Phase Diagram of Electron Systems near the Superconductor-Insulator Transition

The zero temperature phase diagram of Cooper pairs exposed to disorder and a magnetic field is determined theoretically from a variational approach. Four distinct phases are found: a Bose and a Fermi insulating, a metallic, and a superconducting phase, respectively. The results explain the giant negative magnetoresistance found experimentally in In-O, TiN, Be and high-T_c materials.