Deficiency of the scaling collapse as an indicator of a superconductor-insulator quantum phase transition

Abstract

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 2-dimensional superconducting films to magnetic-field driven superconductor-metal transition in 1-dimensional 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 reliable indicator of a QPT. We have also observed a sign-change of the zero-bias anomaly (ZBA) in the non-linear 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 non-linearity 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.Quantum phase transitions (QPT) occur at zero temperature between distinct ground states of matter; they are driven by a non-thermal parameter, g , which can be, for example, pressure or magnetic field. QPTs take place in many systems ranging from magnetic materials 1,2,3 and superconductors 4,5,6,7to cold atoms, 8 atomic nuclei 9,10 and stars. 11 The transition from one ground state to another can be of the first order, as in the case of clean metallic ferromagnets.12 It can also proceed by a smooth evolution of one-ground state to another over broad range of the driving parameter, as in the case of the crossover from Bardeen-Cooper-Schrieffer superconductivity to Bose-Einstein condensation.13 But, perhaps the most interesting is the case of continuous QPTs, which is characterized by the change of the ground state at certain critical value c

Multiple crossing points and possible quantum criticality in the magnetoresistance of thin TiN films

“…Note added. Recently, we became aware of recent work demonstrating that 2D scaling can also be successfully applied in 1D wires, supporting our point that scaling alone does not signal the presence of SIT [34].…”

Signatures of two-dimensional superconductivity emerging within a three-dimensional host superconductor

“…The observed crossover in length scales for electronic granularity and ξ could possibly explain the previously reported but unexplained 2D critical scaling at a quantum phase transition in BPBO. There has been recent work in one-dimensional (1D) disordered superconducting nanowires showing that 2D scaling anomalously provides superior "scaling collapse," which may point to a reverse microscopic phenomenon (49). On the other hand, it was explicitly noted that for BPBO, the scaling data for all of the compositions studied could not be fit to a 3D quantum phase transition and ruled out any temperature-dependent prefactor T −(d−2)=z in the resistivity; hence, d = 2 provided the best scaling for more than three orders of magnitude in the scaling variable (11).…”

Superconducting phase transition in inhomogeneous chains of superconducting islands

“…Therefore, this expression cannot be used at the lowest temperatures of the experiment, where clear critical current is observed in our V-I curves. Equation (29) is presented here for the completeness of the picture. The presence of magnetic field suppresses superconductivity in each aluminum island due to the Meissner currents.…”

“…The collapse of the curves provides evidence that a phase transition occurs in the chain when even number islands become normal. Note that it was recently demonstrated that the exact type of the phase transition cannot be determined from the scaling analysis along because models developed for two-dimensional systems appear to be applicable to onedimensional samples such as superconducting nanowires [29]. Theoretical model of Sec.…”