Effect of a magnetic field up to 9 T on the temperature dependence of the pseudogap in YBa${}_2$Cu${}_3$O${}_{7-\delta }$ films

The work analyzes the effect of a magnetic field $B$ directed along the $c$ axis ($B\parallel c$) up to 9~T on the resistivity $\rho (T)$, fluctuation conductivity (FLC) ${\sigma }^{\mathrm{\prime }}(T)$ and pseudogap ${\mathrm{\Delta }}^{\ast }(T)$ in thin films of YBa${}_2$Cu${}_3$O${}_{7-\delta }$ with a critical temperature of the superconducting transition $T_c=88.8$~K. In contrast to previous work, where the magnetic field was directed along the $ab$ plane ($B\parallel ab$), the influence of the field on the sample is stronger due to the contribution of both spin–orbit and Zeeman effects. It was found that the BEC–BCS transition temperature, $T_{\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}}$, which corresponds to the maximum of the ${\mathrm{\Delta }}^{\ast }(T)$ dependence, shifts to the region of lower temperatures with increasing $B$, and the maximum value of ${\mathrm{\Delta }}^{\ast }(T_{\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}})$ decreases in fields $B>5$~T. It was found that with increasing field, the low-temperature maximum near $T_0$ is smeared and disappears at $B>1$~T. In addition, above the Ginzburg temperature $T_G$, for $B>1$~T, a minimum appears on ${\mathrm{\Delta }}^{\ast }(T)$ at $T_{\min }$, which becomes very pronounced with a subsequent increase in $B$. As a result, the overall value of ${\mathrm{\Delta }}^{\ast }(T_G)$ decreases noticeably, most likely due to the pair-breaking effect. At the same time, $\mathrm{\Delta }{T}_{\mathrm{f}\mathrm{l}}$ and ${\xi }_c(0)$ increase sharply by approximately 3 times with increasing $B$ above 1~T. Our results confirm the possibility of the formation of a vortex state in YBa${}_2$Cu${}_3$O${}_{7-\delta }$ by a magnetic field and its evolution with increasing $B$.