Quantum superconductor-insulator transition: implications of BKT critical behavior

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, T) BKT behavior implies: an explicit quantum scaling function for R(x, T) along the superconducting branch ending at the nonuniversal critical value R-c = R(x(c)); a BKT-transition line T-c(x) proportional to (x - x(c))(z (nu) over bar), where z is the dynamic exponent and (nu) over bar the exponent of the zero-temperature correlation length; independent estimates of z (nu) over bar, z and (nu) over bar 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 the data of Bollinger et al (2011 Nature 472 458) taken on gate voltage tuned epitaxial films of La2-xSrxCuO4 that are one unit cell in thickness. The resulting estimates, z similar or equal to 3.1 and (nu) over bar similar or equal to 0.52, indicate a clean 2D-QSI critical point where hyperscaling, the proportionality between d/lambda(2)(0) and T-c, and the correspondence between the quantum phase transitions in D dimensions and the classical ones in (D + z) dimensions are violated.