Optical Properties of Gated Bilayer Graphene Quantum Dots with Trigonal Warping

We determine the optical properties of gated bilayer graphene quantum dots with trigonal warping (TW) of single-particle energy spectra. The lateral structure of metallic gates confines electrons and holes in a quantum dot (QD) electrostatically. The gated bilayer graphene energy spectrum is characterized by two K-valleys surrounded by three minivalleys with energies depending on the applied vertical electric field. Employing an atomistic tight-binding model, we compute the single-particle QD states and analyze the influence of TW on the energy spectrum as the lateral confining potential depth varies. We find a regime where the QD levels are dominated by the presence of three minivalleys around each K-valley. Next, we compute dipole matrix elements and analyze the oscillator strengths and optical selection rules for optical valence to conduction band transitions. We then include electron-electron interactions by first computing the microscopic Coulomb matrix elements, electron self-energy, and solving the Bethe-Salpeter equation to obtain the excitonic spectrum. Finally, we obtain the absorption spectrum for a shallow confining potential depth, which further amplifies the effects of TW on the optical properties. Our results predict the existence of two degenerate bright exciton states, each built of the three minivalley states that do not exist in the deep confinement regime, where the effects of TW are negligible.
Comment: 9 pages, 6 figures