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

自从1980年代以来，在零温度下二维系统中磁场驱动的超导体到绝缘体的量子相变的性质一直处于争论之中，在观察到量子格里菲斯奇异性之后，这一问题变得更加有争议。它是由超导相的量子涨落和库珀对的定位引起的，还是由这些对的去配对直接驱动的，仍然是一个悬而未决的问题。我们在此通过实验证明，在弱钉扎系统中以及在无限宽膜的限制下，发生了顺序的超导体到玻色绝缘子到费米绝缘子的量子相变。但是，通过将其尺寸限制为小于有效穿透深度，涡旋相互作用会发生变化，并且超导状态会重新进入玻色绝缘状态。结果，在零温度极限下观察到直接的超导体到费米绝缘子。在狭窄的薄膜中，随着磁场的增加，相关的临界指数乘积沿着相应的相边界发散，这是量子格里菲斯奇异性的标志。