Three-dimensional self-consistent simulations of symmetric and asymmetric laterally coupled vertical quantum dots

We use three-dimensional self-consistent simulations within the local spin density approximation to study electron charging effects in symmetric and asymmetric laterally coupled vertical quantum dots. Electron charging spectrum in the symmetric double dot system shows shell structure corresponding to a system of two coupled two-dimensional harmonic oscillators. The regular sequence of bonding and antibonding molecular states retains its character with change in the side gate bias and number of electrons in the system. We also present results for two cases of structural asymmetry, with 5% and 10% asymmetry between the two dots. With structural asymmetry, the single particle eigenstates undergo hybridization with level crossing and anti-crossing. As the number of electrons in the double dot system increases, electrostatic interactions dominate over structural asymmetry and restore the symmetry of the high energy states. Our results also indicate that the greater the structural asymmetry, the larger the number of electrons required for the structural asymmetry to become relatively insignificant. We further explore the 5% asymmetric system by applying different biases to the left and right side gates, with larger bias being applied to the smaller dot. While this restores the symmetry of higher energy states, lower energy states still reflect the structural asymmetry.