  We propose an experimental scheme to realize the valley-dependent gauge
fields for ultracold fermionic atoms trapped in a state-dependent square
optical lattice. Our scheme relies on two sets of Raman laser beams to engineer
the hopping between adjacent sites populated by two-component fermionic atoms.
One set of Raman beams are used to realize a staggered \pi-flux lattice, where
low energy atoms near two inequivalent Dirac points should be described by the
Dirac equation for spin-1/2 particles. Another set of laser beams with proper
Rabi frequencies are added to further modulate the atomic hopping parameters.
The hopping modulation will give rise to effective gauge potentials with
opposite signs near the two valleys, mimicking the interesting strain-induced
pseudo-gauge fields in graphene. The proposed valley-dependent gauge fields are
tunable and provide a new route to realize quantum valley Hall effects and
atomic valleytronics.
