Wave Vector Conservation Research Articles

Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy.

We derive the momentum and pseudomomentum conservation laws from a very general nonrelativistic Lagrangian theory of the interaction of the electromagnetic field with a deforming, dispersive dielectric. From the former of these laws, we obtain the momentum density of an electromagnetic wave in matter to be ${\mathrm{\ensuremath{\epsilon}}}_{0}$E\ifmmode\times\else\texttimes\fi{}B, not the Abraham form of ${\mathrm{\ensuremath{\epsilon}}}_{0}$E\ifmmode\times\else\texttimes\fi{}${\mathrm{\ensuremath{\mu}}}_{0}$H. From the latter of these laws, we obtain the electromagnetic pseudomomentum density in the absence of deformation of the matter to be P\ifmmode\times\else\texttimes\fi{}B plus a dispersive term, not the Minkowski form of D\ifmmode\times\else\texttimes\fi{}B as proposed by Blount (unpublished). We show by quantizing the energy of the wave that the sum of momentum and pseudomomentum, which we name wave momentum, corresponds to N\ensuremath{\Elzxh}k (N an integer), the quantity that enters wave-vector conservation or phase-matching relations in wave interactions and that is consistent with the Jones-Richards experiment.

Light scattering determination of roton densities of states in two-dimensional landau level excitations

We report the observation of inelastic light scattering by large wavevector inter-Landau level excitations of the 2D electron gas in a perpendicular magnetic field. In results from very high electron mobility single GaAs quantum wells we find evidence of excitonic binding and roton minima predicted by Hartree-Fock calculations. Massive breakdown of wavevector conservation due to residual disorder allows this insight into Coulomb interactions.

Fourier transform infrared photoluminescence of Hg1- xCdxTe

A novel double modulation technique for Fourier transform infrared luminescence spectroscopy is described which facilitates sensitive measurements in the long wavelength ( ≈10 μm) region normally dominated by thermal background radiation. This technique has been used to study the luminescence of Hg 1- x Cd x Te (MCT) bulk crystals with x = 0.22 and x = 0.34 grown by the travelling heater method. Luminescence of bulk MCT in the 10 μm range is reported for the first time ( x = 0.22). The dependence of the luminescence spectra on temperature and excitation power has been studied. For the x = 0.22 sample, substantial luminescence line broadening is observed with increasing excitation power. This behaviour is attributed to band filling effects in the conduction band. From the above data, the lifetime of the photogenerated carriers of 0.4 μs is deduced. The temperature dependence of the luminescence indicates contributions from transitions with slightly relaxed wavevector conservation. Corresponding data for a MCT sample with x = 0.34 are presented using excitation powers down to 35 μW (power densities 0.2 Wcm -2).

Fine tuning of wavevector conservation in guided wave devices by photobleaching

A new principle for optimising wavevector conservation and phase-matching in organic based guided wave devices is proposed and demonstrated. Fine tuning of grating coupling into a poly-4BCMU waveguide is demonstrated using controlled changes in the refractive index by photobleaching.

Raman Scattering in Semiconductor Nanocrystals

ABSTRACTWe combine the principles of phonon and electron quantization in confined systems and breakdown of wavevector conservation in the photon-electron and phonon-electron couplings to describe the Raman spectrum of nanocrystals. The approach proposed here is consistent with experimental results and models developed for Raman scattering from quantum wells and superlattices.

Brillouin scattering from corrugated Ag films: Surface-plasmon-mediated enhancement and relaxed wave-vector conservation.

We report the investigation of Brillouin scattering from thermal surface acoustic waves on Ag-coated holographic gratings. The usual wave-vector conservation condition for Brillouin scattering is modified due to the added periodicity in the direction of phonon propagation, but this effect is observed only when surface plasmons act as an intermediate state in the scattering process. The involvement of surface plasmons results in an enhancement of the Brillouin scattering cross section which depends on the grating amplitude.

Surface-field-induced transverse and vertical tunnel junctions

We report on tunneling between a 2D electronic system at the semiconductor/insulator interface influenced by an electric surface field and a 3D counterelectrode with tunneling directions parallel and perpendicular to the surface. Junctions of Yb and Au to electron and hole inversion layers, respectively, show thermally activated tunneling where the tunneling probability is controlled by the electric surface field. Vertical junctions consist of an Yb/oxide/semiconductor tunnel junction on a degenerate p-type Si, InAs, and InSb substrate. The low work function leads to a high electric field that inverts the semiconductor surface and forms a Zener tunnel junction between the electron layer and the bulk valence states. Current-voltage characteristics of junctions on Si are similar to backward diodes with phonon-induced structures at low temperatures. InAs junctions show room-temperature negative differential conductance with peak-to-valley ratios up to 2.7 increasing up to 15 at low temperatures. InSb junctions, which are nearly ohmic at room temperature, yield typical current ratios of 11. Junctions on high-quality InAs substrates exhibit a resonance-like characteristic which is explained in terms of wave vector conservation law.

Localization and wave-vector conservation for optical phonons in AlxGa1-xAs and thin layers of GaAs.

The dependence on the scattering wave vector of a nonequilibrium LO phonon distribution generated by hot-electron relaxation is measured in thick GaAs and ${\mathrm{Al}}_{0.11}$${\mathrm{Ga}}_{0.89}$As layers, and a 500-\AA{} GaAs layer using picosecond Raman scattering in back and forward scattering geometries. The absence of $q=0$ nonequilibrium phonons in the thick samples, and their presence in the 500-\AA{} sample, demonstrates that Raman-active LO phonons in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ have well-defined wave vectors and are not localized by alloy disorder.

Tunneling and transverse wave vector conservation in GaAs/AlGaAs heterostructures

We have studied transverse wave vector conservation in the tunneling of electrons between a quantum well and an n+ electrode while varying the density of electrons in the well. The sample is a ‘‘tunnel capacitor’’ structure in which a GaAs well is separated by an AlGaAs tunnel barrier from the bottom n+ electrode and by a much thicker AlGaAs barrier from the top n+ electrode. In a regime where the transverse wave vector cannot be conserved in the absence of scattering, we present a model that includes scattering effects and show that it agrees with our experimental data and can be used to draw some conclusions about the efficacy of spacer layers to reduce these scattering effects.

Picosecond Raman studies of the Fröhlich interaction in semiconductor alloys.

Picosecond Raman studies on the prototypic alloys ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As and ${\mathrm{In}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As show that substantial nonequilibrium phonon effects occur in spite of the break-down in wave-vector conservation engendered by alloy disorder. Phonon lifetimes, measured to be the same as in pure GaAs, also are unaffected by the disorder. Explicit expressions for the Fr\"ohlich couplings of the two LO phonon modes in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As are obtained to compare with the generation rates of these phonons measured in our experiments.

Leakage-induced and disorder-activated modes from the folded acoustic branches in GaAs-AlAs superlattices.

Low-frequency Raman modes in the acoustic region (5--40 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) are investigated in (001)-oriented GaAs-AlAs superlattices grown by molecular-beam epitaxy and metal-organic chemical-vapor deposition. Besides the well-known folded LA (FLA) modes, we carefully studied the folded TA (FTA) modes and also modes corresponding to the zone edge of the folded acoustic (LA and TA) branches. The former modes fulfill the selection rule of wave-vector conservation and are due to a leakage of the light polarization. The latter are activated by the disorder and are influenced by the interface defects. These disorder-activated (DA) modes, called DAFLA and DAFTA, are propagative modes which are sensitive to the period of the superlattice, contrary to the previously reported DALA and DATA which are localized in the GaAs and AlAs layers and whose frequency is fixed.

Investigation of InGaAs-InP quantum wells by optical spectroscopy

A detailed study of the optical properties of InGaAs-InP single quantum wells (QWS) grown by atmospheric-pressure metal-organic chemical vapour deposition is described. Photoluminescence (PL), photoluminescence excitation (PLE), photoconductivity (PC) and electroreflectance (ER) are employed to study both undoped and modulation-doped quantum wells. The role of extrinsic processes in determining the low-temperature PL spectra is demonstrated from the variation of peak position and linewidth with temperature. The best PL linewidth obtained for a 150 AA well is 5.3 meV, fairly close to the limit imposed by alloy fluctuations in the InGaAs. The role of free carriers in the undoped QWS in determining the energy threshold for optical absorption is demonstrated from a comparison of PLE and PC spectra. Lineshape fitting of the PL spectra is described, and it is deduced that at 160K recombination processes in both doped and undoped QWS proceed with wavevector conservation, although at lower temperatures highly anomalous lineshapes are found in modulation-doped samples. The observation of a threshold in PC spectra under forward bias is interpreted as a transition from the valence-band well to the top of the conduction well. The ratio of the conduction- to valence-band discontinuities is deduced to be approximately 0.4:0.6.

On electron tunneling in the metal-insulator-semiconductor systems including various electron effective masses

It is shown that in some cases of the metal-insulator-semiconductor systems the electron tunnel current may be expressed in the form of one-dimensional integral with modified ‘‘supply function’’ even if the effective mass is not the same in each region of the system. The proposed formula together with description of the semiconductor space charge region (which is not considered in the paper) may be used for modeling of the electron tunnel current-voltage characteristics, e.g., of the metal–SiO2–Si〈100〉 tunnel diodes. The considerations are based on the electron total energy and transverse wave-vector conservation assumptions.

Strain-field scattering of fast-transverse acoustic phonons by dislocations in LiF

The mean-free-paths of transverse acoustic phonons generated in surface hot spots and propagating ballistically along [100] in LiF are calculated exactly for the case of scattering by the static strain fields of edge and screw dislocations of Burger's vector 1 2 a [ 110 ] . Due to wavevector conservation the screw dislocations are shown not to scatter such phonons at all while the edge dislocations lead to mean-free-paths greater than 12 cm for dislocation densities ⩽2×10 8 cm -2 and frequencies ⩽5×10 11 Hz. This is consistent with the observation by Northrop et al. (1982) of the ballistic propagation of such heat-pulse phonons across deformed crystals of 1 cm dimensions.

Wave propagation and localization in a long-range correlated random potential

We examine the effect of long-range spatially correlated disorder on the Anderson localization transition in $d=2+\ensuremath{\epsilon}$ dimensions. This is described as a phase transition in an appropriate non-linear $\ensuremath{\sigma}$ model. We consider a model of scalar waves in a medium with an inhomogeneous index of refraction characterized by scattering strength ${\ensuremath{\gamma}}^{2}$ and spatial correlations of range $a$ decaying (i) exponentially ${\ensuremath{\gamma}}_{1}^{2}{a}^{\ensuremath{-}d}{e}^{\ensuremath{-}\frac{x}{a}}$ and (ii) by power laws ${\ensuremath{\gamma}}_{2}^{2}{({a}^{2}+{x}^{2})}^{\ensuremath{-}m}(mg0)$. A replica-field-theory representation is utilized in the calculation of the one- and two-particle Green's functions. In addition to the usual diffusive Goldstone mode of the field theory arising from energy conservation, the non-linear $\ensuremath{\sigma}$ model is shown to possess a discrete spectrum of low-lying nondiffusive modes associated with approximate wave-vector ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$) conservation in the geometric optics limit $\mathrm{ka}\ensuremath{\gg}1$. For waves it is shown that all states are localized for $d\ensuremath{\le}2$ with diverging localization lengths in the low-frequency limit and that the mobility edge in $d=2+\ensuremath{\epsilon}$ separating high-frequency, localized states from low-frequency, extended states is characterized by the same critical exponents as for spatially uncorrelated disorder provided $mg\ensuremath{\epsilon}$. The problem of electron localization in a long-range correlated random potential is also described within the same universality class.

Resonant inelastic light scattering by free electrons in InP

The single particle and collective excitations of free electrons in doped n-InP have been studied by resonant inelastic light scattering near the E 0 + Δ 0 optical energy gap. The resonant enhancements and spectral lineshapes are similar to those previously reported in n-GaAs. The resonant spectra by longitudinal coupled plasmon-phonons reveal the contributions of processes for which wavevector conservation breaks down.

Luminescence studies of HgCdTe alloys

We report the observation in Hg_(1-x)Cd_(x)Te of band-to-band, band-to-acceptor, and donor-acceptor luminescence for material of x = 0.32 and 0.5, and bound exciton recombination luminescence, for material of x = 0.5. The band-to-band lineshape and variation in intensity with pump power are appropriate to an electron-hole plasma with recombination proceeding without wave vector conservation. Differences between the spectra among the four 0. 5 samples studied are attributed to variations in the Hg vacancy concentration. Shifts in luminescence energy across one of the x = 0.32 samples imply a change in composition across the surface of the sample of 0.03 cm^(-1). The absence of bound exciton luminescence in the x = 0.32 samples is consistent with theoretical calculations by Osbourn and Smith showing a radiative efficiency of 20% for bound excitons in material of this composition and 90% for x = 0.48 material. From line shape separations, we estimate acceptor binding energies of 14.0 ± 1.0 and 15.5 ± 2.0 meV in x = 0.32 and 0.48 materials, respectively, and donor binding energies of 1.0 ± 1.0 and 4.5 ± 2.0 meV, respectively.

Luminescence from HgCdTe alloys

We report the observation in Hg1−xCdxTe of band-to-band, band-to-acceptor, and donor-acceptor luminescence for material of x = 0.32 and 0.48, and bound exciton recombination luminescence, for material of 0.48. The band-to-band line shape and variation in intensity with pump power is appropriate to an electron-hole plasma with recombination proceeding without wave vector conservation. From line shape separations, we estimate acceptor binding energies of 14.0±1.0 and 15.5±2.0 meV in x = 0.32 and 0.48 material, respectively, and donor binding energies of 1.0±1.0 and 4.5±2.0 meV, respectively. Shifts in luminescence energy across the sample imply a change in composition across the sample of 0.03 cm−1.

Light scattering spectroscopy of electrons in GaAs–(AlGa)As heterostructures: Correlation with transport properties

We used the resonant inelastic light scattering method to study high mobility electrons confined in modulation-doped GaAs–(AlGa)As multiple quantum-well heterostructures. In spectra of intersubband transitions we observe a correlation between FWHM and electron mobility. In the lower mobility cases (μ≲30 000 cm2/Vs) we find an unusual dependence of FWHM on incident photon energy. The results are interpreted in terms of wave vector conservation broken by intermediate-state relaxation processes similar to those that limit the electron mobility.

Theory of lattice thermal conductivity: Role of low-frequency phonons

The lattice thermal conductivity arises from contributions by phonons of all frequencies. The mean free path l(ω) is limited mainly by three-phonon interactions, and li(ω)∝ω−2T−1 where ω is the phonon frequency, and T is the absolute temperature. Since the spectral specific heat varies as ω2, the spectral thermal conductivity is independent of frequency, and low frequencies play a larger role than they do in the heat content. The effect of additional scattering processes due to defects must be compared to intrinsic scattering, not just at the highest frequency, but over the full spectral range. This enhances the resistance due to grain boundaries and large obstacles, and reduces the effect of point defects. Some typical examples are discussed. The role of low-frequency phonons may be even further enhanced if longitudinal low-frequency phonons have their interaction with other phonons reduced by wave vector conservation. Such modes would then contribute substantially to the overall thermal conductivity, and this contribution would be sensitive to grain size and to large-scale defects. However, the mean free path must be consistent with ultrasonic attenuation data. This enhanced sensitivity may be observable.