Asymmetry of hole states in vertically coupled Ge double quantum dot

The two lowest single-particle hole states in the vertically coupled Ge/Si double layer quantum dots are investigated numerically by using the single-band heavy hole effective mass approximation and six-band Kronig-Penney model, respectively. The calculated results indicate that within the frame of several-band coupled model, the bonding-antibonding ground-state transition and a bonding-antibonding energy anti-crossover phenomenon are observed with interdot distance increasing. These results have not been observed previously in those single-band model calculations. The analysis of the wavefunction component of bonding-antibonding hole state shows that the contribution ratios of light, heavy and spin-orbital-split-off hole states to the characteristic hole wavefunction vary with the increase of the vertical coupled distance, resulting in the ground state wavefunction changing from bonding states to antibonding ones finally.