Role Of Phonons Research Articles

Isotope effect and the role of phonons in the iron-based superconductors

We studied the isotope effect of phonon in the Fe-based superconductors using a phenomenological two band model for the sign-changing $s$-wave ($\ifmmode\pm\else\textpm\fi{}s$-wave) state. Within this mean-field model, we showed that the large isotope effect is not inconsistent with the $\ifmmode\pm\else\textpm\fi{}s$-wave pairing state and its high transition temperature. In principle, a large phonon isotope coefficient $\ensuremath{\alpha}$ implies a large phonon coupling constant. However, the asymmetric density of states between two bands substantially enhances the value of $\ensuremath{\alpha}$, so that a moderate value of the phonon coupling constant $({\ensuremath{\lambda}}_{\text{ph}}\ensuremath{\approx}0.4)$ can produce a very large value of $\ensuremath{\alpha}(\ensuremath{\approx}0.4)$ as well as a high transition temperature together with an antiferromagnet-induced interaction.

Oxygen isotope effect in a high-temperature superconductor under high pressure

The role of phonons is addressed by combining the information obtained from themeasurements of Raman scattering and magnetic susceptibility in an optimally dopedhigh-temperature superconductor. We show that the high-pressure behavior of the oxygenisotope exponent can be predicted from the changes in both the phonon frequency andsuperconducting transition temperature based on a phonon-mediated d-wave BCS-likemodel. The isotope exponent is found to decrease with increasing pressure butremain small and positive within the pressure regime studied. These results pointto the important role of the electron–phonon interaction for high-temperaturesuperconductivity.

THE EFFECT OF PHONONS ON SPIN-FLUCTUATION SUPERCONDUCTIVITY

We present a study of the role of phonons in the cuprate superconductors. Assuming static spin fluctuations, we find that the self-consistent d-wave state is very sensitive to both the electron-phonon coupling strength and the phonon mode considered.

X-ray edge spectra — a sea-boson perspective

The well-studied X-ray-edge problem is revisited using the sea-boson method. This approach is contrasted with the well-known theories of Mahan, Nozières and De Dominicis (MND). The present approach does not use the sudden approximation and the holes carry a momentum label unlike in the MND theory. We focus on the case of doped semiconductors rather than metals. The problem of electrons in a partially filled conduction band and holes in the initially hole-depleted valence band is recast in the sea-boson language. The resulting hamiltonian is shown to be equivalent to the electron–phonon hamiltonian with the excitons taking on the role of electrons and intra-conduction band particle–hole excitations known as ‘conductrons’ taking on the role of phonons. It is shown that the excitonic pole in the computed absorption spectra is replaced by a branch cut with a simple radical leading to a broadening of the exicton line due to these many-body effects. A critical comparison is made with the MND theory as well as with relevant experiments.

Unified picture of the oxygen isotope effect in cuprate superconductors

High-temperature superconductivity in cuprates was discovered almost exactly 20 years ago, but a satisfactory theoretical explanation for this phenomenon is still lacking. The isotope effect has played an important role in establishing electron-phonon interaction as the dominant interaction in conventional superconductors. Here we present a unified picture of the oxygen isotope effect in cuprate superconductors based on a phonon-mediated d-wave pairing model within the Bardeen-Cooper-Schrieffer theory. We show that this model accounts for the magnitude of the isotope exponent as functions of the doping level as well as the variation between different cuprate superconductors. The isotope effect on the superconducting transition is also found to resemble the effect of pressure on the transition. These results indicate that the role of phonons should not be overlooked for explaining the superconductivity in cuprates.

Isochoric thermal conductivity of solid carbon oxide: the role of phonons and ‘diffusive’modes

The isochoric thermal conductivity of solid CO was investigated in three samplesof different densities in the interval from 35 K to the onset of melting. Inα-CO the temperature dependence of the isochoric thermal conductivity is significantlyweaker than ; in β-CO it increases slightly with temperature. A quantitative description of the experimentalresults is given within the Debye model of thermal conductivity in the approximation of thecorresponding relaxation times and which allows for the fact that the mean-free pathof phonons cannot become smaller than half the phonon wavelength. On thisconsideration the heat is transported by both phonons and ‘diffusive’ modes.

A magnetic isotope effect

The role of phonons in conventional superconductivity — first determined by isotope substitution — has been known for over half a century. But identifying the mechanism in unconventional superconductivity is a much more challenging affair.

Phonons in Hubbard ladders studied within the framework of the one-loop renormalization group

We study the effects of phonons in $N$-leg Hubbard ladders within the framework of a one-loop renormalization group. In particular, we explicitly demonstrate that the role of phonons changes {\em qualitatively} even in the simplest two-leg ladder, as compared to the single-chain system where phonons always dominate. Our numerical results suggest that in the spin-gapped phase of the two-leg ladder, the opening of the spin gap by electron-electron interaction also drives the electron-phonon interaction to strong coupling, but in a {\em subdominant} fashion. Therefore, even though the inclusion of phonons does not alter the phase, their subdominant relevance strongly renormalizes some physical properties below the energy scale of the spin gap. This might shine some light on the recent experiments showing an anomalous isotope effects in high-temperature superconductors.

The role of phonons in establishing a non‐equilibrium quasiparticle state in small gap multiple tunnelling superconducting tunnel junctions

We derive expressions for phonon escape times from a thin superconducting film. The escape time is determined by the rate of scattering conversion for phonons propagating beyond the critical cone for total internal reflection. The conversion is due to different scattering processes for the groups of Cooper pair breaking and sub-gap phonons. For pair breaking phonons the most efficient conversion mechanism is through the interaction with the condensate. For sub-gap phonons the conversion rate is much slower and for plane parallel films is due to elastic scattering at surface or interface roughness resulting in significantly slower escape times. We discuss implications of slow escape time for sub-gap phonons for the properties of the recently observed new non-equilibrium state in small gap multiple tunnelling superconducting tunnel junctions. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Role of phonons in the mechanism of high-temperature superconductivity

While phonons are generally considered to be irrelevant to the mechanism of high-temperature superconductivity, a large number of experimental results indicate otherwise. We argue that the electron–phonon coupling in strongly correlated electron systems is unconventional, and results in a strong spin–charge–phonon coupling. It could contribute significantly to the superconductivity of the cuprates through the synergetic spin–phonon mechanism.

BEDT-TTF organic superconductors: The role of phonons

We calculate the lattice phonons and the electron-phonon coupling of the organic superconductor $\ensuremath{\kappa}\ensuremath{-}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F}{)}_{2}{\mathrm{I}}_{3},$ reproducing all available experimental data connected to phonon dynamics. Low-frequency intramolecular vibrations are strongly mixed to lattice phonons (LP). Both acoustic and optical phonons are appreciably coupled to electrons through the modulation of the hopping integrals $(e$-LP coupling). By comparing the results relevant to superconducting $\ensuremath{\kappa}$- and ${\ensuremath{\beta}}^{*}\ensuremath{-}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F}{)}_{2}{\mathrm{I}}_{3},$ we show that electron-phonon coupling is fundamental to the pairing mechanism. Both e-LP and electron--molecular vibration $(e$-MV) couplings are essential to reproduce the critical temperatures. The e-LP coupling is stronger, but $e\ensuremath{-}\mathrm{MV}$ is instrumental in increasing the average phonon frequency.

Icosahedral quasicrystalAl71Pd21Mn08and itsξ′approximant: Linear expansivity, specific heat, magnetic susceptibility, electrical resistivity, and elastic constants

Linear thermal expansivity (\ensuremath{\alpha}, 1--300 K), heat capacity ${(C}_{p},$ 1--108 K), magnetic susceptibility (\ensuremath{\chi}, 1--300 K), and electrical resistivity (\ensuremath{\rho}, 1--300 K) measurements are reported for a single-grain $i\ensuremath{-}{\mathrm{Al}}_{71}{\mathrm{Pd}}_{21}{\mathrm{Mn}}_{08}$ quasicrystal and its ${\mathrm{Al}}_{72}{\mathrm{Pd}}_{25}{\mathrm{Mn}}_{03}$ approximant, and 300 K elastic constants for the quasicrystal. The approximant $\ensuremath{\alpha}$ $({\ensuremath{\alpha}}_{\mathrm{Ap}})$ and ${C}_{p}$ ${(C}_{\mathrm{pAp}})$ data show ``metallic'' behavior, while the previously reported onset of a transition to a spin-glass state ${(T}_{f}<1.8\mathrm{K})$ dominates ${\ensuremath{\alpha}}_{Q}$ and ${C}_{\mathrm{pQ}}$ below 11 K. ${C}_{\mathrm{pAp}}$ and ${C}_{\mathrm{pQ}}$ superimpose above 16 K when plotted vs $T/{\ensuremath{\Theta}}_{0}$ using the experimental ${\ensuremath{\Theta}}_{0Ap}=455(3)\mathrm{K}$ and an adjusted ${\ensuremath{\Theta}}_{0ApQ}=480(4)\mathrm{K}.$ The 300 K elastic constants extrapolated to $T=0$ give ${\ensuremath{\Theta}}_{0Q}^{\mathrm{el}}=505(1)\mathrm{K},$ suggesting that the normalization is valid only above 16 K. The lattice contribution to ${C}_{\mathrm{pAp}}$ (and, indirectly, ${C}_{\mathrm{pQ}})$ shows strong (unique) deviations from Debye-like behavior (+3% at 0.84 K for the ${C}_{\mathrm{pAp}}$ data fit). The various Gr\"uneisen parameters (\ensuremath{\Gamma}) that are calculated from these data all are positive and normal in magnitude except for a large limiting approximant lattice value, ${\ensuremath{\Gamma}}_{0Ap}^{\mathrm{lat}}=11.3$, which may be related to the large dispersion effects in ${C}_{p}.$ For the approximant, the combination of anisotropic and large resistivities, a small diamagnetic susceptibility, and a ``large'' linear (electronic) contribution to ${C}_{\mathrm{pAp}}$ $({\ensuremath{\gamma}}_{\mathrm{Ap}}=0.794\mathrm{mJ}/{\mathrm{mol}\mathrm{}\mathrm{K}}^{2})$ suggests the existence of a pseudogap in the electronic density of states. The unusually large, highly volume dependent, dispersion at low temperatures for the quasicrystal and its approximant are not consistent with inelastic neutron scattering and other data, and raise questions about the role of phonons in quasicrystals. The present 300 K resistivities can be used with a published correlation to estimate ${\ensuremath{\gamma}}_{Q}\ensuremath{\approx}0.25\mathrm{mJ}/{\mathrm{mol}\mathrm{}\mathrm{K}}^{2}.$

Acoustic Debye temperature and the role of phonons in cuprates and related superconductors

The Debye temperature of a superconducting material may provide information about the role of phonons in its superconducting mechanism. In this paper, the void-free acoustic Debye temperature, ΘD, of various cuprate high temperature superconductors, estimated using the acoustic technique, was found to be in the range of 250–500 K. The electron–phonon coupling constant was estimated from the transition temperature Tc using the standard BCS theory and also the two-dimensional van Hove scenario with related characteristic temperature. The van Hove scenario seems to explain the high temperature superconductivity in the cuprates better than the standard three-dimensional BCS model. The Debye temperature of these copper oxide-based superconductors is compared with that of the new binary intermetallic MgB2 superconductor which has been reported to be a phonon-mediated superconductor.

The role of phonons in the thermodynamics of the martensitic transformation in NiTi

Abstract Measurements of neutron inelastic scattering, thermal expansion and low-temperature heat capacity were used to study the phonon entropy of the martensite-to-austenite transformation in NiTi, which is found to be (0.5 ± 0.05) k B atom−1. The inelastic scattering spectra were corrected for the differing scattering amplitudes of Ni and Ti through a lattice dynamics simulation. The phonon density-of-states (DOS) curves so obtained account for all the transformation entropy measured by calorimetry. From simulations and the measured DOS, the vibrational entropy of austenite was found to be larger than that of martensite because the transverse acoustic (TA2) and longitudinal acoustic modes of austenite are softer than those of martensite. Simulations suggest that this originates with a large and negative first-nearest-neighbour transverse force constant. This φT lnn may also be responsible for the soft modes involved in the mechanism of the martensitic transformation.

The role of phonons in the thermodynamics of the martensitic transformation in NiTi

The role of phonons in the thermodynamics of the martensitic transformation in NiTi

Thermal Transport in BPSCCO System Between 20 and 170 K

Thermal conductivity of superconducting (Bi,Pb)2223 pellet in the temperature range 20–170 K is reported. Electronic contribution to thermal conductivity in the normal state is estimated to be ∼25%. Considering both phonon and phonon + electron approach, we attempted to examine the observed nature of the temperature dependence of thermal conductivity. Our analysis strongly supports the role of phonons as well as electrons in the origin of the thermal conductivity peak in the superconducting state. Some of the microscopic quantities evaluated from the best-fit parameters obtained from phonon + electron approach give reasonable values.

Thermal conductivity of LaB 6: the role of phonons

The thermal conductivity of a high-conductivity metallic LaB 6 single crystal was measured in the temperature range between 0.7 and 30 K. The striking point of the observed temperature dependence is the non-linear behaviour of the thermal conductivity at lowest temperatures, where a linear dependence is expected. Additional measurements of electrical conductivity and in a magnetic field show that the non-linearity originates from a scattering mechanism which leads to the decrease of the electronic component of the thermal conductivity. Scattering processes of conduction electrons by phonons and by magnetic impurities are discussed.

Lattice dynamics, phase transitions and hydrogen effective charges of betaine phosphite: a comparison with betaine phosphate and their deuterated analogues

The temperature dependence of complete infrared reflection spectra of a betaine phosphite single crystal is reported for the polarizations parallel to a and b axes in the wavenumber range from 10 to . They are compared with previous data that were limited to the range . They are also compared with reflectivity spectra of betaine phosphate, betaine arsenate, deuterated betaine phosphite single crystals and betaine compressed powder. These comparisons allow a mode assignment. Spectra were fitted with the factorized form of the dielectric function. The role of phonons in the behaviour of the dielectric constant in the vicinity of the ferroelectric (FE)-paraelectric (PE) phase transition is discussed. The decrease of effective charges along the FE axis below the FE-PE phase transition is assigned to an increase of oxygen-hydrogen electronic orbital hybridization related to the change of average bond-length.

Dissipation of core-hole momentum by phonons in soft-x-ray radiation processes from valence band to core level of wide-gap insulators

The role of phonons in the soft-x-ray radiation process from a valence band to a core level in an insulator is studied theoretically. A three-band system composed of a dispersionless core band, a conduction band, and a valence band, with wide energy gaps between them, is taken as a typical example. Phonons with a finite dispersion are assumed to couple weakly only with a hole in the core band (core hole). Using this model, we calculate the resonant second-order optical process composed of an excitation of an electron from the core band to the conduction band by an incident x ray, and a subsequent transition from the valence band to the core band by radiating another x ray. Without the phonons, the momentum of the core hole is expected to be well defined by the resonance condition of the incident x ray. However, this momentum is dissipated by the phonons. If the radiation occurs completely after this dissipation, we obtain a so-called luminescence, which is independent of the incident x ray. In this case, the spectral shape fully reflects the density of states (DOS) of the valence band. However, if the radiation occurs long before this dissipation effect, we obtain a resonant Raman scattering that depends on the incident x ray. The spectral shape of this Raman scattering has a sharp peak, quite different from the DOS. The relative intensity between these two components is determined by the phonon dispersion, the lifetime of the core hole, and the core-hole\char21{}phonon coupling constant. From this theoretical framework, we have concluded that there are various cases, i.e., Raman-dominant cases and luminescence-dominant cases, as well as intermediate cases, in good agreement with various experimental observations. The B $1s\ensuremath{\leftrightarrow}2p$ transitions of cubic BN are concluded to correspond to a luminescence-dominant case.

Separation dynamics of the resonant soft X-ray radiation into luminescence and coherent Raman scattering in wide gap insulators

Abstract We study theoretically the roles of phonons in spectral shapes of soft X-ray radiation from a valence band to a core level in an insulator, and clarify how this radiation separates into luminescence and Raman scattering. We take a three-band system composed of a dispersionless core band, a conduction band, and a valence band, with wide energy gaps between them. Phonons with finite dispersion are assumed to couple weakly with a hole in the core band (core hole). Using this model, we calculate the resonant second order optical process composed of an excitation of an electron from the core band to the conduction band by an incident X-ray, and subsequent transition from the valence band to the core band by radiating another X-ray. Without phonons, the momentum of the core hole is expected to be well defined by the resonance condition of the incident X-ray. However, this momentum is dissipated by the phonons. If the radiation occurs after this dissipation, we get so-called luminescence which is independent of the incident X-ray. In this case, the spectral shape fully reflects the density of states (DOS) of the valence band. If the radiation occurs before the dissipation, we get resonant Raman scattering which depends on the incident X-ray. The spectral shape of this Raman scattering has a sharp peak, being quite different from the DOS. The relative intensity between these two components is determined by phonon dispersion, the life time of the core hole, and the core-hole–phonon coupling constant. From this theoretical framework, we have concluded that various cases exist—Raman dominant, luminescence dominant and intermediate—which is in good agreement with observations in recent experiments.