Electrostatic Tuning of the Hole Density in ${{\mathrm{NdBa}}_2{\mathrm{Cu}}_{3}O}_{7-\mathit{\delta }}$ Films and its Effect on the Hall Response

We have used the ferroelectric field effect in heterostructures based on superconducting ${\mathrm{NdBa}}_2-{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ and ferroelectric $\mathrm{Pb}\left({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}\right){\mathrm{O}}_3$ to electrostatically modulate in a reversible and nonvolatile fashion the hole carrier density of the superconducting layer. Reversing the ferroelectric polarization induces a constant relative change in the resistivity and Hall constant of $9\%$ and $6\%$, respectively, at all temperatures above the superconducting transition. The cotangent of the Hall angle displays a $T^2$ dependence with a slope that increases as the carrier density is reduced.