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Orientation-dependent electric transport and band filling in hole co-doped epitaxial diamond films

Diamond, a well-known wide-bandgap insulator, becomes a low-temperature superconductor upon substitutional doping of carbon with boron. However, limited boron solubility and significant lattice disorder introduced by boron doping prevent attaining the theoretically-predicted high-temperature superconductivity. Here we present an alternative co-doping approach, based on the combination of ionic gating and boron substitution, in hydrogenated thin films epitaxially grown on (111)- and (110)-oriented single crystals. Gate-dependent electric transport measurements show that the effect of boron doping strongly depends on the crystal orientation. In the (111) surface, it strongly suppresses the charge-carrier mobility and moderately increases the gate-induced doping, while in the (110) surface it strongly increases the gate-induced doping with a moderate reduction in mobility. In both cases the maximum total carrier density remains below $2{\cdot}10^{14}\,$cm$^{-2}$, three times lower than the value theoretically required for high-temperature superconductivity. Density-functional theory calculations show that this strongly orientation-dependent effect is due to the specific energy-dependence of the density of states in the two surfaces. Our results allow to determine the band filling and doping-dependence of the hole scattering lifetime in the two surfaces, showing the occurrence of a frustrated insulator-to-metal transition in the (110) surface and of a re-entrant insulator-to-metal transition in the (111) surface.