  By means of systematically first-principles calculations and model analysis,
a complete phase diagram of the body-centered silicon(BC8-Si) via lattice
constant a and internal atomic coordinate x is explored, which demonstrates
that BC8-Si is a topological Luttinger semimetal(LSM) accompanied with
topologically nontrivial surface states, and the electronic properties of
BC8-Si can be further tuned to a normal insulator or topological Dirac
semimetal by very tiny changing of a and x. These results successfully explain
the contradictory transport reports of BC8-Si. More importantly, the
topological surface states in the LSM phase fill in the gap between the
topological matters and silicon, which provide an opportunity to integrate the
topological quantum devices and silicon chips together.
