Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

An emergent class of two-dimensional Dirac materials is α-T3 lattices that can be realized by adding an atom at the center of each unit cell of a lattice with T3 symmetry. The interaction strength α between this atom and any of its nearest neighbors is a parameter that can be continuously tuned between zero and one to generate a spectrum of materials. We investigate the fundamentally important and practically relevant issue of quasiparticle confinement for the entire spectrum of α-T3 materials. Except for the two end points, i.e., α=0,1, which correspond to the graphene and pseudospin-1 lattices, respectively, the time-reversal symmetry is broken, leading to the removal of level degeneracy and facilitating confinement. Taking the approach of quantum scattering off an electrically generated potential cavity in the quantum-dot regime, we characterize confinement by identifying and examining the scattering resonances. We study a number of cavities with characteristically distinct classical dynamics: circular, annular, elliptical, and stadium cavities. For the circular and annular cavities with classically integrable and mixed dynamics, respectively, the scattering matrix can be analytically obtained, so the scattering cross sections and the Wigner-Smith time delay associated with the resonances can be calculated to quantify confinement. For the elliptical and stadium cavities with mixed and chaotic dynamics in the classical limit, respectively, the scattering-matrix approach is infeasible, so we adopt an efficient numerical method to calculate the scattering wave functions and experimentally accessible measures of confinement such as the magnetic moment. The main finding is that, for all the cases, the regime of small α values offers the best confinement possible among the spectrum of α-T3 materials, which is general and holds regardless of the nature of the corresponding classical dynamics.