Exchange-correlation orbital functionals in current-density functional theory: Application to a quantum dot in magnetic fields

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a two-dimensional quantum dot in external magnetic fields is investigated. Excellent agreement with the quantum Monte Carlo results is obtained when self-interaction corrected correlation energies from the standard local spin-density approximation are added to exact-exchange results. Full self-consistency within the complete current-spin-density-functional framework is found to be of minor importance.

Figure 1

(Color online) Total ground-state energy (minus $6\Omega =6\sqrt{{\omega }_0^2+{\omega }_c^2/4}$) in a six-electron quantum dot as a function of external magnetic field (SI units). The results have been calculated by using the EXX, EXX with LSDA correlation $\left(\text{EXX}+\text{cLSDA}\right)$, and EXX with the corrected LSDA correlation $\left(\text{EXX}+\text{c}\uparrow \downarrow \text{LSDA}\right)$. The LSDA and the QMC results (Ref. 8) are shown for comparison. The arrows mark the points where the ground-state configuration $\left(L_z,S_z\right)$ changes.

Figure 2

(Color online) Angular components of the paramagnetic and diamagnetic currents, $j_{p\theta }$ and $j_{d\theta }$, and their sum for the $\left(-21,3\right)$ state at $B_0=11\text{T}$. The dashed line shows the exchange vector potential for the same configuration.