We develop an effective two-dimensional dynamic interaction potential embodying the screening of holes as carriers by charge density fluctuations and by optical phonons leading to superconductivity in magnesium diborides. The MgB2 system is viewed as an ionic solid containing boron layers with holes as carriers in a unit cell and a polarization function is set up that fulfils the appropriate sum rules on the electronic and ionic polarizabilities. The value of the electron–phonon coupling strength and of the Coulomb screening parameter obtained from the static dielectric function within the two-dimensional model indicates that the superconductor is in the strong coupling regime. The estimated superconducting transition temperature Tc of MgB2 is about 43 K and the pressure derivative of Tc is negative. The isotope effect, coherence length, magnetic penetration depth and volume derivative of Tc are also estimated to be consistent with the earlier results. The implications of the effective interactive potential and its analysis are discussed.

Superconducting transition temperature, isotope and pressure effect in MgB2: phonon and charge fluctuation-mediated pairing mechanism

We have fabricated weakly coupled intergrain nanobridges from MgB2 films by a focused ion beam (FIB) patterning technique and studied their transition properties. The bridges were nominally 300 nm wide and 100 nm long, and crossed a single grain boundary perpendicularly. The temperature-dependent resistance data showed a two-step transition after FIB pattern with more-than-two-decade increase in the resistivity. Current-voltage curves showed the characteristics of an ideal Josephson junction. The measured data were perfectly matched with the theory of the resistively shunted junction model with thermal fluctuations at all measured temperatures. At 4.2 K, the measured data showed the effect of hysteresis in agreement with the estimated McCumber parameter βc>0.3. The hysteresis effect disappeared above 6 K. The critical currents obtained from fitting to the RSJ model were linearly dependent on temperature, implying that the grain boundary played an insulating barrier.

Josephson effects in weakly coupled MgB2 intergrain nanobridges prepared by focused ion beam

A simplified two-band model for describing the longitudinal dielectric function for a layered MgB2 system has been developed to reveal the attractive pairing mechanism leading to the superconducting state. A model dielectric function for σ and π band carriers is set up that fulfils the appropriate sum rules on the electronic and ionic polarizabilities. The value of the in-layer electron–phonon coupling strength and the Coulomb screening parameter for σ (π) band carriers is obtained from the residues of the dielectric function. It is noticed that the σ-holes in the two-dimensional boron planes via the screened phonon coupling is responsible for the attractive interaction and the superconductor is in the strong coupling regime. Within this framework, the superconducting transition temperature Tc of MgB2 is estimated as 42 K and the pressure derivative of Tc is negative. The isotope effect, coherence length, magnetic penetration depth, and volume derivative of Tc are also estimated to be consistent with the earlier results. Within the two-band model of superconductivity in MgB2, we place particular emphasis on intraband channels, carriers either in σ or π bands, as interband effects are negligible. In such a situation the superconductivity originates from either σ or π band carriers. The implications of the effective interactive potential with both σ and π carriers and its analysis are discussed.

http://iopscience.iop.org/article/10.1088/0953-2048/23/7/075016/pdf

Superconducting pairing and the two-gap nature of Al and C doped MgB2: screened phonon-pairing mechanism

We use the Kubo model to calculate the lattice contribution to the thermal conductivity (κph) in MgB2 superconductors. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity in normal state of MgB2 superconductors dominates and is an artifact of strong phonon-impurity and -phonon scattering mechanism. Later on, the electronic contribution to the thermal conductivity (κe) is calculated within relaxation time approximation for π and σ band carriers with s wave symmetry. Such an estimate sets an upper bound on κe and is about 30% of the total heat transfer at room temperature. The validity of the Wiedemann Franz law is also examined and an enhanced Lorenz number is obtained. Both these channels for heat transfer are clubbed and κtot develops a broad peak at about 120 K, before falling off at higher temperatures weakly. The anomalies reported are well-accounted in terms of the scattering mechanism by phonon and electron with impurities. It is shown that the behavior of the thermal conductivity is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between electron and lattice contributions. The contribution of carriers toward κ is substantial and is due to the fact that the carriers are condensed and do not carry entropy. We include comparisons with other theoretical calculations on κe and available experimental data. The numerical analysis of heat transfer in the metallic phase of MgB2 shows similar results as those revealed from experiments.

THERMAL TRANSPORT OF MgB2 SUPERCONDUCTORS: INTERPLAY BETWEEN ELECTRON AND LATTICE-IMPURITY SCATTERING

We use the Kubo model to calculate the lattice contribution to the thermal conductivity (κph) in Mg(B0.94C0.06)2 superconductors. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers and phonons. Later on, the carrier (electron) contribution to the thermal conductivity (κe) is calculated within relaxation time approximation for π and σ band carriers with s-wave symmetry. Such an estimate sets an upper bound on κe and a very small contribution is seen for total heat transfer at room temperature. Both these channels for heat transfer are clubbed and κtot develops a broad peak before falling off at higher temperatures weakly in MgB2. The substitution of 6% carbon-doped MgB2 results in a considerable reduction of κph and κe at low temperatures, in the vicinity as well as above transition temperature. The contribution of carriers towards κ (T) is negligible and is due to the fact that the carriers are condensed and do not carry entropy.

Thermal conductivity of Mg(B0.94C0.06)2 superconductors: role of carrier and lattice–impurity scattering

Reflectance of superconducting MgB 2 thin films ( T c ≈35 K) has been measured in a broad spectral range from 30 to 110,000 cm −1 . A typical plasma edge with a reflectance minimum at 15,000 cm −1 has been found. In the far-infrared region we observe a pronounced rise of the reflectance below 60 cm −1 , which appears below T c and can be associated with superconducting state. The temperature-dependent complex conductivity at infrared frequencies has been determined. The real and imaginary parts of the conductivity below T c show a temperature evolution, which is characteristic for superconducting gap opening (decrease in σ 1 and rise in σ 2 ).

Infrared studies of superconducting MgB2 thin films

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Infrared studies of superconducting MgB2 thin films