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

Abstract

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 ${\alpha }^{2}F(\omega )$ for tunneling along the c axis. Our results are compared with recent experimental tunneling and point-contact data.

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

References in corpus (4)

• Vortex Imaging in the pi-Band of Magnesium Diboride
• Electronic Structure, Electron-Phonon Coupling, and Multiband Effects in MgB2
• Direct evidence for two-band superconductivity in MgB_2 single crystals from directional point-contact spectroscopy in magnetic fields
• Search for E_2g phonon modes in MgB_2 single crystals by point-contact spectroscopy

Cited by in corpus (19)

• Probing multiband superconductivity by point-contact spectroscopy
• Properties of the superconducting state in a two-band model
• Two-band Eliashberg equations and the experimental Tc of the diboride Mg1-xAlxB2
• Critical Field of Al-Doped MgB2 Samples: Correlation with the Suppression of Sigma-Band Gap
• Electronic, dynamical and superconducting properties of CaBeSi
• A Study of Carbon Substitutions in MgB_2 within the two-band Eliashberg theory
• Proximity and Josephson effects in microstructures based on multiband superconductors
• Advances in point-contact spectroscopy: two-band superconductor MgB2 (A review)
• Pressure dependence of critical temperature in MgB2 and two bands Eliashberg theory
• Multiband superconductivity in Pb, H under pressure and CaBeSi from {\it ab-initio} calculations
• Point contact spectroscopy in Fe-based superconductors: recent advancements and future challenges
• Revisiting optical properties of MgB${}_2$ with a high-quality sample prepared by a HPCVD method
• Response Theory of the Electron-Phonon Coupling
• Superconductivity of Magnesium Diboride: Theoretical Aspects
• Prospects to attain room temperature superconductivity
• Point-contact study of the LuNi2B2C borocarbide superconducting film
• The determination of the electron-phonon interaction from tunneling data in the two-band superconductor MgB2
• Microscopic insight on the pump-probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory
• Quantifying proximity-induced superconductivity from first-principles calculations