  We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical
behavior on the two dimensional (2D) quantum superconductor-insulator (QSI)
transition driven by the tuning parameter x. Concentrating on the sheet
resistance R(x) BKT behavior implies: an explicit quantum scaling function for
R(x) along the superconducting branch ending at the nonuniversal critical value
R_c=R(x_c); a BKT-transition line T_c(x) that is proportional to (x-x_c)^(z*nu)
where z is the dynamic and nu the exponent of the zero temperature correlation
length; independent estimates of z*nu, z and nu from the x dependence of the
nonuniversal parameters entering the BKT expression for the sheet resistance.
To illustrate the potential and the implications of this scenario we analyze
data of Bollinger et al. taken on gate voltage tuned epitaxial films of
La_(2-x)Sr_xCuO_4 that are one unit cell thick. The resulting estimates z=2.35
and nu=0.63 point to a 2D-QSI critical point where hyperscaling, the
proportionality between d/\lambda^2(0) and T_c, and the correspondence between
quantum phase transitions in D and classical ones in (D+z) dimensions are
violated and disorder is relevant.
