Hubbard-U and disproportionation in superconducting boron doped diamond

Synthetic and natural diamonds containing small amounts of boron are conducting with apparent activation energy of 0.37 eV at high temperature and approximate to 0.01 eV at low temperature. If the boron/carbon ratio is increased above about 1 parts per thousand, the higher activation energy starts to decrease to zero. By applying high pressure and high temperature Ekimov et al. managed to raise the B/C ratio above 1%. This material is superconducting below a few Kelvin. It is shown here that at low B/C ratio the MIR absorption at 0.37 eV can be identified with vertical Hubbard-U. Increasing the boron concentration Hubbard-U decreases to zero. Apparently B+/B- becomes more stable than B/B as a sub-lattice phase. It is shown that this is due to the smaller distance between the boron sites. The presence of B+, B, and B-_(-) in highly boron doped diamond is supported by NMR, Raman, and IR data in combination with simple calculations.