Critical fieldsHcandHc2of superconducting niobium

Abstract

New measurements of the thermodynamic critical field $H_c$ and the upper critical field $H_{c2\mathrm{}}$ of a niobium crystal are interpreted by using realistic microscopic theory. The theory of $H_{c2\mathrm{}}$ combined with band theory allows the $H_{c2\mathrm{}}$ measurements to be compared with de Haas—van Alphen measurements. Eliashberg theory allows the $H_c$ measurements to be compared with other experiments that are sensitive to the electron-phonon interaction. Our measurements of $H_{c2\mathrm{}}$ confirm the band theory of niobium as adjusted to match de Haas—van Alphen data. Our measurements of $H_c$ enable us to deduce the value of the electron-phonon-coupling parameter $\lambda$. Finally, we note a discrepancy between the value of the renormalization parameter $1+\lambda$ that is needed to match the $H_{c2\mathrm{}}$ data with the band theory and the value of $1+\lambda$ that is required to give the observed $H_c$.