  The weak magnetic field induced reduction of the low-temperature superfluid
density in cuprate superconductors is studied based on the kinetic energy
driven superconducting mechanism. The electromagnetic response kernel is
evaluated by considering both couplings of the electron charge and electron
magnetic momentum with a weak magnetic field and employed to calculate the
superfluid density, then the main features of the weak magnetic field induced
reduction of the low-temperature superfluid density are well reproduced. The
theory also shows that the striking behavior of the weak magnetic field induced
reduction of the low-temperature superfluid density is intriguingly related to
both depairing due to the Pauli spin polarization and nonlocal response in the
vicinity of the d-wave gap nodes on the Fermi surface to a weak magnetic field.
