Valley-dependent electron optics using quantum dots in bilayer graphene

Abstract

Electrostatically defined quantum dots (QDs) with layer-antisymmetric gating in Bernal-stacked bilayer graphene (BLG) open a local gap and generate a mass-like term with opposite sign in the two valleys, producing strongly valley-dependent scattering without magnetic fields, strain, or spin-orbit coupling. Building on this mechanism, we propose a tunable platform based on such QDs for valley-dependent electron optics in BLG. Using a four-band continuum model and a generalized multiple-scattering formalism, we analyze scattering of Gaussian electron beams from single- and multi-dot architectures and compute valley-resolved currents and angular profiles. A single dot produces distinct valley-dependent deflection, while multi-dot configurations enable enhanced control: identical-dot arrays act as valley splitters, whereas oppositely gated pairs function as valley filters. Combining these elements yields tunable generation, steering, and filtering of highly valley-polarized currents with strong suppression of forward transmission. The required energy scales, gate asymmetries, and device dimensions are within experimentally accessible regimes for dual-gated BLG, establishing quantum-dot arrays as a realistic platform for controllable valley-resolved electron optics.