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It is shown that potential barriers in bilayer graphene (BLG) and monolayertransition metal dichalcogenides (TMDs) can split a valley unpolarized incidentcurrent into reflected and transmitted currents with opposite valleypolarization. Valley asymmetric transmission inevitably occurs because of thelow symmetry of the total Hamiltonian and when total external reflection occursthe transmission is 100% valley polarized in BLG and 100% spin and valleypolarized in TMDs, except for exponentially small corrections. By adjusting thepotential, 100% polarization can be obtained regardless of the crystallographicorientation of the barrier. A valley polarizer can be realized by arranging fora collimated beam of carriers to be incident on a barrier within the range ofangles for total external reflection. The transmission coefficients of barrierswith a relative rotation of $\pm\pi/3$ are related by symmetry. This allows twobarriers to be used to demonstrate that the current is valley polarized. Asoft-walled potential is used to model the barrier and the method used to findthe transmission coefficients is explained. In the case of monolayer TMDs, a4-band k.p Hamiltonian is used and the k.p parameters are obtained by fittingto ab-initio band structures.

physical review. b./physical review. b

Complete Spin and Valley Polarization by Total External Reflection from  Potential Barriers in Bilayer Graphene and Monolayer Transition Metal  Dichalcogenides