Electrostatic doping of high T$_{c}$ superconductors*

The application of field effect transistor concepts to electrostatically doped strongly correlated electron systems has been the focus of intense research during the last years [C. H. Ahn et al., Rev. Mod. Phys. 78, 1185 (2006)]. In this talk we will show our recent results on Electronic Double Layer Transistor (EDLT) techniques applied to high T$_{c}$ cuprates. The EDLT configuration, which employs ionic liquids as gate dielectrics, has succeeded in achieving unprecedented charge transfers, of the order of 10$^{15}$ carriers/cm$^{2}$. This large accumulation and depletion of carriers allows us to explore the phase diagram of YBa$_{2}$Cu$_{3}$O$_{7-x}$ and La$_{2}$CuO$_{4+\delta}$. We will focus on the physics of the superconductor to insulator transition [X. Leng et al., Phys. Rev. Lett. 107, 027001 (2011)] and discuss the magneto-transport properties of the underdoped and overdoped regions of the phase diagram [X. Leng, et al., arXiv:1108.0083v1].