Electrostatically confined trilayer graphene quantum dots

Electrically gating of trilayer graphene (TLG) opens a band gap offering the possibility to electrically engineer TLG quantum dots. We study the energy levels of such quantum dots and investigate their dependence on a perpendicular magnetic field $B$ and different types of stacking of the graphene layers. The dots are modeled as circular and confined by a truncated parabolic potential which can be realized by nanostructured gates or position-dependent doping. The energy spectra exhibit the intervalley symmetry ${E}_K^e(m)=\ensuremath{-}{E}_{{K}^{\ensuremath{'}}}^h(m)$ for the electron $(e)$ and hole $(h)$ states, where $m$ is the angular momentum quantum number and $K$ and ${K}^{\ensuremath{'}}$ label the two valleys. The electron and hole spectra for $B=0$ are twofold degenerate due to the intervalley symmetry ${E}_K(m)={E}_{{K}^{\ensuremath{'}}}[\ensuremath{-}(m+1)]$. For both ABC $[\ensuremath{\alpha}=1.5$ (1.2) for large (small) $R]$ and ABA $(\ensuremath{\alpha}=1)$ stackings, the lowest-energy levels show approximately a ${R}^{\ensuremath{-}\ensuremath{\alpha}}$ dependence on the dot radius $R$ in contrast with the $1/{R}³$ one for ABC-stacked dots with infinite-mass boundary. As functions of the field $B$, the oscillator strengths for dipole-allowed transitions differ drastically for the two types of stackings.