Electronic Specific Heat Of Two-gap Superconductors

Electronic specific heat at superconducting state is very important to know the electronic behaviors, predicate the bands number which crossover the Fermi surface. Specific heat jump value can be used to determine the kind of interaction between electron and phonon, the gap is isotropic or anisotropic gap. The equations of electronic specific heat at normal and superconducting states also play a very important role in thermodynamic equation to calculate critical magnetic field, condensation energy. Hence, the electronic specific heat has already obtained by model theories: phenomenological models as two fluid model, G- L theory andαmodel; microscopic theory as BCS theory .More theoretical application to study the electronic specific heat, and in current, used two fluid model for medium coupling, BCS for weak coupling with distinctive value of gap for that element or compound superconductor andαmodel for a strong coupling. With considering that BCS curve is a normalized curve, so any deviation on this curve is anomaly and has new physical mean. The feature of existence the second gap is an anomaly on the curve of electronic specific heat at lower critical temperature that appeared as a hump or an excess in the electronic specific heat. In general, any deviation on BCS curves. Experimentally, the anomalies of weak coupling superconductor are more oblivious than the strong coupling superconductors. Theoretically, transition elements with two gaps can be used the extension of BCS theory to superconductivity. For two-gap superconducting compounds, there is one general method;αmodel as a phenomenological model where the electronic specific heat contains the average two exponential terms with partials of Sommerfeld constant.The main work and results are in the following:1. Discussion an electronic specific heat at superconducting stat in model theories and the thermodynamic properties with crystal structure of two- gap superconductor compounds.2. Propose new phenomenological equation, suggested by this work to study the behaviors of electronic specific heat of two- gap superconductors; Nb3Sn, MgB2 NbSe2, multigap superconductor; YNi2B2C. Equation of electronic specific heat in two-gap Superconductor contains electronic specific heat of two bands: electronic specific heat in every band can be represented by asymptotic formula of BCS and phenomenological term resembles to that of fluid model where the power is not a constant but depends on the interaction coupling between electron and phonon. Every branch of electronic specific heat contains one part of Sommerfeld constant. Phenomenological equation of electronic specific heat taken into account with the interaction–coupling and the Fermi surface sheets number, as a result of the applications of this method the results:1) Sommerfeld partials in every band of two-gap superconducting calculate in accordance with an accurate relations, their values are not estimated values and does not related to BCS gap. Sommerfeld partials values depend on the gap ratio and the number of distinct Fermi sheets. If the ratio large gap to small gap larger than ten (ΔL /ΔS> 10) and the number of distinct Fermi sheets is large, the dominant partial will be for large band. Sommerfeld partial for small-large band intersect at 2.92 when the number of Fermi sheets are two sheets, and then this value decreases with increasing the number of a distinct Fermi surface sheets at approximately more than four sheets there is not any intersection point.2) The curves of electronic specific heat of MgB2, Nb3Sn, NbSe2 and YNi2B2C are agree with experiment curves at superconducting state where the anomalies will be appear at lower critical temperature if the curve of large band is under of that for small band; this occurs when the weight reduce of Sommerfeld is small, distinct Fermi sheets number are small, interaction coupling between electron and phonon is medium coupling or a strong coupling. This state appears like Nb and Nb3Sn where after the anomaly region and at still high temperature, the exponential increase due to the main gap. Compare with BCS, only the curve of large band is like BSC curve. For the a small band of MgB2, the situation is quite different; according to the equation of electronic specific heat of two gap superconductors, the electronic specific heat in small band has not two stages; on the contrary, it has three stages. Over the small hump region the relation between temperature and the resultant electronic specific seem approximately as linear relation, this characteristic indicates to the compensation between the two bands.3) Electronic specific heat jump (ΔC /γTC ); MgB2 has the smallest value and the largest value is found for Nb3Sn, these values are 1.1, 1.7, 1.9, 2.03 and 2.45, for MgB2, Nb, YNi2B2C, NbSe2 and Nb3Sn, respectively.4) Crossing point between electronic specific heat curves of normal-superconducting stat occurs at 0.5Tc , 0.565 Tc , 0.58 Tc 0.584 Tc for MgB2, YNi2B2C, NbSe2, Nb3Sn, respectively, these values agree with experiment results.