Thermodynamics of Two - Band Superconductors: The Case of MgB${}_2$

Abstract

Thermodynamic properties of the multiband superconductor MgB${}_2$ have often been described using a simple sum of the standard BCS expressions corresponding to $\sigma$- and $\pi$-bands. Although, it is \textit{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 $\alpha$-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 $\alpha$-model with the Eliashberg results, which delivers for the first time the theoretical verification to use the $\alpha$-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.

arXiv comment27 pages, 10 figures, 1 table, submitted to Phys. Rev. B

References in corpus (40)

• Superconductivity of metallic boron in MgB_2
• Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps
• Superconductivity of MgB2: Covalent Bonds Driven Metallic
• Electron-phonon interaction in the normal and superconducting states of MgB2
• Specific Heat of Mg ^{11}B_2
• Phonon dispersion and electron-phonon coupling in MgB_2 and AlB_2
• Specific heat in the superconducting and normal state (2-300 K, 0-16 Teslas), and magnetic susceptibility of the 38-K superconductor MgB2: evidence for a multicomponent gap
• Two-gap superconductivity in MgB${}_2$: clean or dirty?
• Upper critical field pecularities of superconducting YNi2B2C and LuNi2B2C
• Multiband model for tunneling in MgB2 junctions
• Specific heat of MgB${}_2$ in a one- and a two-band model from first-principles calculations
• Effect of magnetic and non-magnetic impurities on highly anisotropic superconductivity
• Band filling and interband scattering effects in MgB${}_2$: C vs Al doping
• Carbon doping of superconducting magnesium diboride
• An Overview of the Basic Physical Properties of MgB${}_2$
• Properties of the superconducting state in a two-band model
• Effects of Al doping on the structural and electronic properties of Mg(1-x)Al(x)B2
• Field Dependence of Electronic Specific Heat in Two-Band Superconductors
• Effect of Al doping on the optical phonon spectrum in Mg(1-x)Al(x)B(2)
• Two-band Eliashberg equations and the experimental Tc of the diboride Mg1-xAlxB2
• MgB_2 under pressure: phonon calculations, Raman spectroscopy, and optical reflectance
• The Tc amplification by quantum interference effects in diborides
• Effects of Boron Purity, Mg Stoichiometry and Carbon Substitution on Properties of Polycrystalline MgB${}_2$
• Evidence for Single-gap Superconductivity in Mg(B_{1-x}C_x)_2 Single Crystals with x=0.132 from Point-Contact Spectroscopy
• Specific heat of MgB_2 after irradiation
• Evidence for strong electron-phonon coupling in MgCNi_3
• Retention of Two-Band Superconductivity in Highly Carbon-Doped MgB2
• Systematic study of the two band/two gap superconductivity in carbon-substituted MgB2 by point-contact spectroscopy
• High Tc superconductivity at a critical strain and charge density in diborides
• Crystal structure of the Mg${}_{1-x}$Al${}_x$B${}_2$ superconductors near x=0.5
• Superconducting properties and c-axis superstructure of Mg1-xAlxB2
• ${}^{11}$B and ${}^{27}$Al NMR spin-lattice relaxation and Knight shift study of Mg${}_{1-x}$Al${}_x$B${}_2$. Evidence for anisotropic Fermi surface
• Thermodynamics of anisotropic-gap and multiband clean BCS superconductors
• Specific Heat Discontinuity in Impure Two-Band Superconductors
• muSR study of carbon-doped MgB2 superconductors
• On the rate of Tc suppression by the interband impurity scattering in MgB2
• Influence of the van Hove singularity on the specific heat jump in BCS superconductors
• Nonmagnetic impurity effects in MgB${}_2$
• Bernoulli Potential, Hall Constant and Cooper Pairs Effective Masses in Disordered BCS Superconductors
• Coherent response of a low T_c Josephson junction to an ultrafast laser pulse

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