  In analogy with light refraction at optical boundary, ballistic electrons
also undergo refraction when propagate across a semiconductor junction.
Establishing a negative refractive index in conventional optical materials is
difficult, but the realization of negative refraction in electronic system is
conceptually straightforward, which has been verified in graphene p-n junctions
in recent experiments. Here, we propose a model to realize double refraction
and double focusing of electric current by a normal-hexagonal semiconductor
junction. The double refraction can be either positive or negative, depending
on the junction being n-n type or p-n type. Based on the valley-dependent
negative refraction, a spin splitter (valley splitter) is designed at the p-n
junction system, where the spin-up and spin-down electrons are focused at
different regions. These findings may be useful for the engineering of double
lenses in electronic system and have underlying application of spin splitter in
spintronics.
