Generalized Phonon Density Of States Research Articles

Generalized phonon density of states of La2−xSrxCuO4cuprate superconductor

Many body quantum dynamics of phonons is steadily developed by considering the various effects of anharmonicities, defects (consider as doping or impurity concentration) and electron–phonon interactions in model Hamiltonian (instead of BCS Hamiltonian) for a high-temperature superconductor (HTS). This enables to obtain the expressions for the renormalized phonon spectrum, the renormalized phonon density of states (RPDOS). The RPDOS can be resolved into diagonal and nondiagonal parts where the nondiagonal component is found highly impurity-dependent. Considering the suitable Born–Mayer–Huggins (BMH) interaction potential, the renormalized phonon spectrum, RPDOS and generalized phonon density of states (GPDOS) of the La[Formula: see text]Sr[Formula: see text]CuO4layered superconductor have been numerically analyzed and it was found that these quantities depend on doping concentration, anharmonicities, and temperature. The results are compared with the inelastic neutron scattering experimental data of GPDOS for La[Formula: see text]Sr[Formula: see text]CuO4and are found in good agreement. The ratio of deviation in GPDOS to GPDOS at critical temperature ([Formula: see text] K) shows the implicit difference at [Formula: see text]. The impact of defects, anharmonicities, and electron–phonon interactions in the cuprate superconductors virtually modify the scenario of GPDOS and affirm a large number of exotic peaks in the spectrum.

Observation of drastic change of generalized phonon density-of-states in nanostructured half-Heusler using inelastic neutron scattering

To understand the role of the nanophase in reducing the lattice contribution of the thermal conductivity of thermoelectrics, the structure and phonon density of a p-type half-Heusler thermoelectric ingot (ingot-HH, nominal composition of (Hf0.5Zr0.5)Co(Sb0.8Sn0.2)), and its nano form prepared from ball milling (nano-HH), were studied using neutron diffraction and neutron inelastic scattering techniques. They are both cubic, F4¯3m, with lattice parameters a = 6.0649(3) Å (nano) and 6.0629(1) Å (ingot), but the nano and ingot materials exhibit markedly different generalized phonon density-of-states (GDOS) at 300 K due to the substantially reduced grain size in the nano sample. These overall changes in GDOS, together with the increase in grain boundary scattering, account for the sharp reduction of the thermal conductivity in the nano-hot-pressed (nano-hp-HH) sample, which has a similar average grain size to that of nano-HH.

Generalized phonon density of states of Mo3Sb7and Mo3Sb5.4Te1.6from inelastic neutron scattering and lattice dynamical calculations

The temperature dependence of the generalized phonon density of states (GDOS) of polycrystalline Mo(3)Sb(7) and Mo(3)Sb(5.4)Te(1.6) was studied from 300 K down to 2 K using inelastic neutron scattering. Even though Mo(3)Sb(7) undergoes a magnetic as well as a structural phase transition at T* = 53 K, no appreciable change in the recorded spectra has been revealed. The generalized density of states of the nonmagnetic Mo(3)Sb(5.4)Te(1.6) compound shows similar main characteristics, though substituting Sb by Te leads to a shift of the entire spectrum towards higher energy. The temperature dependence of the GDOS reveals an anomalous softening of phonons with decreasing temperature in Mo(3)Sb(7) which cannot be captured by the harmonic approximation while Mo(3)Sb(5.4)Te(1.6) exhibits a normal behavior. This feature might be related to a strong interplay between magnetic excitations and phonons at the core of the anomalous thermal transport displayed by Mo(3)Sb(7). In general, the main characteristics of the experimentally derived GDOS of Mo(3)Sb(7) can be reproduced by lattice dynamical calculations.

Low-frequency excitations ofC60chains inserted inside single-walled carbon nanotubes

The low frequency excitations of C60 chains inserted inside single-walled carbon nanotubes (SWNTs) have been studied by inelastic neutron scattering (INS) on a high quality sample of peapods. The comparison of the neutron-derived generalized phonon density of states (GDOS) of the peapods sample with that of a raw SWNTs allows the vibrational properties of the C60 chains encapsulated in the hollow core of the SWNTs to be probed. Lattice dynamical models are used to calculate the GDOS of chains of monomers, dimers and polymers inserted into SWNTs, which are compared to the experimental data. The presence of strong interactions between C60 cages inside the nanotube is clearly demonstrated by an excess of mode density in the frequency range around 10 meV. However, the presence of a quasi-elastic signal indicates that some of the C60\'s undergo rotational motion. This suggests that peapods are made from a mixture of C60 monomers and C60 n-mer (dimer, trimer ... polymer) structures.

Doping evolution of the phonon density of states and electron-lattice interaction inNd2−xCexCuO4+δ

We use inelastic neutron scattering to study the evolution of the generalized phonon density of states (GDOS) of the $n$-type high-$T_c$ superconductor Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$ (NCCO), from the half-filled Mott-insulator ($x=0$) to the $T_c=24$ K superconductor ($x=0.15$). Upon doping the CuO$_2$ planes in Nd$_2$CuO$_{4+\delta}$ (NCO) with electrons by Ce substitution, the most significant change in the GDOS is the softening of the highest phonon branches associated with the Cu-O bond stretching and out-of-plane oxygen vibration modes. However, the softening occurs within the first few percent of Ce-doping and is not related to the electron doping induced nonsuperconducting-superconducting transition (NST) at $x\approx 0.12$. These results suggest that the electron-lattice coupling in the $n$-type high-$T_c$ superconductors is different from that in the $p$-type materials.

Cold-neutron scattering study of La 2− xSr xCuO 4

The generalized phonon density of states (GPDOS) for La 2− x Sr x CuO 4 ( x=0.0, 0.08, 0.12, 0.15 and 0.21) powder samples are determined from inelastic cold-neutron scattering measurements using the TOF-type cold-neutron spectrometer, AGNES, mainly above the tetragonal-to-orthorhombic structural phase transition temperature. The softening of modes at about 12 meV was observed in the GPDOS for La 1.85Sr 0.15CuO 4. This phenomenon is related with the instability of the K 2NiF 4-type tetragonal structure.

Lattice dynamics and electron-phonon coupling in superconducting HgBa2CuO4 investigated by inelastic neutron scattering

The generalized phonon density of states (GDOS) is obtained from the measuring data and compared to model calculations. By means of the partial densities of states which are obtained from these calculations observed structures in the GDOS can be attributed to particular vibrations of atoms. Most significant are shifts of high frequency oxygen modes which are observed upon cooling. These findings seem to be connected with the transition into the superconducting state.

Phonon density of states inR2CuO4and superconductingR1.85Ce0.15CuO4(R=Nd,Pr)

Inelastic-neutron-scattering measurements of the generalized phonon density of states (GDOS) for the electron-doped superconductors ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$ and ${\mathrm{Pr}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$ have been carried out with the use of both a filter-detector method and time-of-flight spectroscopy. A measurement of the GDOS for the insulating ${\mathrm{Pr}}_{2}$${\mathrm{CuO}}_{4}$ was also done for comparison with that of ${\mathrm{Pr}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$, while a more limited set of data was obtained for ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4}$. Comparison between the GDOS spectrum of the ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$ with that of ${\mathrm{Pr}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$ shows differences in the shape of some structures in the GDOS spectrum. Furthermore, there are substantial changes in the GDOS spectrum of ${\mathrm{Pr}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$ as compared to that of ${\mathrm{Pr}}_{2}$${\mathrm{CuO}}_{4}$, particularly in the energy regime between 33 and 63 meV.In the ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$ system, where electron-tunneling measurements have been performed, there are similarities between the GDOS spectrum and the Eliashberg-coupling function ${\mathrm{\ensuremath{\alpha}}}^{2}$F(\ensuremath{\omega}) obtained from the tunneling data in the energy regions where comparisons can be made. To the extent that this comparison is valid, it suggests that phonons are to some extent involved in the electron-pairing mechanism in these electron-doped superconductor systems. We have also determined the ground-state crystal-field excitations associated with the rare-earth ions (${\mathrm{Nd}}^{3+}$, ${\mathrm{Pr}}^{3+}$). The ${\mathrm{Nd}}^{3+}$ crystal-field levels are observed at energies of 13, 20.7, 26.4, and 93 meV in superconducting ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$. For the ${\mathrm{Pr}}_{2}$${\mathrm{CuO}}_{4}$ system, the ${\mathrm{Pr}}^{3+}$ crystal-field excitations are found at 18.6 and 87.9 meV. These peaks broaden and split when doped to form superconducting ${\mathrm{Pr}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4}$. The observed crystal-field levels in the above systems are in good agreement with those reported by other groups.