  This work investigates the feasibility of electrical valley filtering for
holes in transition metal dichalcogenides. We look specifically into the scheme
that utilizes a potential barrier to produce valley-dependent tunneling rates,
and perform the study with both a k.p based analytic method and a recursive
Green's function based numerical method. The study yields the transmission
coefficient as a function of incident energy and transverse wave vector, for
holes going through lateral quantum barriers oriented in either armchair or
zigzag directions, in both homogeneous and heterogeneous systems. The main
findings are the following: 1) the tunneling current valley polarization
increases with increasing barrier width or height, 2) both the valley-orbit
interaction and band structure warping contribute to valley-dependent
tunneling, with the former contribution being manifest in structures with
asymmetric potential barriers, and the latter being orientation-dependent and
reaching maximum for transmission in the armchair direction, and 3) for
transmission ~ 0.1, a tunneling current valley polarization of the order of 10%
can be achieved.
