Electronic spectrum of a two-dimensional quantum dot array in the presence of electric and magnetic fields in the Hall configuration

We report calculations of the electronic spectrum of a two-dimensional lattice of coupled quantum dots, subject to external electric and magnetic fields in the Hall configuration. The quantum dots array was modeled by a periodic superposition of truncated, parabolic potential wells. By adopting the Landau gauge, a single-particle Hamiltonian was formulated, and its eigenfunctions were obtained as appropriately symmetrized, magnetic field-dependent Bloch functions. The magnetic field was consistently included in the corresponding Wannier functions, which were approximated by the eigenvectors of an isolated quantum dot in the presence of the external magnetic field, and multiplied by the Peierls’s phase.

Figure 1

Energy spectrum for the system, in the absence of external fields. $d=100\mathrm{\AA }$, $l_{\text{dot}}=30\mathrm{\AA }$.

Figure 2

Energy spectrum for the system, for a magnetic field corresponding to $N_{\varphi }=\frac{1}{3}$. $d=100\mathrm{\AA }$, $l_{\text{dot}}=30\mathrm{\AA }$.

Figure 3

Dimensionless energy spectrum, as a function of the external magnetic field intensity.

Figure 4

Energy spectrum, as a function of the magnetic field intensity. $d=100\mathrm{\AA }$, $l_{\text{dot}}=30\mathrm{\AA }$.

Figure 5

Energy spectrum for the system, for a magnetic field corresponding to $N_{\varphi }=\frac{1}{3}$, when an electric field of $F=10\mathrm{KV}∕\mathrm{cm}$ is also applied. $d=100\mathrm{\AA }$, $l_{\text{dot}}=30\mathrm{\AA }$.

Figure 6

Energy spectrum, as a function of the external magnetic field intensity, when an external electric field $F=10\mathrm{KV}∕\mathrm{cm}$ is also applied. $d=100\mathrm{\AA }$, $l_{\text{dot}}=30\mathrm{\AA }$.