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The nature of the magnetic-field driven superconductor-to-insulatorquantum-phase transition in two-dimensional systems at zero temperature hasbeen under debate since the 1980s, and became even more controversial after theobservation of a quantum-Griffiths singularity. Whether it is induced byquantum fluctuations of the superconducting phase and the localization ofCooper pairs, or is directly driven by depairing of these pairs, remains anopen question. We herein experimentally demonstrate that in weakly-pinningsystems and in the limit of infinitely wide films, a sequentialsuperconductor-to-Bose insulator-to-Fermi insulator quantum-phase transitiontakes place. By limiting their size smaller than the effective penetrationdepth, however, the vortex interaction alters, and the superconducting statere-enters the Bose-insulating state. As a consequence, one observes a directsuperconductor-to-Fermi insulator in the zero-temperature limit. In narrowfilms, the associated critical-exponent products diverge along thecorresponding phase boundaries with increasing magnetic field, which is ahallmark of the quantum-Griffiths singularity.

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