Thermodynamics of two-band superconductors: The case ofMgB2

Abstract

Thermodynamic properties of the multiband superconductor MgB 2 have often been described using a simple sum of the standard BCS expressions corresponding to σ-and π-bands. Although, it is a priori not clear if this approach is working always adequately, in particular in cases of strong interband scattering. Here we compare the often used approach of a sum of two independent bands using BCS-like α-model expressions for the specific heat, entropy and free energy to the solution of the full Eliashberg equations. The superconducting energy gaps, the free energy, the entropy and the heat capacity for varying interband scattering rates are calculated within the framework of two-band Eliashberg theory. We obtain good agreement between the phenomenological two-band α-model with the Eliashberg results, which delivers for the first time the theoretical verification to use the α-model as a useful tool for a reliable analysis of heat capacity data. For the thermodynamic potential and the entropy we demonstrate that only the sum over the contributions of the two bands has physical meaning.

Manifestations of impurity-induceds±⇒s++transition: multiband model for dynamical response functions

“…In the clean limit, one sees two different excitation gaps for the two bands. In accord with earlier calculations for s ++ superconductors [20], the interband impurity scattering mixes the pairs in the two bands, so that the states appear in the a-band at the energy range of the b-band gap. These states are gradually filled in with increasing scattering rate.…”

“…Interband scattering is expected to modify the gap functions and the tunneling DOS in the superconducting state in a multiband superconductor. In the weak coupling regime the impurity effects have been discussed in [19] within the Born limit and extended in [20] to the strong coupling case. In the following, we will calculate the gap functions, and the superconducting DOS by solving the nonlinear Eliashberg equations in the s ± and s ++ superconductors for various values of the interband nonmagnetic scattering rate, going beyond the Born approximation.…”

Multigap superconductivity in single crystals of Ba0.65Na0.35Fe2

“…One, therefore, certainly needs to check other self-consistent models to compare the results. In this scenario, within the framework of the Eliashberg approach for MgB 2 Dolgov et al 53 have shown that the α model is sufficiently accurate to find the superconducting gap values, although the gap's partial contribution lacks full agreement. Another recently proposed γ model by Kogan et al 54 is also an effective approach that takes into account the interband pairing potential and is successfully tested for two band superconductors, MgB 2 and V 3 Si.…”

The Study on Hybridized Two-Band Superconductor

“…Since Moskalenko [1,2] Suhl et al [3] introduced the twoband model that accounts for multiple energy bands in the vicinity of the Fermi energy contributing electron pairing in superconductor, the two-band model has been applied to high temperature superconductor in copper oxides [4][5][6][7][8][9][10], MgB 2 superconductor [11][12][13], and heavy Fermion superconductor [14,15]. Dolgov et al [16] studied the thermodynamic properties of the two-band superconductor: MgB 2 . The superconducting energy gap, free energy, the entropy, and heat capacity were calculated within the framework of twoband Eliashberg theory.…”