Deficiency Of The Scaling Collapse As An Indicator Of A Superconductor-Insulator Quantum Phase Transition

Finite-size scaling analysis is a well-accepted method for identification and characterization of quantum phase transitions (QPTs) in superconducting, magnetic, and insulating systems. We formally apply this analysis in the form suitable for QPTs in two-dimensional (2D) superconducting films to magnetic-field-driven superconductor-metal transition in one-dimensional (1D) MoGe nanowires. Despite being obviously inapplicable to nanowires, the 2D scaling equation leads to a high-quality scaling collapse of the nanowire resistance in the temperature and resistance ranges comparable or better to what is accepted in the analysis of the films. Our results suggest that the appearance and the quality of the scaling collapse by itself is not a definitive indicator of a QPT. We have also observed a sign change of the zero-bias anomaly (ZBA) in the nonlinear resistance, occurring exactly at the critical field of the accidental QPT. This behavior is often taken as an additional confirmation of the transition. We argue that in nanowires, the nonlinearity is caused by electron heating and has no relation to the critical fluctuations. Our observation suggests that similar to the scaling collapse, the sign change of ZBA can be a misleading indicator of QPT.