  The 2D superconductor-insulator transition in disordered ultrathin amorphous
bismuth films has been tuned both by electrostatic electron doping using the
electric field effect and by the application of parallel magnetic fields.
Electrostatic doping was carried out in both zero and nonzero magnetic fields,
and magnetic tuning was conducted at multiple strengths of electrostatically
induced superconductivity. The transitions were analyzed using finite size
scaling with critical exponent products nu*z = 0.65-0.7. The parallel critical
magnetic field increased with electron transfer as (dn_c-dn)^0.33, where dn is
the electron transfer and dn_c is its critical value, and the critical
resistance decreased linearly with dn. However at lower temperatures, in the
insulating regime, the resistance became larger than expected from
extrapolation of its temperature dependence at higher temperatures, and scaling
failed. These observations imply that although the electrostatic- and parallel
magnetic field- tuned superconductor-insulator transitions would appear to
belong to the same universality class and to be delineated by a robust phase
boundary that can be crossed either by tuning electron density or magnetic
field, in the case of the field-tuned transition at the lowest temperatures,
some different type of physical behavior turns on in the insulating regime.
