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CONDENSED MATTER
Determination of the electron-phonon coupling constants from the experimental temperature dependences of superconducting gaps in MgB$_2$
S. A. Kuzmicheva,
T. E. Kuzmichevab,
S. N. Chesnokova a M. V. Lomonosov Moscow State University, Faculty of Physics
b P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow
Abstract:
Experimental temperature dependences
$\Delta_{\sigma,\pi}(T)$ of the energy of superconducting gaps for MgB
$_2$ samples with the critical temperatures
$22$ K
${}< T_c < 41$ K have been fitted by selecting the renormalized electron-phonon coupling constants
$\lambda_{ij}$ with the use of the Moskalenko-Shul system of equations, the expression for the frequency of collective plasma oscillations obtained by Leggett for two-gap superconductors, and two fitting parameters. We previously obtained the dependences
$\Delta_{\sigma,\pi}(T)$ by the multiple Andreev reflection spectroscopy of superconductor-constriction-superconductor junctions based on MgB
$_2$ with various degree of disorder of the crystal structure. It has been shown that the intraband pairing constants are decisive for the superconductivity mechanism in MgB
$_2$; in this case, $\sqrt{V_{\sigma\sigma}V_{\pi\pi}}/V_{\sigma\pi}=8{-}22$ and the ratio of the interband constants
$\alpha$ can range from
$3$ to
$11$. The set of the Eliashberg coupling constants
$\lambda_{ij}^0$ has been qualitatively determined for relatively pure MgB
$_2$ with maximum values
$T_c\approx40$ K. The leading constant is $0.7<\lambda_{\sigma\sigma}^0\approx \lambda_{\text{eff}}^0<0.9$ and depends on the choice of the upper integration limit in the Bardeen-Cooper–Schrieffer (BCS) model and the effective Coulomb repulsion
$\mu_{\text{eff}}^*$. The characteristic ratio for the gap in the
$\sigma$ band is
$2\Delta_\sigma/k_{\text{B}}T_c=5.0{-}6.5$.
Received: 09.01.2014
Revised: 05.02.2014
DOI:
10.7868/S0370274X14050129
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