  The central role that materials play in human history is exemplified by the
three-age division of prehistory into the stone, bronze, and iron ages.
References to our present time as the information age or silicon age epitomizes
the important role that this semiconducting material came to play in the
development of computers and devices that permeate our daily lives. Here we
show that the electronic states in silicon have nontrivial topological
structures that are captured by a network of Berry flux lines that link at
points of high symmetry in the Brillouin zone. This complex network has
ice-nodal points where fluxes satisfy ice rules, making silicon a "nodal-chain
insulator". Fixing the longitudinal momentum parallel to such flux lines yields
a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. This
complex Berry-flux network implies a topologically stable two-fold degeneracy
along the X-W direction in all of silicon bands, a fact that is supported by
crystal symmetry arguments as well as direct inspection of the vast literature
on silicon band structures. Similarly to nodal-chain semimetals, we find
drumhead-like states in the regions that are delimited by the projections of
the bulk Berry flux network on the surface Brillouin zone.
