Role of surface-bound hole states in electric-field-driven superconductivity at the (110)-surface of diamond

Abstract

Hole states in electric-field-driven superconductivity at the (110)-surface of diamond are examined by means of first-principles calculations and one-dimensional tight-binding model calculations. It is found that surface-bound hole states confined near the surface by application of an electric field $E$ play a key role in superconductivity. Indeed, there is a critical external electric field $|{E}_{\mathrm{c}}|$ ($\ensuremath{\simeq}0.4$ V/\AA{}) for observing the superconductivity, which can be attributed to the second surface-bound hole state. With McMillan's formula and calculated phonon-electron coupling constants, we demonstrate that, in electric fields $l|{E}_{\mathrm{c}}|$ which correspond to a surface carrier density of $\ensuremath{\sim}2.3\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$, superconductivity may not be practically observed while the superconductivity transition temperature suddenly increases at $|{E}_{\mathrm{c}}|$.