Effect of soft phonons on superconductivity: A re-evaluation and a positive case for Nb3Sn

The effect of low frequency phonons on superconductivity (which was described as detrimental in a previous paper) is re-assessed following the work of Bergmann and Rainer. An anomalously large positive contribution to T_c is quantitatively evaluated for soft phonons in Nb₃Sn using neutron data of Axe and Shirane. Low frequency phonons appear helpful in raising T_c, but the coupling to high frequency phonons is of greater ultimate importance.     

Dynamical properties of the Peierls-Fröhlich state on the many-phonon-coupling model

The amplitude and phase phonons and the frequency dependent conductivity below the mean-field Peierls-Fröhlich transition temperature T_c, and the Kohn anomaly and fluctuation induced charge-density-wave conductivity above T_c, are discussed on the basis of the many-phonon-coupling model recently introduced by Rice, Duke and Lipari. For dominant intramolecular phonon coupling an isotope effect in T_c is related to the isotopic shift in the small polaron binding energy.     

A simple theory of 40 K superconductivity in MgB2: first-principles calculations of Tc, its dependence on boron mass and pressure

We have studied the superconducting properties of MgB₂ from first-principles under isotropic, uniaxial, and biaxial compressions. We find that the in-plane boron phonons near the zone-center are very anharmonic and strongly coupled to the planar B σ bands near the Fermi level. This mode is found to be the key to quantitatively explain the observed high T_c, the total isotope effect and the pressure dependence of T_c. We propose that a stringent test on the hole and phonon based theories of the superconductivity in MgB₂ would be a measurement of the biaxial ab-compression dependence of T_c.     

Calculation of Tc and the ratio 2Δ(0)/kBTc of MgB2 within a two-band model of superconductivity

Superconductivity in the MgB₂ superconductor is described within the framework of a two-band Eliashberg formalism. Different gaps are assumed to open on the different parts of the Fermi surface of this compound. Separation of the order parameter (OP) into two components is achieved by taking the Fourier transform of the OP using the momentum states of the σ- and π-bands of MgB₂. Expressions for the T_c and the ratio 2Δ_σ(0)/k_BT_c for this superconductor are obtained. Numerical values for these two properties are obtained for a range of values of the cut-off frequency of the phonons responsible for the superconductivity and for a range of values of the ratio between the two energy gaps. This was done for various values of the normalized partial densities of states on the σ-sheet of the Fermi surface.     

Quantum theory of nonresonant electromagnetic and ultrasonic absorption in glasses

We develop quantum theory of nonresonant ultrasonic and electromagnetic absorption in glasses at low temperatures. In the quantum region where ?ω?kT the nonresonant absorption coefficients are proportional to ω³ which seems to be in agreement with the existing experimental data.The existence of characteristic temperature T_c (or characteristic energy E_c = kT_c) of the order of 10 + 20 K is established. At higher interlevel spacing E the concept of two-level systems in their conventional form is not applicable because of their strong coupling to the phonons. Neither the perturbation theory is applicable for calculation of absorption in the frequency interval ?ω?_c or at temperature interval T?T_c = E_c/k.     

Spin-phonon coupling in Van Vleck paramagnets

We investigate the effect of phonons on the phase transition of exchange induced Van Vleck paramagnets. We approximate the full crystalline-field level scheme of the magnetic ions by two singlet levels. It is shown that the coupling of the magnetic excitations to the phonons reduces appreciably the temperature dependence of the former near the ordering temperatureT _c . Special attention is focussed on Pr₃Tl and it is discussed to what extent the present mechanism might explain recent inelastic neutron-scattering data.     

Superconductors containing impurities with crystal-field split energy levels

We investigate theoretically the problem of a superconducting matrix containing paramagnetic rare earth impurities with crystal-field split energy levels. There are two competing mechanisms which change the superconducting transition temperatureT _c. One is inelastic charge scattering of conduction electrons from the aspherical part of the 4f charge distribution, which leads to an increase inT _c similar to that of optical phonons. The other and often predominant mechanism comes from the exchange interaction, which depressesT _c and can be very effective even among non-magnetic levels via off-diagonal matrix elements. Crystalline fields serve to alter the effectiveness of the two kinds of scattering depending upon the symmetry character of the low-lying levels, and in favorable cases one may study separately the effects of the two types of scattering by adding different impurities to a given host. We find that crystal-field levels at energies quite high compared tok _B·T_c can still have an important effect onT _c. It is shown that the crystalline-field splitting should be directly observable as structure in the tunneling characteristics.     

Influence of magnetoelastic effects on lattice vibrations in the ferromagnetic invar alloy Fe0.65Ni0.35

Neutron scattering measurements have been made of phonons in a Fe₆₅Ni₃₅ crystal at several temperatures. Marked softening of the [110] acoustic shear modes and a dip in the dispersion relation are found at low temperatures. Above the magnetic ordering temperature T_c, the frequency shift is removed completely, which suggests phonon perturbation by magnetoelastic coupling.     

Optical phonons in CuAlS2

The optical phonons at k=0 of CuAlS₂ have been investigated by Raman scattering, infrared reflectivity and absorption measurements from 50 to 1000 cm^-1 at T=300 K. Eleven of the thirteen expected optically active phonons have been observed and identified with respect to their symmetry types. The phonon frequencies appear in a range from 498 to 76 cm^-1 with predominant polar modes at 445 and 266 cm^-1. The dielectric dispersion for E ⊥ c and E ∥ c has been determined by Kramers-Kronig integrations.     

Interpretation of temperature dependence of the in-plane electrical resistivity in YBa2Cu4O8: Electron–phonon approach

In this paper, we undertake a quantitative analysis of observed temperature-dependent in-plane normal state electrical resistivity of single crystal YBa₂Cu₄O₈. The analysis is within the framework of classical electron–phonon i.e., Bloch-Gruneisen model of resistivity. It is based on the inherent acoustic (low frequency) phonons (ω_ac) as well as high frequency optical phonons (ω_op), the contributions to the phonon resistivity were first estimated. The optical phonons of the oxygen breathing mode yields a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons. Estimated contribution to in-plane electrical resistivity by considering both phonons i.e., ω_ac and ω_op, along with the zero-limited resistivity, when subtracted from single crystal data infers a quadratic temperature dependence over most of the temperature range [80 ? T ? 300]. Quadratic temperature dependence of ρ_diff. = [ρ_exp − {ρ₀ + ρ_e−ph (=ρ_ac + ρ_op)}] is understood in terms of electron–electron inelastic scattering. The relevant energy gap expressions within the Nambu-Eliashberg approach are solved imposing experimental constraints on their solution (critical temperature T_c). It is found that the indirect-exchange formalism provides a unique set of electronic parameters [electron–phonon (λ_ph), electron-charge fluctuations (λ_pl), electron–electron (μ) and Coulomb screening parameter (μ^*)] which, in particular, reproduce the reported value of T_c.     

Phonon properties of vanadium-substituted lanthanum niobate derived from heat-capacity measurements

We have measured the 3–400 K heat capacity of vanadium-substituted lanthanum niobate LaNb_1−x,V_xO₄ (0 < x⩽0.35) to determine how the relevant averaged properties, or moments, of the phonon spectrum 〈ωⁿ〉 relate to certain other lattice properties of these compounds, most noteworthy of which is a large decrease in the paraelastic-ferroelastic transformation temperature T_c with x. The pertinent moments, represented by their corresponding Debye temperatures, are θ_D(−3) corresponding to the lowest frequency modes; θ_D(0) associated with the geometric mean frequency of the entire spectrum; and θ_D (2) identified with the high-frequency modes that are sampled at the upper end of the temperature range. We find that θ_D(−3) falls rapidly with x and this effect can be correlated with the comparably sharp drop in T_c. There is little effect of composition on θ_D(0) and θ_D (2) because the phonons that govern soft-mode behavior represent only a small fraction of the mode population. In the vicinity of T_c the temperature dependences of the free energies of the tetragonal and monoclinic phases are so similar that the discontinuity in C_p is immeasurably small.     

Critical changes in vibrational modes in a magnetic debye crystal with a magnon-phonon coupling

Using the Green function technique we calculate the mean square of the vibrational amplitude of an ion (or equivalently the Debye Waller factor W, or the Mössbauer recoil free fraction ?) in a magnetic Debye crystal near the magnetic phase transition temperature T_c. We find that the magnon-phonon coupling which leads to the phonon spectrum broadening and frequency shift leads to sharp changes in W near T_c. The frequency shift leads to an increase in W, the broadening leads to a decrease in W. These results can explain the anisotropic critical changes in W near T_c observed recently in the magnetostrictive materials RFe₂ and RCo₂ (R = rare earth). In addition we calculate the expected changes in the second order Doppler shift near T_c. We find that when T approaches T_c from above a positive discontinuity and decrease in absolute value of slope of the thermal shift should occur.     

AC susceptibility and temperature modulation studies of gadolinium near the Curie point

Measurements of the ac susceptibility and temperature modulation studies of the ac and dc magnetic properties of polycrystalline gadolinium in the vicinity of the Curie point T_c are reported. Field-independent exchange-enhanced paramagnetism was observed above T_c. Below T_c the initial field-independent susceptibility was observed for applied fields < 8 A/m rms and exhibited a frequency dependence characteristic of a magnetic after-effect. Within about 3 K of T_c this susceptibility is strongly influenced by domain nucleation and a temperature dependent magnetic relaxation time was observed.     

BCS theory of driven superconductivity

We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature T_c, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of T_c. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify T_c. Our results hold universally for the large class of normal BCS superconductors.     

Soft modes below the incommensurate transition in K2SeO4

A coordinated series of Raman and Brillouin scattering measurements were carried out in K₂SeO₄ with emphasis on temperatures near and below the incommensurate structural phase transition (T_i=129 K). Below the lock-in phase transition (T_c=99 K) Raman scattering from both the amplitude mode and the phase mode analog was observed. However, only the amplitude mode could be followed into the incommensurate phase. Details of the amplitude mode frequency and damping are reported for temperatures considerably closer to T_i than previously possible. Our results do not confirm the diverging linewidth extrapolated from earlier Raman work. We also report here the first Brillouin scattering results in K₂SeO₄. Although substancial interaction effects between the acoustic phonons and the soft amplitude mode are evident near T_i, the coupled mode lineshapes can be well described without the introduction of a relaxing self energy for the soft mode. Finally, limits on the characteristics of the phason are drawn from our failure to observe it directly in the incommensurate phase.     

Low-frequency electrical resistance of iron,cobalt, and nickel in the vicinity of their Curie temperatures

Alternating-current electrical resistance measurements between 17 Hz and 100 kHz were made on high purity Fe, Co, and Ni wires in the vicinity of their Curie temperatures (T _c). The electrical resistance was independent of frequency for temperatures (T) aboveT _c. As the temperature was lowered, however, there was an abrupt jump in the electrical resistance atT _c followed by a gradual decrease toward its dc value. The magnitude of the electrical resistance jump atT _c increased as the square root of the frequency. The enhancement of the electrical resistance forT≦T _c is produced by an abrupt decrease of the skin depth atT _c which, in turn, is due to the sudden increase in the initial magnetic permeability atT _c. Measurements of the ac electrical resistance in the vicinity of the Curie temperature of certain ferromagnetic metals can be utilized to 1) accurately determine the Curie temperature using frequencies as low as 17 Hz, and 2) quantitatively determine the initial magnetic permeability as a function of temperature and heat treatment.     

Functional derivative of Tc with α2(ω)F(ω) for an anisotropic superconductor

The functional derivative δT_c/δα²(ω)F(ω) of the critical temperature (T_c) with the electron-phonon spectral density (α²(ω)F(ω)) gives information on the effectiveness of various phonon modes in enhancing T_c. For an anisotropic superconductor, it is found that δT_c/δα²(ω)F(ω) goes negative at some small but finite phonon energy. This contrasts with the isotropic case for which it is well known that the functional derivative is positive everywhere. Thus, very low energy phonons reduce T_c in an anisotropic superconductor which is similar to the known effects of static impurities that wash out anisotropy and hence reduce T_c.     

Softening of acoustic and optical modes in ferroelastic phase in Hg2Br2

The softening of an acoustic and an optical phonons in Hg₂Br₂ has been investigated by means of the light scattering technique.It has been observed that the cube of the frequency of the soft optical phonon varies proportionally with the temperature below T_c.An expression for the relation of the elastic constant C₆₆ to the temperature has been derived from the phenomenological thermodynamic potential function. The observed temperature dependence of the elastic constant and the optical phonon frequency is described when we assume that the order parameter Q varies as $\text{Q ∝ [T ? T}{}_0\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>6</mtext>}}$.     

Proton spin-lattice relaxation study of the phase transition in TlH2AsO4

Measurements of the temperature and frequency dependence of the proton laboratory and dipolar frame spin-lattice relaxation rates in powdered TlH₂AsO₄ demonstrate that the ⁷⁵As quadrupole resonance frequency changes from v_Q ≈ 38 MHz at T ?T_c to v_Q 〈 10 MHz at T 〉 T_c. The structural phase transition at T_c = 251 K is thus connected with a disordering of the protons in the O–H … O bonds surrounding the AsO₄ groups.     

Specific features of the central peak in the Raman spectra of a lithium niobate crystal

The low-frequency Raman scattering (RS) spectra of a LiNbO₃ ferroelectric crystal are studied in the temperature range 300–1423 K. The central peak characterizing the relaxation susceptibility of the crystal lattice is observed over the entire temperature range studied, including at temperatures much lower than the Curie temperature (T _c = 1470 K). Far from T _c, the characteristics of the central peak are shown to be unlike those expected in the framework of the standard approaches. (i) The central-peak width γ_R increases as the temperature increases to T ～ 1300 K, and the critical slowing down (γ_R ∝ T _c ? T) occurs only above this temperature. (ii) A central peak arises in the RS geometry where the scattering by “nonferroelectric” E phonons is allowed. The experimental results are interpreted with allowance for relaxation dynamics in local regions of the crystal lattice.