Can one extract the electron-phonon-interaction from tunneling data in case of the multigap superconductor MgB$_2$?

Details Can one extract the electron-phonon-interaction from tunneling data in case of the multigap superconductor MgB$_2$? Can one extract the electron-phonon-interaction from tunneling data in case of the multigap superconductor MgB$_2$?

2003-01-28

arxiv.org/abs/cond-mat/0301542v1

Phys. Rev., B68, 132503 (2003)

Physics

Condensed Matter

Superconductivity

5 pages, 3 figures. Submitted to Phys. Rev. B (Brief Reports)

Scientific paper

10.1103/PhysRevB.68.132503

In the present work we calculate the tunneling density of states (DOS) of MgB% $_{2}$ for different tunneling directions by directly solving the two-band Eliashberg equations (EE) in the real-axis formulation. This procedure reveals the fine structures of the DOS due to the optical phonons. Then we show that the numeric inversion of the standard \emph{single-band} EE (the only available method), when applied to the \emph{two-band} DOS of MgB$_{2}$, may lead to wrong estimates of the strength of certain phonon branches (e.g. the $E_{2g}$) in the extracted electron-phonon spectral function $\alpha^{2}F(\omega)$. The fine structures produced by the two-band interaction at energies between 20 and 100 meV turn out to be clearly observable only for tunneling along the $ab$ planes, when the extracted $\alpha ^{2}F(\omega)$ contains the combination $\alpha ^{2}F_{\sigma \sigma}(\omega)$\textbf{+}$\alpha ^{2}F_{\sigma \pi }(\omega)$, together with a minor $\alpha ^{2}F_{\pi \pi}(\omega )$\textbf{+}$\alpha ^{2}F_{\pi \sigma} (\omega)$ component. Only in this case it is possible to extract information on the $\sigma$-band contribution to the spectral functions. For any other tunneling direction, the $\pi$-band contribution (which does not determine the superconducting properties of MgB$_{2}$) is dominant and almost coincides with the whole $\alpha^2F(\omega)$ for tunneling along the c axis. Our results are compared with recent experimental tunneling and point-contact data.

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