Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

Magnetization measurements under hydrostatic pressure up to $10.5\mathrm{kbar}$ in zirconium dodecaboride $\mathrm{Zr}{\mathrm{B}}_{12}$ superconductor ($T_c\simeq 6.0\mathrm{K}$ at $p=0$) were carried out. A negative pressure effect on $T_c$ with $d{T}_c∕dp=-0.0225\left(3\right)\mathrm{K}∕\mathrm{kbar}$ was observed. The electron-phonon coupling constant ${\lambda }_{\mathrm{el}\text{−}\mathrm{ph}}$ decreases with increasing pressure with $d\ln {\lambda }_{\mathrm{el}\text{−}\mathrm{ph}}∕dp\simeq -0.20\%∕\mathrm{kbar}$. The magnetic field penetration depth $\lambda$ was studied in the Meissner state and, therefore, probes mainly 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 $\lambda \left(0\right)=140\left(30\right)\mathrm{nm}$ and ${\Delta }_0=1.251\left(9\right)\mathrm{meV}$, respectively. ${\Delta }_0$ scales linearly with $T_c$ as $2{\Delta }_0∕k_B{T}_c=4.79\left(1\right)$. The studies of the pressure effect on $\lambda$ reveal that ${\lambda }^{-2}$ increases with pressure with $d\ln {\lambda }^{-2}\left(0\right)∕dp=0.60\left(23\right)\%∕\mathrm{kbar}$. This effect cannot be explained within the framework of conventional adiabatic electron-phonon pairing, suggesting the possibility that close to the surface an unconventional nonadiabatic character of the electron-phonon coupling takes place.