Exact continuum theory of anti-Klein tunneling in bilayer graphene

Abstract

Exact conditions for anti-Klein transmission zeros are found analytically with a 4-component continuum approach which includes trigonal warping. Anti-Klein tunneling occurs at oblique incidence on steps and barriers with soft and hard walls as well as in the known case of normal incidence on a hard step. The necessary energy and angle of incidence depend on the crystallographic orientation of the step or barrier. At normal incidence on an armchair step in unbiased bilayer graphene, anti-Klein tunneling occurs because both the continuum and the tight binding Hamiltonians are invariant under layer and site interchange. At oblique incidence, anti-Klein tunneling is valley-dependent even in the absence of trigonal warping. An experimental arrangement that functions both as a detector of anti-Klein tunneling and a valley polarizer is suggested. There are cases where anti-Klein tunneling occurs in the 4-component theory but not in the 2-component approximation.