Single-phonon Processes Research Articles

A review of electron–phonon coupling seen in the high‐Tc superconductors by angle‐resolved photoemission studies (ARPES)

AbstractWe review recent experimental results and phenomenological models of the electron–phonon interaction in high‐Tc superconductors as seen by angle‐resolved photoemission (ARPES). We focus on the relatively higher doped systems for which the data is reminiscent of a single phonon process and highlight evidence for the relevance of several specific phonon modes to these materials. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phonon processes and the spin–lattice relaxation of two inequivalent Cs sites in Cs 2CuCl 4 and Cs 2CoCl 4 single crystals

The nuclear spin–lattice relaxation rates for 133Cs nucleus in Cs 2CuCl 4 and Cs 2CoCl 4 single crystals grown using the slow evaporation method were measured as a function of temperature. Two groups of 133Cs resonance lines for both crystals are obtained. They are due to the two crystallographically inequivalent types of 133Cs nuclei, Cs(I) and Cs(II). The inversion recovery trace of the central line of 133Cs was represented by a linear combination of four exponential functions. Thus, the relaxation behaviors of Cs(I) and Cs(II) in Cs 2CuCl 4 and Cs 2CoCl 4 single crystals are best explained by the T 1 − 1 = γ T + δ , and have spin–lattice relaxation rates in the slow region. We concluded that the relaxation behaviors of Cs(I) and Cs(II) in these crystals can be explained by a direct single-phonon process. The spin–lattice relaxation behaviors were quite similar for both crystals and were dominated by the phonon mechanism. These facts indicate that the Cs 2CuCl 4 and Cs 2CoCl 4 single crystals have the same A 2BX 4 structure, and their dynamic properties, such as their nucleus phonon interactions, are similar.

Phase transition and ferroelastic property studied by using the 133Cs nuclear magnetic resonance in a CsHSO 4 single crystal

The 133Cs spin–lattice relaxation time in a CsHSO 4 single crystal was measured in the temperature range from 300 to 450 K. The changes in the 133Cs spin–lattice relaxation rate near T c1 (=333 K) and T c2 (=415 K) correspond to phase transitions in the crystal. The small change in the spin–lattice relaxation time across the phase transition from II to III is due to the fact that during the phase transition, the crystal lattice does not change very much; thus, this transition is a second-order phase transition. The abrupt change of T 1 around T c2 (II–I phase transition) is due to a structural phase transition from the monoclinic to the tetragonal phase; this transition is a first-order transition. The temperature dependences of the relaxation rates in phases I, II, and III are indicative of a single-phonon process and can be represented by T 1 −1= A+ BT. In addition, from the stress–strain hysteresis loop and the 133Cs nuclear magnetic resonance, we know that the CsHSO 4 crystal has ferroelastic characteristics in phases II and III.

Local structure of LiB[sub 3]O[sub 5] single crystal from [sup 7]Li nuclear magnetic resonance

The local structure of LiB3O5 single crystal was investigated with 7Li (I=3/2) nuclear magnetic resonance measurements. We observed four different spectra, which could be divided into two groups corresponding to two kinds of lithium atoms, LiA and LiB, lying at crystallographically equivalent sites and magnetically inequivalent sites. From these results, the quadrupole coupling constants and the asymmetry parameters were determined at room temperature and are e2qQ/h=143±1 kHz and η=0.6±0.1 for 7Li. The directions of the principal axes of the electric field gradient tensors were also determined. The spectra for the two groups have the same principal values of the electric field gradient tensor, but different orientations, and originate from magnetically inequivalent sites. Also, the 7Li spin-lattice relaxation rate was measured, and the measured relaxation rate was found to be proportional to the temperature. The temperature-dependent single phonon process is considered to be more effective than the Raman ...

Paramagnetic to antiferromagnetic transition in AMnCl3 (A=Rb and Cs) single crystals as observed by Rb87 and Cs133 spin-lattice relaxation

RbMnCl 3 and CsMnCl3 order antiferromagnetically at Néel temperatures TN=94.6 K and TN=67 K, respectively. The Rb87 and Cs133 spin-lattice relaxation times in these crystals were measured in the temperature range of 270–60 K. The large change in the relaxation rate that is observed near TN indicates that the magnetic phase in these crystals undergoes a paramagnetic to antiferromagnetic transition. In both crystals, the temperature dependencies of the relaxation rates for T<TN and T>TN are in accordance with a single-phonon process.

Effect of temperature on noncontact atomic force microscopy images

The purpose of this paper is to carry out a theoretical analysis of the effect of temperature on atomic force microscopy images using a model of a single-atom tip on the substrate. Assuming that the effect of temperature arises from the change in phonon distribution of the substrate, we first formulate the force acting on the tip in terms of the Debye–Waller factor (DWF) within a single phonon process. Next we calculate the force acting on the tip from substrate lattice with several current types of the potential for interaction between the tip and substrate. The types of potential are: (1) Gaussian; (2) exponential; (3) Morse; (4) Lennard–Jones. The general results are: (1) the effects of temperature increase with increasing temperature; (2) at low temperatures, the effects of zero-point motion play an important role.

Phase Transition Mechanism Studied by1H and87Rb Spin-Lattice Relaxation Time in a RbHSO4Single Crystal

The 1 H and 87 Rb NMR spin-lattice relaxation times for a RbHSO 4 single crystal were measured in the temperature range of 300–170 K for study of the paraelectric (I) to ferroelectric (II) phase transition near T c =264 K. Proton spin-lattice relaxation time on the RbHSO 4 yielded a minimum, attributed to the effect of molecular motion. The activation energy for the reorientational motion in phase I was determined to be 16.54 kJ/mol, whereas, for the molecular motion in the phase II it was 25.53 kJ/mol. The change of the 87 Rb spin-lattice relaxation rate near 264 K corresponds to a phase transition in the crystal. The temperature dependences of the relaxation rate for 87 Rb in this crystal were in accordance with the single phonon process dominated by the phonon mechanism. The activation energies in phases I and II were obtained to be 2.66 kJ/mol and 17.25 kJ/mol, respectively. From 1 H and 87 Rb NMR investigations, the phase transition does play an important role by Rb nucleus, although the activation e...

Quantum effect of solvent on molecular vibrational energy relaxation of solute based upon path integral influence functional theory

Path integral influence functional theory has been applied to the investigation of the quantum effect of the solvent on vibrational relaxation of the solute. A classical bath approximation was attained by taking the ℏ→0 limit with respect to the solvent degrees of freedom. A comparison of the calculated relaxation time for the quantum solvent with that for the classical one showed that the quantum effect is very large and, at the same time, it depends much upon the process, i.e., single-phonon process, two-phonon process, or three-phonon process. This indicates that the so-called quantum correction does not work since the relaxation is usually a mixture of these multiphonon processes. A numerical example for CN− in water also demonstrates that, although the classical approximation for the solvent significantly overestimates the relaxation time, it presents reliable energy transfer pathways or relaxation mechanism.

Absorption of electromagnetic field of the millimeter-wave band in perfect dielectric crystals

The dielectric losses in high-quality crystals of sapphire, ruby, fluorite, and quartz are measured at a frequency of 36 GHz in the temperature range 4.2–300 K by the spherical dielectric resonator method. The absorption coefficient of the electromagnetic field per unit wavelength Γ in the crystals is found to agree both in order of magnitude and in its temperature dependence with the Gurevich theory, which treats the absorption as being the result of an electrophonon interaction of the field with acoustical phonons as a result of the anharmonicity of the crystal lattice. It is found that the crystals studied have extremely low absorption in the millimeter-wave band even at moderately low temperatures (e.g., for sapphire Γ≈10−8 at T≈40 K). Measurements are made of the residual absorption of the electromagnetic field at low temperatures, which is due to a single-phonon process of field absorption at defects of the crystal structure. It is found that the temperature dependence of the absorption of an electromagnetic field in a crystal is correlated with that for the absorption of hypersound.

R-Line Thermal Shift and Thermal Broadenings of R, R′ and B Lines for Ruby**The project partly supported by National Natural Science Foundation of China, Grant No. 19744001

The unified theoretical calculation of thermal shifts (TS) of R1 and R2 lines and thermal broadenings (TB) of R, R′ and B lines for ruby was carried out for the first time. The calculated results are in very good agreement with a great number of experimental data. Especially, by using quantum theory and taking into account all the admixtures of wavefunctions within d3 electronic configuration, all the ΓM in electron-phonon interaction (EPI), the electronic energy spectrum and lattice-vibration Spectrum, the very important contributions to TS and TB from single-phonon direct process were theoretically calculated in detail. The microscopic essentials of various contributions are revealed, and the mistakes in previous work are remedied.

Temperature dependence of the spin-lattice relaxation time in local triplet-excited states of a doped C60 fullerene crystal

The temperature dependence of the spin-lattice relaxation time of triplet-excited impurity centers of a C60 fullerene crystal is investigated within the framework of the spin-phonon coupling mechanism which arises as a result of the admixture of rotational to translational motions of the molecules due to acoustic lattice vibrations. General expressions are obtained for the transition probabilities for the direct single-phonon and Raman two-phonon processes. The method of atom-atom potentials is used to carry out a concrete calculation of the spin-lattice relaxation time for an isotopic impurity in a C60 crystal.

Acoustophosphorescence double resonance in impurity C70 fullerene crystal

An acoustophosphorescent double resonance is investigated in terms of a low-temperature spin-phonon interaction mechanism determined by a coupling of translational and rotational molecular motions. Numerical values are obtained for the transition times of direct single-phonon processes in high, as well as zero, magnetic fields for a triplet excited isotopic impurity in crystalline C70 fullerene. The dependence of the transition rate on the propagation direction of the acoustic wave is analyzed in detail.

Mechanism of charge transport in polypyrrole, poly(N-methyl pyrrole) and their copolymers

The temperature dependence of the dc conductivity of electrochemically polymerized films of polypyrrole, poly(N-methyl pyrrole) and their copolymers, poly(N-methyl pyrrole-pyrrole), having different percentage of BF−4 ions has been investigated in the temperature range 77–350 K. The observed behavior could be explained in terms of Mott’s variable range hopping model involving a single phonon process. The estimated values of polaron radius yield the realistic values of density of states at the Fermi level which are in good agreement with the values reported earlier for other polyconjugated systems.

Quantum and semiclassical calculations of gas-surface energy transfer and sticking

In this paper we review some recent models for gas-surface scattering in which the gas particle can interact and exchange energy with the vibrational modes of the solid. Probabilities for energy transfer and sticking are computed for He, Ne, and Ar incident on a Cu surface, for a number of particle energies and surface temperatures. All of the models are applied to the same set of systems, and the results are compared. In all cases the lattice vibrations are treated quantum mechanically. A close-coupling approach which includes only single-phonon processes is presented. It is accurate for He and H 2, and Ne at low energies and temperatures. Two common approaches to the problem based on an uncorrelated particle-bath state, the forced oscillator and time dependent Hartree method, are discussed. They are compared with each other and with the close-coupling calculation in the one-phonon limit. Mean field approaches which attempt to improve upon these zero-correlation models are presented and compared with the above models. A one-phonon multiconfiguration self consistent field model is also presented. The nature of atom-surface sticking is examined over a wide range of energies, temperatures, and masses.

Nuclear spin conversion of methane in pure and rare-gas mixed crystals

Spin species conversion has been observed by means of neutron scattering. Methane, matrixisolated in rare-gas crystals has been investigated by measuring the time dependence of the detailed balance factor of inelastic neutron spectra. The temperature dependence of conversion rates in the interval between 2 and 5 K turns out to be stronger than predicted by a single phonon process. In general, conversion times are of the order of hours in this temperature region. The influence of the matrix is well described by a coupled phonon density of states. Crystals of pure and krypton doped methane have been examined by measuring the time dependence of the total neutron scattering cross section. For pure methane, the temperature dependence of the conversion rates shows two regimes for both free rotator and ordered molecules. Below 5 K, the behavior is described by a single phonon process and above by an Arrhenius law. Rates are enhanced by krypton dotation, which is explained by changed level spacings due to orientational disorder.

Impurity-phonon interaction effect on the phonon density of states in MgO: V 2+

The effective phonon density of states of MgO: V 2+ is obtained from the emission vibronic structure of the V 2+ impurity ion under the assumption that the vibronic transition is mainly a single-phonon process. The validity for doing so is supported by the consistent fitting of the temperature dependences of the width and the shift of the zero-phonon line of MgO: V 2+ and the specific heat of pure MgO. The phonon softening and phonon stiffening is found by comparing the effective phonon density of states to the theoretically calculated one of the pure MgO lattice.

Low-temperature resistivity from electron-dual-phonon processes for alkali metals.

A calculation of the contribution from electron--dual-phonon scattering to the low-temperature electrical resistivity for alkali metals is carried out. It is found that the low-temperature resistivity from umklapp electron--dual-phonon scattering processes follows nearly the same exponential rule ${\mathrm{BT}}^{4}$ exp(-FTHETA'/T) as resulted from umklapp electron--single-phonon scattering, where FTHETA' is dependent on the minimum available wave vector of phonons and the coefficient B is proportional to (m/M${)}^{2}$, the square of the mass ratio of electron to ion. However, the constant FTHETA' we find from dual-phonon processes is only half of that from single-phonon processes. It is expected that this scattering mechanism has a significant effect on the low-temperature resistivity of some light alkali metals with high Debye temperature at very low temperatures. Our calculation shows that the resistivity of the lithium that resulted from dual-phonon processes will be larger than the one from single-phonon processes when the temperature is below 4 K.

Hopping transport of localized pi electrons in amorphous carbon films.

The temperature dependence of the dc and ac conductivities has been studied in sputtered arnorphous carbon films. The dc conductivity is proportional to T with n =15— 17 below room temperature. The mechanism is discussed in terms of the mobility-edge conduction, variable-range hopping, and small-polaron hopping. Quantitatively, these models could not interpret the observed behaviors. Instead, the multiphonon tunneling of localized electrons with weak electron-lattice coupling is suggested to be the dominant transport mechanism. This may be attributed to the ~-bonded nature of sputtered amorphous carbon. The ac conductivity is strongly correlated to the dc conductivity, which has never been explained by the current theories based on the pair approximation. Alternatively, the continuous-time random-walk approximation is shown to be a useful approach. I. INTRODUCTION It is believed that amorphous carbon (a-C) prepared by evaporation or sputtering is predominantly sp bonded with an optical gap of 0.4— 0.7 eV. ' At a carbon sp site, there are three strong o. bonds and one weak m bond lying normal to the o. bonding plane. The ~ states will form both the valence- and conduction-band states. ' The sp sites must be clustered together in aromatic units. The large size of such clusters could produce localized states near the Fermi level E+. The eFect of disorder in a ~-electron system is therefore of particular interest. The present authors have shown that the temperature dependence of the dc conductivity in sputtered a-C is empirically described by o. d, =o.oT, with n =15— 17, which may suggest that the nonpolaronic multiphonon tunneling of localized m electrons (weak coupling with lattice) dominates charge transport. Measurement of ac conductivity could provide direct information about the hopping rate of localized electrons. In the present study, the temperature dependences of both dc and ac conductivities are reported. Possible transport mechanisms, mobility-edge conduction, variable-range hopping (single-phonon process), and multiphonon hopping with strongly (small-polaron) and weakly coupled states, are discussed. It is suggested that the conventional mobility-edge conduction or small-polaron conduction could not explain the overall features of transport in a-C. It is also found that the ac conductivity is strongly correlated with the dc conductivity. This feature, which has never been explained by the current theory based on the pair approximation, is interpreted well in terms of the continuous-time random-walk (CTRW) approximation.

Comparison of inelastic scattering of Ne and He on Ag(111)

Time-of-flight measurements of He beams and of high resolution Ne beams on an Ag(111) surface along the 〈11 2 〉 direction are reported. In order to compare the scattering probabilities of He and Ne, the same crystal and similar experimental conditions like surface temperature and angular resolution are used. Both for Ne and He beams with kinetic energies of ∼ 20 meV single phonon processes dominate at least for small momentum transfers. The features in the time-of-flight spectra can be attributed to the Rayleigh mode, the quasi-longitudinal surface resonance and, in the case of Ne, to scattering processes with zero momentum transfer. The relative intensities of these modes are discussed in terms of the lateral momentum transfer. For Ne the intensity of inelastic scattering processes normalized to the specular intensity is larger than for He.

Simple approximation to thermal attenuation in low energy atom-surface scattering: single phonon processes

Simple approximation to thermal attenuation in low energy atom-surface scattering: single phonon processes