OJCM  Vol.7 No.3 , July 2017
On the s±-Wave Superconductivity in the Iron-Based Superconductors: A Perspective Based on a Detailed Study of Ba0.6K0.4Fe2As2 via the Generalized-Bardeen-Cooper-Schrieffer Equations Incorporating Fermi Energy
Abstract: Guided by the belief that Fermi energy EF (equivalently, chemical potential μ) plays a pivotal role in determining the properties of superconductors (SCs), we have recently derived μ-incorporated Generalized-Bardeen-Cooper-Schrieffer equations (GBCSEs) for the gaps (Δs) and critical temperatures (Tcs) of both elemental and composite SCs. The μ-dependent interaction parameters consistent with the values of Δs and Tcs of any of these SCs were shown to lead to expressions for the effective mass of electrons (m*) and their number density (ns), critical velocity (v0), and the critical current density j0 at T = 0 in terms of the following five parameters: Debye temperature, EF, a dimensionless construct y, the specific heat constant, and the gram-atomic volume. We could then fix the value of μ in any SC by appealing to the experimental value of its j0 and calculate the other parameters. This approach was followed for a variety of SCs—elemental, MgB2 and cuprates and, with a more accurate equation to determine y, for Nitrogen Nitride (NbN). Employing the framework given for NbN, we present here a detailed study of Ba0.6K0.4Fe2As2 (BaAs). Some of the main attributes of this SC are: it is characterized by -wave superconductivity and multiple gaps between 0 - 12 meV; its Tc ~ 37 K, but the maximum Tc of SCs in its class can exceed 50 K; EF/kTc = 4.4 (k = Boltzmann constant), and its Tc plotted against a tuning variable has a dome-like structure. After drawing attention to the fact that the -wave is an inbuilt feature of GBCSEs, we give a quantitative account of its several other features, which include the values of m*, ns, vo, and coherence length. Finally, we also deal with the issue of the stage BaAs occupies in the BCS-Bose-Einstein Condensation crossover.
Cite this paper: Malik, G. (2017) On the s±-Wave Superconductivity in the Iron-Based Superconductors: A Perspective Based on a Detailed Study of Ba0.6K0.4Fe2As2 via the Generalized-Bardeen-Cooper-Schrieffer Equations Incorporating Fermi Energy. Open Journal of Composite Materials, 7, 130-145. doi: 10.4236/ojcm.2017.73008.

[1]   Kamihara, Y., Watanabe, T., Hirano, M. and Hosono, H. (2008) Iron-Based Layered Superconductor La[O1-xFx]FeAs (x = 0.05-0.12) with Tc = 26 K, Journal of the American Chemical Society, 130, 3296-3297.

[2]   Bang, Y. and Stewart, G.R. (2017) Superconducting Properties of the s±-Wave State: Fe-Based Superconductors. Journal of Physics: Condensed Matter, 29, 46.

[3]   Suhl, H., Matthias, B.T. and Walker, L.R. (1959) Bardeen-Cooper-Schrieffer Theory in the case of Overlapping Bands. Physical Review Letters, 3, 552-554.

[4]   Malik, G.P. and Malik, U. (2003) High-Tc Superconductivity via Superpropagators. Physica B, 336, 349-352.

[5]   Malik, G.P. (2010) On the Equivalence of the Binding Energy of a Cooper Pair and the BCS Energy Gap: A Framework for Dealing with Composite Superconductors. International Journal of Modern Physics B, 9, 1159-1172.

[6]   McMillan, W.L. (1968) Transition Temperature of Strong-Coupled Superconductors. Physical Review, 167, 331-344.

[7]   Shan, L., et al. (2011) Observation of Ordered Vortices with Andreev Bound States in Ba0.6K0.4Fe2As2. Nature Physics, 7, 325-331.

[8]   Li, L.-J., et al. (2008) Superconductivity above 50 K in Tb1-xThxFeAsO. Physical Review B, 78, 4.

[9]   Stewart, G.R. (2011) Superconductivity in Iron Compounds. Reviews of Modern Physics, 83, 1589-1652.

[10]   Ding, H. (2008) Observation of Fermi-Surface-Dependent Nodeless Superconducting Gaps in Ba0.6K0.4Fe2As2. Europhysics Letters, 83, 4.

[11]   Lee, H. (2012) Iron-Based Superconductors: Nodal Rings. Nature Physics, 8, 364-365.

[12]   Ren, C., Wang, Z.-S., Luo, H.-Q., Yang, H., Shan, L. and Wen, H.-H. (2008) Evidence for Two Energy Gaps in Superconducting Ba0.6K0.4Fe2As2 Single Crystals and the Breakdown of the Uemura Plot. Physical Review Letters, 101, 4.

[13]   Popovich, P., Boris, A.V., Dolgov, O.V., Golubov, A.A., Sun, D.L., Lin, C.T., et al. (2010) Specific Heat Measurements of Ba0.68K0.32Fe2As2 Single Crystals: Evidence for a Multiband Strong-Coupling Superconducting State. Physical Review Letters, 105, 4.

[14]   Zhang, Y., Yang, L.X., Chen, F., Zhou, B., Wang, X.F., Chen, X.H., et al. (2010) Out-of-Plane Momentum and Symmetry-Dependent Energy Gap of the Pnictide Ba0.6K0.4Fe2As2 Superconductor Revealed by Angle-Resolved Photoemission Spectroscopy. Physical Review Letters, 105, Article ID: 117003.

[15]   Guidini, A. and Perali, A. (2014) Band-Edge BCS-BEC Crossover in a Two-Band Superconductor: Physical Properties and Detection Parameters. Superconductor Science and Technology, 27, 10.

[16]   Weiss, J.D., Jiang, J., Polyanski, A.A. and Hellstorm, E.E. (2013) Mechanochemical Synthesis of Pnictide Compounds and Superconducting Ba0.6K0.4Fe2As2 Bulks with High Critical Current Density. Superconductor Science and Technology, 26, Article ID: 074003.

[17]   Taen, T., Ohtake, F., Pyon, S., Tsuyoshi, T. and Kitamura, H. (2013) Critical Current Density and Vortex Dynamics in Pristine and Proton-Irradiated Ba0.6K0.4Fe2As2. Superconductor Science and Technology, 28, Article ID: 085003.

[18]   Ding, H., Nakayama, K., Richard, P., Souma, S., Sato, T., Takahashi, T., et al. (2015) Electronic Structure of Optimally doped Ba0.6K0.4Fe2As2: A Comprehensive Angle-Resolved Photoemission Spectroscopy Investigation. Journal of Physics: Condensed Matter, 23, Article ID: 135701.

[19]   Ricayzen, G. (1969) The Theory of Bardeen, Cooper, and Schrieffer. In: Parks, R.D., Ed., Superconductivity, Marcell Dekker, Inc., New York, 51-115.

[20]   Malik, G.P. and de Llano, M. (2013) Some Implications of an Alternate Equation for the BCS Energy Gap. Journal of Modern Physics, 4, 6-12.

[21]   Mu, G., Luo, H., Wang, Z., Shan, L., Ren, C., Wen, H.-H., et al. (2009) Low Temperature Specific Heat of the Hole-doped Ba0.6K0.4Fe2As2Single Crystals and Electron-Doped SmFeAsO0.9F0.1 Samples. Physical Review B, 79, Article ID: 174501.

[22]   Malik, G.P., Chávez, I. and de Llano, M. (2013) Generalized BCS Equations and the Iron-Pnictide Superconductors. Journal of Modern Physics, 4, 474-480.

[23]   Malik, G.P. (2016) Superconductivity-a New Approach Based on the Bethe-Salpeter Equation in the Mean-Field Approximation. Series on Directions in Condensed Matter Physics, World Scientific, Singapore city.

[24]   Malik, G.P. (2016) On the Role of Fermi Energy in Determining Properties of Superconductors: A Detailed Study of Two Elemental Superconductors (Sn and Pb), a Non-cuprate (MgB2), and Three Cuprates (YBCO, Bi-2212 and Tl-2212). Journal of Superconductivity and Novel Magnetism, 29, 2755-2764.

[25]   Malik, G.P. (2014) BCS-BEC Crossover without Appeal Scattering Length Theory. International Journal of Modern Physics B, 28, Article ID: 1450054.

[26]   Malik, G.P. (2017) A Detailed Study of the Role of Fermi Energy in Determining Properties of Superconducting NbN. Journal of Modern Physics, 8, 99-109.

[27]   Rotter, M., Tegel, M. and Johrendt, D. (2008) Superconductivity at 38 K in the Iron Arsenide (Ba1-xKxFe2As2). Physical Review Letters, 101, Article ID: 107006.

[28]   Kwei, G.H. and Lawson, A.C. (1991) Vibrational Properties and Atomic Debye Temperatures for La2CuO4 from Neutron Powder Diffraction. Physica C: Superconductivity, 175, 135-142.

[29]   Tacon, M., Bosak, A., Souliou, S.M., Dellen, G., Loew, T., Heid, R., et al. (2014) Inelastic X-Ray Scattering in YBa2Cu3O6.6 Reveals Giant Phonon Anomalies and Elastic Central Peak Due to Charge-Density-Wave Formation. Nature Physics, 10, 52-58.

[30]   Malik, G.P. and Varma, V.S. (2015) A Study of Superconducting La2CuO4 via Generalized BCS Equations Incorporating Chemical Potential. World Journal of Condensed Matter Physics, 5, 148-159.

[31]   Malik, G.P. (2015) A Study of Heavy-Fermion Superconductors via BCS Equations Incorporating Chemical Potential. Journal of Modern Physics, 6, 1233-1242.