Combined tight-binding and configuration interaction study of unfolded electronic structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> color center in Si

We have theoretically studied the $G$ center in bulk silicon material using the empirical tight-binding model for calculations of unfolded band structures with configuration interaction correction for the exciton at $\mathrm{\ensuremath{\Gamma}}$ point of the Brillouin zone. The $G$ center in B configuration (emissive) being a candidate structure as the telecom single- and entangled-photon source has two substitutional carbons and one interstitial atom embedded into the bulk in six equally possible configurations. Taking advantage of the low computation effort of the tight-binding and unfolding approaches, it is possible to calculate and analyze the behavior of a variety of electronic configurations. Our tight-binding model is able to describe not only the behavior of the $G$ center in the silicon bulk but using the unfolding approach, it can also pinpoint the contributions of different elements of the supercell on the final pseudoband structure. Moreover, the configuration interaction correction with single-particle basis states computed by our unfolded tight-binding model predicts a very small fine-structure splitting of the ground state exciton, both for bright and dark doubletes, in the studied system. That underscores the possibility of the silicon $G$ center to become a very good emitter of single and entangled photons for quantum communication and computation applications.