Size dependent nature of the magnetic-field driven superconductor-to-insulator quantum-phase transitions

The nature of the magnetic-field driven superconductor-to-insulator quantum-phase transition in two-dimensional systems at zero temperature has been under debate since 1980s, and became even more controversial after observation a quantum-Griffiths singularity. Whether it is induced by quantum fluctuations superconducting phase localization Cooper pairs, or directly depairing these remains an open question. We herein experimentally demonstrate that weakly-pinning limit infinitely wide films, sequential superconductor-to-Bose insulator-to-Fermi insulator takes place. By limiting their size smaller than effective penetration depth, however, vortex interaction alters, state re-enters Bose-insulating state. As consequence, one observes direct superconductor-to-Fermi zero-temperature limit. In narrow associated critical-exponent products diverge along corresponding boundaries with increasing magnetic field, which hallmark