Effect of a magnetic field up to 9 T on the temperature dependence of the pseudogap in YBa$_2$Cu$_3$O$_{7-δ}$ 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 $ρ(T)$, fluctuation conductivity (FLC) $σ'(T)$ and pseudogap $Δ^(T)$ in thin films of YBa$2$Cu$3$O${7-δ}$ 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, $T{\mathrm{pair}}$, which corresponds to the maximum of the $Δ^(T)$ dependence, shifts to the region of lower temperatures with increasing $B$, and the maximum value of $Δ^*(T_{\mathrm{pair}})$ 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 $Δ^(T)$ at $T_{\min}$, which becomes very pronounced with a subsequent increase in $B$. As a result, the overall value of $Δ^(T_G)$ decreases noticeably, most likely due to the pair-breaking effect. At the same time, $ΔT_{\mathrm{fl}}$ and $ξ_c(0)$ increase sharply by approximately 3 times with increasing $B$ above 1T. Our results confirm the possibility of the formation of a vortex state in YBa$_2$Cu$3$O${7-δ}$ by a magnetic field and its evolution with increasing $B$.