen reflectivity band. The reflectivity data can be fitted to simple dispersion theory. The fundamental optical frequency from this fit is (9.564\ifmmode\pm\else\textpm\fi{}0.019)\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ (319 ${\mathrm{cm}}^{\ensuremath{-}1}$). The index of refraction $n$ and extinction coefficient $k$ were calculated as functions of wavelength between 20 and 38 \ensuremath{\mu} using dispersion theory.