Thickness-tuned superconductor-insulator transitions under magnetic field in a -NbSi

We have studied the thickness-induced superconductor-to-insulator transition in the presence of a magnetic field for a-NbSi thin films. Analyzing the critical behavior of this system within the ``dirty boson model,'' we have found a critical exponent product of νdz~0.4. The corresponding phase diagram in the $(H,d)$ plane is inferred. This small exponent product, as well as the nonuniversal value of the critical resistance found at the transition, calls for further investigations in order to thoroughly understand these transitions.