  As a superconducting thin film becomes disordered and subject to an
increasing magnetic field, a point is reached when it undergoes a transition
from a superconducting to an insulating state. We use the Bogoliubov-De-Gennes
equations and a novel Monte-Carlo approach to study this transition
numerically, starting from a microscopic hamiltonian. The key effect of
disorder is to create 'islands' of strong superconductivity, coupled by regions
that are only weakly superconducting. In the case of weak disorder, an
increasing magnetic field eventually destroys the superconducting state
throughout the material, leading to an insulator. On the other hand, when
disorder is strong, superconductivity persists in the islands, and the effect
of a magnetic field is to suppress the coupling between them, resulting in
strong superconducting phase fluctuations, again leading to an insulating
state. These findings may be relevant to the high-temperature superconductors,
where intrinsic disorder may play a role.
