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.
Categories: cond-mat.supr-con