Electrostatic Modulation of the Superfluid Density in an Ultrathin ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ Film

By capacitively charging an underdoped ultrathin ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ film with an electric field applied across a gate insulator with a high dielectric constant, relative changes of the areal superfluid density $n_{s\square }$ of unprecedented strength were observed in measurements of the film kinetic inductance. Although $n_{s\square }$ 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 $T_c\propto n_{s\square }(T=0)$ in the underdoped regime of copper-oxide superconductors.

Figure 1

Cross section of the multilayer electric-field-effect device. N: normal; SC: superconducting.

Figure 2

(a) Temperature dependence of the inverse kinetic inductance at three values of the gate voltage ($V_G=0,\pm 3\mathrm{V}$) and of its normalized deviation for $|V_G|=3\mathrm{V}$ from the $V_G=0$ data of an underdoped ($x=0.1$) 2-UC-thick LSCO film. The full curve is the prediction of Eq. (3); (b) universal temperature dependence $f(t)$ of the normalized $L_k^{-1}$ vs $T$ curves of (a). Notice the $t^2$ dependence of $[1-f(t)]$ at low temperatures ($t<0.45$) highlighted by the dashed straight line.

Figure 3

Comparison of the field-induced relative changes of the critical temperature and of the inverse kinetic inductance at very low temperature ($T=0.6\mathrm{K}$, $T/T_c\approx 0.07$) for an underdoped ($x=0.1$) 2-UC-thick LSCO film as a function of the applied electrostatic field. The dashed straight line is a fit according to Eq. (2).