Magnetic field effects on $T_c$ and the pseudogap onset temperature in cuprate superconductors

We study the sensitivity of $T_c$ and the pseudogap onset temperature, $T^{\ast }$, to low fields, $H$, for cuprate superconductors, using a BCS-based approach extended to arbitrary coupling. We find that $T^{\ast }$ and $T_c$, which are of the same superconducting origin, have very different $H$ dependences. The small coherence length makes $T^{\ast }$ rather insensitive to the field. However, the presence of the pseudogap at $T_c$ makes $T_c$ more sensitive to $H$. Our results for the coherence length $\xi$ fit well with existing experiments. We predict that very near the insulator $\xi$ will rapidly increase.