Interfacial superconductivity in Cu/Cu$_{\rm{2}}$O and its effect on shielding ambient electric fields

A model is presented for two-dimensional superconductivity at semiconductor-on-metal interfaces mediated by Coulomb interactions between electronically-active interface charges in the semiconductor and screening charges in the metal. The junction considered is native Cu$_{\rm{2}}$O on Cu in which an interfacial double charge layer of areal density $n$, comprising superconducting holes in Cu$_{\rm{2}}$O and mediating electrons in Cu, is induced in proportion to a sub-monolayer of adsorbed $^{\rm{4}}\rm{He}$ atoms. Evidence for superconductivity on copper with prior air exposure is revealed in new analysis of previously published work function data. Based on a theory developed for layered superconductors, the intrinsic transition temperature $T_{\rm{C}}$ = $\beta$ $n$$^{\rm{1/2}}$/$\zeta$ is determined by $n$ and transverse distance $\zeta$ $\simeq$ 2.0 $\rm{\r{A}}$ between the charge layers; $\beta$ = 1.933(6) $e$$^{\rm{2}}$$\bar{\lambda}$$_{\rm{C}}$/k$_{\rm{B}}$ = 1247.4(3.7) K-$\rm{\r{A}}$$^{\rm{2}}$ is a universal constant involving the reduced Compton wavelength of the electron $\bar{\lambda}$$_{\rm{C}}$. This model is applied to understanding the shielding of copper work-function patch and gravitational compression electric fields reported in the Witteborn-Fairbank gravitational electron free fall experiment. Interfacial superconductivity with $n$ $\simeq$ 1.6 $\times$ 10$^{\rm{12}}$ $\rm{cm}^{\rm{-2}}\rm{,}$ $T_{\rm{C}}$ $\simeq$ 7.9 K and Berezinski\u{i}-Kosterlitz-Thouless temperature $T_{\rm{BKT}}$ $\simeq$ 4.4 K accounts for the shielding observed at temperature $T$ $\simeq$ 4.2 K. Helium desorption and concomitant decreases in $n$ and $T_{\rm{C}}$ replicate the temperature transition in ambient electric fields on falling electrons, as observed by Lockhart et al., and the vanishing of superconductivity above $T$ $\simeq$ 4.8 K.