Energy levels of ABC-stacked trilayer graphene quantum dots with infinite-mass boundary conditions

Abstract

Using the continuum model, we investigate the confined states and the corresponding wave functions of ABC-stacked trilayer graphene (TLG) quantum dots (QDs). First, a general infinite-mass boundary condition is derived and applied to calculate the electron and hole energy levels of a circular QD in both the absence and presence of a perpendicular magnetic field. Our analytical results for the energy spectra agree with those obtained by using the tight-binding model, where a TLG QD is surrounded by a staggered potential. Our findings show that ($i$) the energy spectrum exhibits 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, ($ii$) the zero-energy Landau level (LL) is formed by the magnetic states with $m\ensuremath{\leqslant}0$ for both Dirac valleys, that is different from monolayer and bilayer graphene QD with infinite-mass potential in which only one of the cones contributes, and ($iii$) groups of three quantum Hall edge states in the tight-binding magnetic spectrum approach the zero LL, which results from the layer symmetry in TLG QDs.