Two-stage crossover from thermal to quantum flux creep of dilute vortex ensembles in various high-$T_c$ superconducting thin films

The thermal-to-quantum flux creep crossover at low vortex densities has been studied in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7,$ ${\mathrm{TlBa}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{7-\delta },$ and ${\mathrm{HgBa}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{6+\delta }$ thin films using ac susceptibility. The crossover temperatures $T_{\mathrm{cr}}$ are 10–11, 17, and 30 K, respectively. Both thermal and quantum flux creep is suppressed as the vortex density is decreased. We observe a two-stage nature in the crossover behavior which appears to be a general property of all the three materials studied.