We study topological bound states in quantum dots defined by an electric field in bilayer graphene. An external field is perpendicular to the bilayer, and changes sign in a finite region that defines the quantum dot. The electric field opens a gap in the bilayer graphene, and the reversed field creates a domain wall with one-dimensional chiral gapless bands localized therein. The finite size of dots leads to quantization of these bands and the appearance of discrete bound states localized at the dot boundary. We consider rectangular dots oriented along the armchair and zigzag directions. We go beyond a simple continuum one-valley model and use an atomistic tight-binding approach. This allows us to identify new effects related to the atomic structure of graphene and the strengths of the electric field, as well as the valley mixing, valley position, and valley asymmetry.
W. Jaskólski (Wed,) studied this question.