By capacitively charging an underdoped ultrathin La2−xSrxCuO4 film with an electric field applied across a gate insulator with a high dielectric constant, relative changes of the areal superfluid density n s of unprecedented strength were observed in measurements of the film kinetic inductance.Although n s appears to be substantially reduced by disorder, the data provide, for the first time on the same sample, direct compelling evidence for the Uemura relation Tc ∝ n s (T = 0) in the underdoped regime of copper-oxide superconductors.PACS numbers: 74.62. Yb, 74.78.Bz, 74.25.Nf, 74.90.+n It is widely accepted that copper-oxide superconductors in the underdoped regime are doped charge transfer insulators whose properties strongly depend on the concentration of the "free" electrical carriers. If the doping level is measured by a parameter x expressing the number of free carriers per Cu site in the CuO 2 planes, in the hole-doped materials superconductivity typically sets in at x ≈ 0.05, reaches its maximum strength at x ≈ 0.15, and disappears above x ≈ 0.30. Usually, x is changed by non-isovalent chemical substitution of the antiferromagnetic insulating parent compound (x = 0): for instance, by substituting a Sr +2 ion for one of the La in the range 10 −4 − 10 −3 were also observed in surface impedance measurements at microwave frequencies [8], whose interpretation, however, was less transparent because of the non-linear response of the SrTiO 3 gate insulator to the applied electric field.In this Letter we describe an experiment in which the temperature and electric-field dependences of L −1 k were investigated by capacitively charging an epitaxially grown ultrathin (two-unit-cell-thick) LSCO film in the underdoped regime (x = 0.1) with an electrostatic field E applied across a gate insulator with a high dielectric constant. We find that the field-induced change ∆L −1 k (T, E) is a non-monotonic function of T which, for the highest fields accessible to the experiment (E ≈ 2 × 10 8 V/m), reaches a maximum corresponding to ∼ 20% of L −1 k (0, 0) at T /T c ≈ 0.7 and saturates to ∼ 10% of L −1 k (0, 0) at very low temperatures. These large modulations offer new interesting opportunities to explore the intriguing superconducting behavior of the copper oxides. As an illustration, the field-induced relative changes ∆L −1k (0, 0) measured at very low temperature were correlated, for the first time on the same sample, with the corresponding relative variations ∆T c (E)/T c (0). Both quantities were found to vary linearly with E and, quite remarkably, ∆L −1, a result providing direct compelling evidence for the validity of Uemura's relation [9] T c ∝ n s (0)/m * for underdoped copper-oxide superconductors. We consider this observation as the central result emerging from this work.To achieve a substantial electrostatic modulation of n s in a thin film, it is essential that its thickness d is of the order of the Thomas-Fermi charge screening length λ T F , the field-induced charges being confined in a layer
