Anomalous electron-phonon coupling probed on the surface of ZrB${}_{12}$ superconductor

Abstract

Magnetization measurements under hydrostatic pressure up to 10.5 kbar in zirconium dodecaboride ZrB${}_{12}$ superconductor ($T_c\simeq 6.0$ K at $p=0$) were carried out. A negative pressure effect on $T_c$ with $\mathrm{d}{T}_c/\mathrm{d}p=-0.0225(3)$ K/kbar was observed. The electron-phonon coupling constant ${\lambda }_{el-ph}$ decreases with increasing pressure with $\mathrm{d}\ln {\lambda }_{el-ph}/\mathrm{d}p\simeq -0.20$%/kbar. The magnetic field penetration depth $\lambda$ was studied in the Meissner state and, therefore, probes only the surface of the sample. The absolute values of $\lambda$ and the superconducting energy gap at ambient pressure and zero temperature were found to be $\lambda (0)=$140(30) nm and ${\Delta }_0=$1.251(9) meV, respectively. ${\Delta }_0$ scales linearly with $T_c$ as $2{\Delta }_0/k_B{T}_c=4.79(1)$. The studies of the pressure effect on $\lambda$ reveal that ${\lambda }^{-2}$ increases with pressure with $\mathrm{d}\ln {\lambda }^{-2}(0)/\mathrm{d}p=0.60(23)$ %/kbar. This effect can not be explained within the framework of conventional adiabatic electron-phonon pairing, suggesting that close to the surface, an unconventional {\it non-adiabatic} character of the electron-phonon coupling takes place.

5 pages, 3 figures