Abstract
We investigate the electron transport in the linear regime in previously proposed quantum wire valley filters [Phys Rev B $\bf{88}$, 125422 (2013)] in bilayer graphene. The electron transmission rates are calculated with a tight-binding model by recursive Green's function method. The filtering effects are illustrated by the study of electron transmission through two back-to-back filters. For each filter, two kinds of structure - called type-I and type-II devices are considered which use different band alignments to provide electron confinement in the quantum wire, with the type-II device being more easily accessible by the present experimental gating technology. Each filter is controlled by a transverse electric field, and we study the two configurations where the two filters are transversely biased by parallel and antiparallel fields, respectively. A sharp contrast of transmission rates is found between parallel and anti-parallel configurations when each filter can generate a sizable valley polarization. The numerical results are explained with an auxiliary two band model. This work gives quantitative predictions to the electron transport in the filters together with some physical understandings about the numerical results.