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dc and ac magnetic susceptibility, magnetization, specific heat, and Raman scattering measurements are combined to probe low-lying spin excitations in $\ensuremath{\alpha}$-${\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Ir}}_{x}{\mathrm{Cl}}_{3}$ ($x\ensuremath{\approx}0.2$), which realizes a disordered spin liquid. At intermediate energies ($\ensuremath{\hbar}\ensuremath{\omega}g3\text{ }\text{ }\mathrm{meV}$), Raman spectroscopy evidences linearly $\ensuremath{\omega}$-dependent Majorana-like excitations, obeying Fermi statistics. This points to robustness of a Kitaev paramagnetic state under spin vacancies. At low energies below 3 meV, we observe power-law dependences and quantum-critical-like scalings of the thermodynamic quantities, implying the presence of a weakly divergent low-energy density of states. This scaling phenomenology is interpreted in terms of the random hoppings of Majorana fermions. Our results demonstrate an emergent hierarchy of spin excitations in a diluted Kitaev honeycomb system subject to spin vacancies and bond randomness.

We present resonant Raman scattering (RRS) studies on single-variant, spontaneously ordered GaInP{sub 2} alloys in backscattering geometries on the (001) growth surface and on a (110) cleaved surface. A systematic study of RRS in the (110) backscattering geometry enables us to resolve the controversy regarding the assignment of the ordering-induced phonon mode at 205 cm-1 in this scattering geometry, and shows that this phonon mode is a forbidden longitudinal mode in this geometry but appears in the Raman spectra due to Froehlich scattering. (c) 2000 The American Physical Society.

Resonant Raman scattering is used to study the nature of the recently discovered nitrogen-induced level E{sub +} located in the conduction band of GaAs{sub 1-x}N{sub x} (0.001{

Resonance Raman scattering and electroreflection measurements on laterally composition modulated GaP/InP short-period superlattices are presented. The electroreflectance spectra give the fundamental band-gap energy of the lateral superlattice at 1.69{plus_minus} 0.05eV, which is about 210 meV lower than the band-gap energy of a GaInP random alloy with the same overall composition. In resonance Raman spectra measured with the polarization of both excitation and scattered photons along the composition modulation direction, the GaP-like longitudinal optical phonon redshifts by 4.0{plus_minus} 0.5cm{sup {minus}1} near the resonance with the fundamental energy gap. A comparison of the experimental data with a model calculation gives the average In composition in the In-rich region as 0.70{plus_minus} 0.02, and the average Ga composition in the Ga-rich region as 0.68{plus_minus}0.02. {copyright} {ital 1999} {ital The American Physical Society}

We propose ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures as a model system to study the phenomenon of photoluminescence (PL) up-conversion and demonstrate low-temperature up-converted PL (UPL) in these heterostructures. We find that a mechanism to prevent up-converted carriers in the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ layer from thermalizing back to the GaAs layer is essential for efficient UPL. We also find that neither a type-II band alignment nor existence of long-lived intermediate states is an essential requirement of UPL. The results of time-resolved UPL measurements are interpreted within the current models.

The spontaneously ordered ${\mathrm{Ga}}_{0.52}{\mathrm{In}}_{0.48}\mathrm{P}$ alloy comprises domains, each of which is characterized by an order parameter \ensuremath{\eta}. We have used the low-temperature near-field photoluminescence technique with a high spatial resolution $(l~2500\AA{})$ to study the statistical distribution of the order parameter \ensuremath{\eta} of single-variant ordered alloys. We have found that for large-domain samples, \ensuremath{\eta} varies only slightly between domains and the line width broadening of the excitonic photoluminescence peak comes mainly from alloy scattering within a single domain rather than from a broad distribution of \ensuremath{\eta}.

We report on room-temperature polarized far-infrared reflectance in partially ordered GaInP performed with the incidence plane parallel to the growth and ordering directions. Measurements in the s-polarization geometry show only one feature related to the vibrations in the plane of ordering. On the contrary, those performed using p polarization display a structure appearing in the range of InP-like vibrations as the order parameter increases, which we relate to a resonance with longitudinal-optic mode character due to the anisotropy of the longitudinal phonons. {copyright} {ital 1997} {ital The American Physical Society}

The effects of spontaneous ${\mathrm{CuPt}}_{B}$ ordering on the lattice dynamics of ${\mathrm{GaInP}}_{2}$ alloys are studied by room-temperature Raman-scattering experiments on a series of ${\mathrm{GaInP}}_{2}$ samples with various degrees of ordering, grown by organometallic vapor phase epitaxy. In measurements on the (001) growth plane, we have observed several changes in the optical-phonon range of the Raman spectrum, the most notable of which is the emergence of an extra peak at 354 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}.$ This peak is identified as a longitudinal-optical mode due to the superlattice effect in the ordered alloys. The acoustic-phonon range of the (001) Raman spectra of the ordered samples shows extra peaks at 60 and 205 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ which are identified as the folded transverse and longitudinal-acoustic phonons, respectively. For the optical phonons, the Raman selection rules and the identification of the extra peak are tested by measuring right-angle Raman scattering. The results are consistent with the trigonal ${C}_{3\ensuremath{\nu}}$ symmetry of the ordered alloys.

We have performed micro-Raman-scattering experiments on ordered ${\mathrm{GaInP}}_{2}$ alloy samples in three different geometries where the phonon wave vector is either parallel or perpendicular to the ordering axis of the crystal. By comparing results from the (1\ifmmode\bar\else\textasciimacron\fi{}11) backscattering and right-angle scattering measurements with the ${C}_{3v}$ symmetry of the crystal, we found that the recently discovered peaks at 205 and 354 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the Raman spectra of ordered alloys are due to longitudinal-phonon modes with ${A}_{1}$ symmetry in these geometries. In the (110) backscattering geometry, selection-rule forbidden longitudinal-phonon modes appear in the Raman spectra measured in parallel polarizations. Possible mechanisms for this selection-rule violation are discussed.

Using time-resolved small-signal exciton absorption bleaching at low temperature as a spectroscopic technique, the optical transition energies from all three valence bands in spontaneously ordered Ga{sub x}In{sub 1{minus}x}P have been measured with high accuracy. The origin of the bleaching signal and the contributions of reflection, strain, and binding energy are discussed. With three measured energies from each sample, all parameters in the quasicubic perturbation model can be fitted. Good agreement is obtained with a spin-orbit-splitting parameter of 103 meV, nearly independent of the degree of ordering. The ratio of band-gap reduction to crystal-field-splitting parameter is found to be 2.7, slightly higher than previous works. This difference is attributed to a more accurate determination of light-hole-like band-gap energy. {copyright} {ital 1997} {ital The American Physical Society}

Efficient, low-temperature conversion of infrared light into visible light ~red, orange, green! is reported at single heterojunctions and undoped quantum wells of GaAs and ordered AlxGa 12xInP 2; an increase in photon energy of 700 meV is obtained. The signal originates from the high-band-gap layers and disappears only if the excitation energy is tuned below the GaAs band gap. The intensity of the up-converted photoluminescence ~PL! is found to decrease significantly slower with increasing temperature than that of the regular PL and it remains observable up to 200 K. Interface-induced cold Auger processes along with the presence of trapped states for both electrons and holes in these ordered alloys account for this nonlinear mechanism. A colinear double-beam experiment confirms this.@S0163-1829~96!50132-3# Up-conversion is the observation of radiative transitions at higher energies than that of the excitation source. In general, the observation of up-conversion requires either high temperatures to achieve, for example, ~i! a thermal population of holes for momentum ~k! conserving bulk Auger processes, or ~ii! a thermal population of phonon modes for anti-Stokes Raman lines, 1 or it relies on a nonlinear mechanism, such as two-photon absorption via real or virtual states. In addition, the excited carriers should not immediately relax back to their ground states to enable the observation of radiative transitions from the excited state. Experimental observation of up-conversion at cryogenic temperatures ~cold up-conversion! in solids was reported only rarely and they concerned only small energy gains or high excitation densities. 2‐5 Recently, Kim et al. 6 observed up-conversion ~‘‘anti-Stokes luminesence’’ ! in an asymmetric doublequantum-well system, which they attributed to quantum oscillations. In a recent theoretical paper, Zegrya and Kharchenko 7

We have determined the pressure dependences of the band offsets in the GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunctions by measuring the pressure dependences of the harmonic-oscillator-like electron-energy-level spacings \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$ of two ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As parabolic quantum wells at hydrostatic pressures up to \ensuremath{\sim}26 kbar at 2 K using photoluminescence-excitation spectroscopy. We found that the conduction-band offset for x\ensuremath{\approxeq}0.3 increases with pressure at a rate of 0.73\ifmmode\pm\else\textpm\fi{}0.25 meV/kbar. Using this result and the finding that the pressure coefficient of the direct-band-gap energy of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As is independent of x for x=0-0.4, we found that the fractional conduction- (valence-) band offset ${\mathit{Q}}_{\mathit{c}}$ (${\mathit{Q}}_{\mathit{v}}$) of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As increases (decreases) with pressure at a rate of 0.0020\ifmmode\pm\else\textpm\fi{}0.0007 ${\mathrm{kbar}}^{\mathrm{\ensuremath{-}}1}$. From this result, we conclude that the previous determinations of the band-offset values of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As by high-pressure measurements overestimated (underestimated) the fractional conduction- (valence-) band offset by 0.06\ifmmode\pm\else\textpm\fi{}0.02, and the corrected ${\mathit{Q}}_{\mathit{c}}$ value at atmospheric pressure should be 0.63\ifmmode\pm\else\textpm\fi{}0.04.

The thermal conductivity of suspended single-layer graphene was measured as a function of temperature using Raman scattering spectroscopy on clean samples prepared directly on a prepatterned substrate by mechanical exfoliation without chemical treatments. The temperature at the laser spot was monitored by the frequency of the Raman 2$D$ band of the Raman scattering spectrum, and the thermal conductivity was deduced by analyzing heat diffusion equations assuming that the substrate is a heat sink at ambient temperature. The obtained thermal conductivity values range from $\sim$1800 Wm$^{-1}$K$^{-1}$ near 325 K to $\sim$710 Wm$^{-1}$K$^{-1}$ at 500 K., 4pages, 3 figures

We have measured the photoluminescence (PL) of HgTe/CdTe superlattices under high hydrostatic pressures up to 30 kbar at liquid-nitrogen temperature. We observed several photoluminescence peaks with energies ranging from \ensuremath{\sim}130 to \ensuremath{\sim}700 meV. The most prominent peak at \ensuremath{\sim}130 meV, which has been attributed to the recombination across the superlattice band gap, moves higher in energy with a pressure coefficient of \ensuremath{\lesssim}1 meV/kbar. Other peaks, whose origins are not well established, have higher energies and their pressure coefficients are in the range of 0--2 meV/kbar. A calculation based on the envelope-function approximation gives a pressure coefficient of at least \ensuremath{\sim}6.5 meV/kbar for the superlattice band gap. This is far outside the error bars of the measured pressure dependence of the main peak, \ensuremath{\lesssim}1 meV/kbar. Varying the input parameters for the calculation, including the valence-band offset, changes the result of the calculation by less than 10%. Possible explanations for this disagreement, including a modification of the current model of HgTe/CdTe superlattice bands and a reinterpretation of the PL peaks, are examined.

We have used resonant inelastic light-scattering spectroscopy in the depolarized backscattering configuration z (y',x')z to probe the single-particle excitations of two n-type remotely doped wide parabolic GaAs/Al x Ga 1-x As quantum wells, with design curvatures corresponding to empty conduction-band harmonic-oscillator spacings of 4.4 and 3.3 meV. For the former sample, a series of spectra, for excitations near the E 0 +Δ 0 gap of the bulk material at the center of the well, reveal two light-scattering peaks with shifts ∼0.85 and ∼3.0 meV, which are strongly resonant withresonance widths of ≤3 meV

We have investigated the energies of the electronic states of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As strongly coupled double quantum wells and uncoupled multiple quantum wells as functions of hydrostatic pressure up to 35 kbar. The energies of the quantum-well states at 4 K were determined at each pressure by photoluminescence excitation spectra. The pressure coefficients of the energies of the allowed transitions between the valence-band and conduction-band quantized states of wide (200 \AA{}) uncoupled wells were all equal to the pressure coefficient of the bulk GaAs band gap. For a strongly coupled double quantum well consisting of two 72-\AA{} wells separated by an 18-\AA{} barrier, the energies of the allowed transitions all showed a decrease in their pressure coefficients beginning near 20 kbar. These results are interpreted in terms of a drop in the conduction-band quantum-well confinement energy, due to \ensuremath{\Gamma}-X mixing, as the X valleys of the barrier materials are brought nearly equal to the energies of the confined electron states by pressure. An envelope-function-approximation model which includes \ensuremath{\Gamma}-X mixing at the interfaces is compared quantitatively with these results and found to be consistent for a certain range of the phenomenological mixing strength of the model.

The intensity ratio between two major Raman bands in graphene is one of the most important pieces of information for physics of graphene and has been believed to represent various intrinsic properties of graphene without critical assessment of extrinsic effects. We report a micro-Raman spectroscopy study on the Raman intensity ratio of the $2D$ band to the $G$ Raman band of graphene varying the thickness of dielectric layers $({\text{SiO}}_{2})$ underneath it. The ratio is shown to change by almost 370% when the thickness is varied by 60%. The large variation in the ratio is well explained by theoretical calculations considering multiple Raman scattering events at the interfaces. Our analysis shows that the interference effect is critical in extracting the intrinsic $2D$ to $G$ intensity ratio and therefore must be taken into account in extracting various physical properties of graphene from Raman measurements.

The nature of the conduction-band minimum of GaA 1 - x N x (x≤0.7) is probed by performing resonant Raman scattering (RRS) on thin layers of GaAs 1 - x N x epitaxially grown on Ge substrates. Strong resonance enhancement ofthe LO-phonon Raman intensity is observed with excitation energies near the E 0 as well as E + transitions. However, in contrast to the distinct LO-phonon linewidth resonance enhancement and activation of various X and L zone-boundary phonons brought about slightly below and near the E transition, respectively, we have not observed any resonant LO-phonon linewidth broadening or activation of sharp zone-boundary phonons near the E 0 transition. The observed RRS results reveal that the conduction-band minimum of GaAs 1 - x N x predominantly consists of the delocalized GaAs bulklike states of Γ symmetry.

A measurement of the hole density in the ferromagnetic semiconductor ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ is notoriously difficult using standard transport techniques due to the dominance of the anomalous Hall effect. Here we report a spectroscopic measurement of the hole density in four ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ samples $(x=0,0.038,$ 0.061, and 0.083) at room temperature using a Raman-scattering intensity analysis of the coupled plasmon--LO-phonon mode and the unscreened LO phonon. The unscreened LO-phonon frequency linearly decreases as the Mn concentration increases up to 8.3%. The hole density determined from the Raman scattering shows a monotonic increase with increasing x for $xl~0.083,$ exhibiting a direct correlation to the observed ${T}_{c}.$ The optical technique reported here provides an unambiguous means of determining the hole density in this important class of ``spintronic'' semiconductor materials.

The anisotropy associated with angular variation of the phonon wave vector q with respect to the ordering axis z{sup {prime}} of a spontaneously ordered GaInP{sub 2} with order parameter {eta}{congruent}0.46 is studied by carefully performing micro-Raman measurements in scattering geometries where q is either parallel or perpendicular to z{sup {prime}}. The LO mode at {similar_to}380cm{sup {minus}1} and the TO mode at {similar_to}330cm{sup {minus}1} exhibit distinct phonon frequency shifts of {minus}1.2cm{sup {minus}1} and +2.1cm{sup {minus}1}, respectively, as the angle {phi} between q and z{sup {prime}} varies from 0{degree} to 90{degree}. This small angular dispersion is explained on the basis of the bond-stiffening along the ordering axis with increasing order parameter {eta}, providing strong evidence for a small A{sub 1}-E splitting in comparison to the large LO-TO splitting for these modes. In addition, an even larger angular dispersion, +2.5cm{sup {minus}1}, for the vibrational mode at {similar_to}354cm{sup {minus}1} is observed. Two additional phonon modes, which have previously been labeled as missing to account for all nine Raman-active optical modes, are observed and experimentally identified with E(x) and E(y) tensors.

Photoluminescence excitation (PLE) spectroscopy was performed on an undoped and several remotely doped wide parabolic GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As wells of various well widths and electron sheet densities. For an undoped parabolic well of width 4640 \AA{}, the PLE peak energies are consistent with calculated energies of allowed exciton transitions. The spectra for a remotely doped well of the same width are dominated by a series of uniformly spaced peaks with spacing (\ensuremath{\sim}3.1 meV) approximately equal to the harmonic-oscillator spacing of the bare parabolic conduction-band-edge curvature. Measurements of the dependence of the peak spacing on well width and electron sheet density are presented.