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 ≈ 0.01 eV at low temperature. If the boron/carbon ratio is increased above about 1‰, 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.

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► Activation energy (= 0.37 eV) in blue diamonds is identified as “Hubbard-U” for 2B → B+ + B−.
► B+ and B− sites are identified in the experimental data and in calculations.
► There are large sp2 components in the wavefunction of B+ and neutral B centers.
► At high concentration of B, U → 0 since the B+/B− subphase is stabilized relative to B/B.
► Superconductivity is due to the interaction between (B+/B−) and (B/B) electronic states, and phonons.