Are critical resistance and exponents at the 2D superconductor-insulator transition universal?
In plain words
Theory predicted that at the switch between superconductor and insulator the film resistance takes a universal value set by Planck constant and the electron charge, with simple scaling laws. Experiments find different values and exponents in different films.
Precise statement
The dirty-boson theory (Fisher 1990) predicts a universal critical sheet resistance $R_{c} = h/(4e^{2})$ and universal $z\nu$ at the B- or disorder-tuned transition. Measured $R_{c}$ varies by a factor of several and $z\nu$ ranges from $\sim 0.6$ to above 2; Ga films show a divergent effective $z\nu$ characteristic of a quantum Griffiths singularity (Xing et al. 2015). Classify the universality classes of the 2D transition with $1/r$ Coulomb interaction and quenched disorder, and determine whether $R_{c}$ and $z\nu$ are universal within each class.
What would settle it
Scaling analyses at $T$ far below the crossover scale in several material classes, with sample-to-sample comparison of $R_{c}$ and $z\nu$, matched to a theory assigning each to a class.
Status in the literature
Unverified note
A discontinuous (first-order) disorder-driven transition was reported in amorphous InOx films (Charpentier et al., Nature Physics 21, 104, 2025), which would place at least some films outside any continuous universality class.