Metal-insulator transition and superconductivity in boron-doped diamond

Abstract

We report on a detailed analysis of the transport properties and superconducting critical temperatures of boron-doped diamond films grown along the {100} direction. The system presents a metal-insulator transition (MIT) for a boron concentration $({n}_{B})$ on the order of ${n}_{c}\ensuremath{\sim}4.5\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, in excellent agreement with numerical calculations. The temperature dependence of the conductivity and Hall effect can be well described by variable range hopping for ${n}_{B}<{n}_{c}$ with a characteristic hopping temperature ${T}_{0}$ strongly reduced due to the proximity of the MIT. All metallic samples (i.e., for ${n}_{B}>{n}_{c}$) present a superconducting transition at low temperature. The zero-temperature conductivity ${\ensuremath{\sigma}}_{0}$ deduced from fits to the data above the critical temperature $({T}_{c})$ using a classical quantum interference formula scales as ${\ensuremath{\sigma}}_{0}\ensuremath{\propto}{({n}_{B}∕{n}_{c}\ensuremath{-}1)}^{\ensuremath{\nu}}$ with $\ensuremath{\nu}\ensuremath{\sim}1$. Large ${T}_{c}$ values $(\ensuremath{\geqslant}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ have been obtained for boron concentration down to ${n}_{B}∕{n}_{c}\ensuremath{\sim}1.1$ and ${T}_{c}$ surprisingly mimics a ${({n}_{B}∕{n}_{c}\ensuremath{-}1)}^{1∕2}$ law. Those high ${T}_{c}$ values can be explained by a slow decrease of the electron-phonon coupling parameter $\ensuremath{\lambda}$ and a corresponding drop of the Coulomb pseudopotential ${\ensuremath{\mu}}^{*}$ as ${n}_{B}\ensuremath{\rightarrow}{n}_{c}$.