Electron-phonon Coupling Constant Lambda Research Articles

Optical properties of the iron arsenic superconductorBaFe1.85Co0.15As2

The transport and complex optical properties of the electron-doped iron-arsenic superconductor BaFe1.85Co0.15As2 with Tc = 25 K have been examined in the Fe-As planes above and below Tc. A Bloch-Gruneisen analysis of the resistivity yields a weak electron-phonon coupling constant lambda_ph ~ 0.2. The low-frequency optical response in the normal state appears to be dominated by the electron pocket and may be described by a weakly-interacting Fermi liquid with a Drude plasma frequency of omega_p,D ~ 7840 cm-1 (~ 0.972 eV) and scattering rate 1/tau_D ~ 125 cm-1 (~ 15 meV) just above Tc. The frequency-dependent scattering rate 1/tau(omega) has kinks at ~ 12 and 55 meV that appear to be related to bosonic excitations. Below Tc the majority of the superconducting plasma frequency originates from the electron pocket and is estimated to be omega_p,S ~ 5200 cm-1 (lambda0 ~ 3000 Angstroms) for T << Tc, indicating that less than half the free carriers in the normal state have collapsed into the condensate, suggesting that this material is not in the clean limit. Supporting this finding is the observation that this material falls close to the universal scaling line for a BCS dirty-limit superconductor in the weak-coupling limit. There are two energy scales for the superconductivity in the optical conductivity and photo-induced reflectivity at Delta1 ~ 3.1 +/- 0.2 meV and Delta2 ~ 7.4 +/- 0.3 meV. This corresponds to either the gaping of the electron and hole pockets, respectively, or an anisotropic s-wave gap on the electron pocket; both views are consistent with the s+/- model.

IsLaFeAsO1−xFxan Electron-Phonon Superconductor?

In this Letter, we calculate the electron-phonon coupling of the newly discovered superconductor LaFeAsO1-xFx using linear response. For pure LaFeAsO, the calculated electron-phonon coupling constant lambda=0.21 and logarithmic-averaged frequency omegaln=206 K give a maximum Tc of 0.8 K, using the standard Migdal-Eliashberg theory. For the F-doped compounds, we predict even smaller coupling constants. To reproduce the experimental Tc, a 5-6 times larger coupling constant would be needed. Our results indicate that electron-phonon coupling is not sufficient to explain superconductivity in the whole family of Fe-As-based superconductors, probably due to the importance of strong-correlation effects.

Physical Properties of the Noncentrosymmetric SuperconductorMg10Ir19B16

Specific heat, electrical resistivity, and magnetic susceptibility measurements on a high quality sample of Mg10Ir19B16 provide a self-consistent determination of its superconducting properties. They indicate that Mg10Ir19B16 is a type-II superconductor [T{C}=4.45 K, kappa(0) approximately 20], with an electron-phonon coupling constant lambda{ep}=0.66. An analysis of the T-dependent specific heat shows that superconducting properties are dominated by an s-wave gap (Delta=0.7 meV). Point contact tunneling data provide evidence for multiple superconducting gaps, as expected from strong asymmetric spin-orbit coupling.

Intrinsic thermodynamic properties of the pyrochlore superconductorRbOs2O6extracted by condensation energy analysis

We develop a general procedure for the analysis of bulk thermodynamic data of a superconductor for samples containing a metallic non-superconducting second phase. The method is based on the condensation energy and it allows the extraction of the intrinsic properties of a superconductor even for non-ideal samples. Applying this procedure to the recently discovered geometrically frustrated beta-pyrochlore superconductor RbOs2O6 (Tc = 6.4 K) yields a Sommerfeld coefficient as high as 79 mu J/g/K^2 (44 mJ/mol_f.u./K^2). RbOs2O6 is inferred to be a strong type-II superconductor (kappa(Tc) = 23) in the intermediate-coupling regime similar to niobium (lambda_ep \approx 1). From the upper critical field mu_0 H_c2 \approx 6 T at 0 K, we estimate a Ginzburg-Landau coherence length xi \approx 74 AA. The condensation energy is 860 mu J/g (483 mJ/mol_f.u.) resulting in 1/(8 pi) (gamma_1 Tc^2)/DeltaU_1 \approx 0.15, a value well in the range of conventional phonon-mediated superconductors. The superconducting electronic specific heat indicates conventional s-wave pairing. The experimental Sommerfeld coefficient of 44 mJ/mol_f.u./K^2 is about 4 times larger than the one found in band structure calculations. Together with the electron-phonon coupling constant lambda_ep \approx 1 this leaves an additional lambda_add \approx 2.4 for enhancement due to other mechanisms.

Band Filling and Interband Scattering Effects inMgB2: Carbon versus Aluminum Doping

We argue, based on band structure calculations and the Eliashberg theory, that the observed decrease of T(c) of Al and C doped MgB2 samples can be understood mainly in terms of a band filling effect due to the electron doping by Al and C. A simple scaling of the electron-phonon coupling constant lambda by the variation of the density of states as a function of electron doping is sufficient to capture the experimentally observed behavior. Further, we also explain the long standing open question of the experimental observation of a nearly constant pi gap as a function of doping by a compensation of the effect of band filling and interband scattering. Both effects together generate a nearly constant pi gap and shift the merging point of both gaps to higher doping concentrations, resolving the discrepancy between experiment and theoretical predictions based on interband scattering only.

Superconductivity in doped sp3 semiconductors: the case of the clathrates.

We present a joint experimental and theoretical study of the superconductivity in doped silicon clathrates. The critical temperature in Ba(8)@Si-46 is shown to strongly decrease with applied pressure. These results are corroborated by ab initio calculations using MacMillan's formulation of the BCS theory with the electron-phonon coupling constant lambda calculated from perturbative density functional theory. Further, the study of I(8)@Si-46 and of gedanken pure silicon diamond and clathrate phases doped within a rigid-band approach show that the superconductivity is an intrinsic property of the sp(3) silicon network. As a consequence, carbon clathrates are predicted to yield large critical temperatures with an effective electron-phonon interaction much larger than in C60.

First-principles calculation of the superconducting transition inMgB2within the anisotropic Eliashberg formalism

We present a study of the superconducting transition in MgB2 using the ab-initio pseudopotential density functional method and the fully anisotropic Eliashberg equation. Our study shows that the anisotropic Eliashberg equation, constructed with ab-initio calculated momentum-dependent electron-phonon interaction and anharmonic phonon frequencies, yields an average electron-phonon coupling constant lambda = 0.61, a transition temperature Tc = 39 K, and a boron isotope-effect exponent alphaB = 0.31 with a reasonable assumption of mu* = 0.12. The calculated values for Tc, lambda, and alphaB are in excellent agreement with transport, specific heat, and isotope effect measurements respectively. The individual values of the electron-phonon coupling lambda(k,k') on the various pieces of the Fermi surface however vary from 0.1 to 2.5. The observed Tc is a result of both the raising effect of anisotropy in the electron-phonon couplings and the lowering effect of anharmonicity in the relevant phonon modes.

Infrared and optical properties of pure and cobalt-dopedLuNi2B2C

We present optical conductivity data for Lu(Ni$_{1-x}$Co$_x$)$_2$B$_2$C over a wide range of frequencies and temperatures for x=0 and x=0.09. Both materials show evidence of being good Drude metals with the infrared data in reasonable agreement with dc resistivity measurements at low frequencies. An absorption threshold is seen at approximately 700 cm-1. In the cobalt-doped material we see a superconducting gap in the conductivity spectrum with an absorption onset at 24 +/- 2 cm-1 = 3.9$ +/- 0.4 k_BT_c suggestive of weak to moderately strong coupling. The pure material is in the clean limit and no gap can be seen. We discuss the data in terms of the electron-phonon interaction and find that it can be fit below 600 cm-1 with a plasma frequency of 3.3 eV and an electron-phonon coupling constant lambda_{tr}=0.33 using an alpha^{2}F(omega) spectrum fit to the resistivity.

Optical properties of c-axis oriented superconducting MgB2 films.

Temperature dependent optical conductivities and dc resistivity of c-axis oriented superconducting (T(c) = 39.6 K) MgB2 films (approximately 450 nm) have been measured. The normal state ab-plane optical conductivities can be described by the Drude model with a temperature independent Drude plasma frequency of omega(p,D) = 13 600+/-100 cm(-1) or 1.68+/-0.01 eV. The normal state resistivity is fitted by the Bloch-Grüneisen formula with an electron-phonon coupling constant lambda(tr) = 0.13+/-0.02. The optical conductivity spectra below T(c) of these films suggest that MgB2 is a multigap superconductor.

TWO UNUSUAL DETERMINATIONS OF ELECTRONIC AND LATTICE THERMAL PARAMETERS IN YBa2Cu3O7 Films

This paper deals with the nanosecond transient electrical resistance following either an optical pulse or the sudden application of a critical current in YBCO films. The observed bi-exponential decay of the photoresistance yields both the electron-phonon relaxation time τep and the phonon escape time τγ to the substrate. A novel treatment of these data allows to derive the low-temperature electron specific heat and the electron-phonon coupling constant lambda in the acoustic regime. Secondly, the nucleation time of phase-slip centers in narrow bridges is analyzed to provide τγ. Finally, the accurate knowledge of τγ is used to determine the temperature inside a dissipation center.

Femtosecond thermomodulation studies of low and high-T/sub c/ superconductors

The authors report femtosecond pump-probe measurements of electronic energy relaxation in conventional metallic and high-T/sub c/ oxide superconductors. In conventional metallic superconductors, the energy relaxation rate of electrons is used to determine the electron-phonon coupling constant lambda . The agreement between the lambda values measured and those obtained by other techniques is excellent, confirming the theoretical predictions of P.B. Allen (1987). A novel Cu overlayer technique was developed in order to measure certain metals which do not have a strong optical transition to states near the Fermi level at a laser energy, of 1.98 eV. The effect of different Cu overlayer thicknesses has been studied. In the new copper-oxide high-T/sub c/ superconducting materials, electronic energy relaxation is monitored by measuring changes epsilon /sub 2/. The observed changes in epsilon /sub 2/ are related to the dynamics of the Cu d to O p band charge transfer excitation occurring in the CuO/sub 2/ planes. By depleting a YBa/sub 2/Cu/sub 3/O/sub 7- delta / sample of oxygen, one can simultaneously vary the Fermi level and the T/sub c/ and make dramatic changes in the pump-probe signal. An estimate of lambda , in several high-T/sub c/ materials, is also made using Allen's theory to fit the relaxation behavior of epsilon /sub 2/.

Low-temperature enhancement of the thermopower of amorphous (Zr0.64Ni0.36)1-xAlx alloys

Enhancements of the low-temperature thermopower of amorphous melt-quenched (Zr0.64Ni0.36)1-xAlx alloys with x=0, 0.05 , 0.10, 0.15, 0.20 and 0.25 are shown to be in good agreement with the predictions for the electron-phonon enhancement. The results imply that the low-frequency part of the Eliashberg function alpha 2( omega ) F( omega ) is proportional to omega n with n>1 for these alloys. These alloys are weak-coupling superconductors, and the addition of Al reduces the electron-phonon coupling constant lambda despite the tendency to strong coupling in simple amorphous metals.

Properties of the new high T/sub c/ materials: an analysis based on fermiology

A small value of the Fermi energy, E/sub f/, in the new high T/sub c/ oxides and its consequences are the subject of this study. It is shown that the small value of E/sub f/ allows separation of the electronic contribution to the heat capacity in the high-temperature region E/sub f/k/sub B/>T> theta /sub D/ to determine the value of the electron-phonon coupling constant lambda . The linear temperature dependence of the normal resistance is mainly due to a large anisotropy of the system. A small value of E/sub f/ allows the lattice contribution to the thermal conductivity to play a dominant role. A strong electron-phonon coupling is manifested in the increase of the thermal conductivity in the region T<T/sub c/, and the appearance of such coupling is also connected with a small value of E/sub f/.<<ETX>>

Low-temperature specific heat study of Ni100-xZrx(x=30-80) metallic glasses

The low-temperature specific heats of six melt-spun Ni100-xZrx, x=30, 40, 50, 60, 70 and 80 metallic glasses have been measured in the temperature range of 1.5-6K. Ni-Zr metallic glasses have no magnetic moments at least above 30 at.% Zr. Furthermore, they show a superconducting transition above 40 at.% Zr which enables the authors to deduce the electron-phonon coupling constant lambda . These facts are useful for estimating the density of states at the Fermi level and Debye temperature unambiguously. The results of the electronic specific-heat coefficient gamma increase monotonically with increasing Zr concentration. On the other hand, the Debye temperature theta D decreases monotonically with increasing Zr. The correlations between N(EF) obtained in the present work and other results both in experimental and theoretical works are discussed. The correlations between the Debye temperature theta D and crystallisation temperature Tx have been discussed in relation to Lindemann's melting theory.

Superconductivity of amorphous Mg0.7Zn0.3-xGaxalloys

The authors report on low-temperature measurements (0.1K<or=T<or=1.5K) of the specific heat and electrical resistivity of amorphous Mg0.7Zn0.3-xGax alloys (0.06<or=x<or=0.20) prepared by melt spinning. Superconductivity is observed for all samples. The transition temperature increases from approximately=0.1K to approximately=0.3K as the Ga concentration increases towards x=0.20. This increase is accomplished by a 10% increase in the electron-phonon coupling constant lambda . The specific heat data show that these alloys are weak-coupling superconductors ( lambda approximately=0.3). The upper critical field measured for x=0.20 is analysed in terms of the WHH theory. Finally, the normal-state specific heat data taken in a magnetic field of 2 T show contributions from Ga nuclei.

Anomalous temperature dependence of the resistivity of some intermetallic compounds

The resistivity rho of some intermetallic compounds such as Nb3Sn, V3Si, UAl2, etc. has an anomaly at a temperature T0 near 100K. The resistivity rises steeply with T below T0 and less steeply above it. Here the authors account for this anomalous temperature dependence using the 'classical' s-d model. Below T0 the s-like and d-like states are hybridised by a small electronic matrix element Jsd (Jsd approximately=10-50 meV) and the electron-phonon coupling constant lambda is large. Above T0 the electron-phonon scattering rate h(cross)/ tau exceeds Jsd, and the s-like and d-like states are decoupled. The electrical conductivity is then due mainly to the s-like states which possess a smaller electron-phonon coupling constant lambda , giving rise to a smaller value of d rho /dT. The anomaly occurs when the mean free path l is about an order of magnitude larger than the interatomic spacing d.

Amorphous superconductingZrxCu1−x: Electronic properties, stability, and low-energy excitations

Amorphous Zr/sub x/Cu/sub 1-x/ alloys (0.50< or =x< or =0.74) prepared by melt-spinning are investigated by means of electrical and thermal measurements. The negative temperature coefficient of the electrical resistivity suggests that the criterion 2k/sub F/roughly-equalk/sub p/ is always fulfilled in this system (k/sub F/ = Fermi wave number, k/sub p/ = position of the first maximum of the structure factor S(k)). The high density of states N/sub ..gamma../(E/sub F/) as inferred from specific-heat measurements originates from the d electrons of Zr. The bare density of states (determined from N/sub ..gamma../(E/sub F/) with the aid of the electron-phonon coupling constant lambda) is three times higher than calculated from the free-electron model and almost independent of the Zr concentration. Phonon-electron scattering as determined by thermal-conductivity measurements shows a similar deviation from free-electron behavior. A decisive test of the Nagel-Tauc condition for high (meta-) stability of the metallic glasses is not possible due to the apparent failure of both free-electron and rigid-band models. All samples investigated are superconducting and belong to the extreme-type-II superconductors. Fluctuation-induced paraconductivity extends up to 1.5T/sub c/. An analysis of the electron-phonon coupling constant lambda as determined from T/sub c/ indicates that the electron-ion matrix element variesmore » strongly across the Zr/sub x/Cu/sub 1-x/ series. The size of lambda, the jump of the specific heat at T/sub c/, and its drop at low temperatures show that Zr-Cu alloys are weak- to intermediate-coupling superconductors. The relatively high T/sub c/ values of the Zr-rich metallic glasses allow the observation of a linear specific-heat term for T<« less Authors: Samwer, K. ; Loehneysen, H.v. Publication Date:1982-07-01 OSTI Identifier:5036836 Resource Type:Journal Article Resource Relation:Journal Name: Phys. Rev. B: Condens. Matter; (United States); Journal Volume: 26:1 Research Org:I. Physikalisches Institut der Universitaet Goettingen, D-3400 Goettingen, West Germany Country of Publication:United States Language:English Subject: 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COPPER ALLOYS; ELECTRICAL PROPERTIES; SUPERCONDUCTIVITY; ZIRCONIUM ALLOYS; AMORPHOUS STATE; ELECTRIC CONDUCTIVITY; ELECTRON-PHONON COUPLING; ENERGY-LEVEL DENSITY; EXPERIMENTAL DATA; SPECIFIC HEAT; STABILITY; TYPE-II SUPERCONDUCTORS; ALLOYS; DATA; INFORMATION; NUMERICAL DATA; PHYSICAL PROPERTIES; SUPERCONDUCTORS; THERMODYNAMIC PROPERTIES 360104* -- Metals & Alloys-- Physical Properties; 656102 -- Solid State Physics-- Superconductivity-- Acoustic, Electronic, Magnetic, Optical, & Thermal Phenomena-- (-1987)

Electronic properties and electron-phonon coupling in zirconium and niobium hydrides

The electronic structure of the two 4d transition-metal cubic dihydrides ZrH/sub 2/ and NbH/sub 2/ is investigated by means of an augmented-plane-wave (APW) band-structure calculation. The position of the Fermi level in a peak of the density of states (DOS) in the case of cubic ZrH/sub 2/ leads to an interpretation of the tetragonal distortion observed in all the group-IV transition-metal dihydrides in terms of a Jahn-Teller effect which lifts the degeneracy of the doubly degenerate band in the GAMMAL direction; these results are in agreement with magnetic susceptibility, electronic specific heat and thermoelectric power data. The main features of the DOS of the metal 4d states are similar for ZrH/sub 2/ and NbH/sub 2/, while the position and width of the low-lying bands are found to depend substantially upon the compound under study. These two bands which result from metal-hydrogen and hydrogen-hydrogen interactions overlap the metal d bands located at higher energies, contrary to the case of rare-earth dihydrides for which an energy gap was obtained. Our theoretical results are in good agreement with photoemission and x-ray emission spectra. We have evaluated the electron-phonon coupling constant lambda using the results of our APW calculation in conjunction with neutron scatteringmore » data. For both ZrH/sub 2/ and NbH/sub 2/, and contrary to the case of superconducting PdH, the electron-optical phonon contribution is small, due essentially to the low value of the DOS of s type at the H site at the Fermi energy and to the hardening of the optic modes. Moreover, the electronic term of the electron--acoustic-phonon contribution is reduced from its value in the pure metal. The two compounds are not found to be superconducting, in agreement with experimental results.« less

THE ELECTRON-PHONON COUPLING CONSTANT OF AMORPHOUS METALS

Extending the free-electron theory of electronic transport in simple amorphous metals, the Eliashberg function alpha 2F( omega ) and the electron-phonon coupling constant lambda are calculated for such materials. A formula relating lambda to the temperature coefficient of the resistivity at higher temperatures (T>or approximately= theta D/2) is derived. The validity of this formula is tested for amorphous Ga.

Proximity electron tunneling spectroscopy I. Experiments on Nb

A quantitative proximity electron tunneling spectroscopy (PETS) id demonstrated for the study of strong coupling superconductors which do not form suitable insulating oxides for conventional McMillan--Rowell tunneling spectroscopy. Proximity junctions of the form C-Al/sub 2/O/sub 3/-Al/S are employed, with Al thickness d/sub N/< or =100 A. Here S is the superconductor of interest and C is any convenient counterelectrode. The physical basis for the method, experimental techniques, and data obtained from foils of Nb are presented. The results for Nb include the energy-dependent pair potential ..delta../sub s/(E), the renormalization function Z(E), effective phonon spectrum ..cap alpha.. /sup 2/F(..omega..), electron-phonon coupling constant lambda, and Coulomb pseudopotential ..mu..*. A full discussion of the underlying theory and details of the methods of analysis employed to obtain, in addition, the pair potential of the Al proximity layer are contained in a following paper.