Density functional study of collective electron localization: detection by persistent current.

We apply the optimized effective potential (OEP) implementation of density functional theory (DFT) to the model system of interacting spinless electrons on a quantum ring. The ring encircles a magnetic flux that induces a persistent current. In a perfect rotationally invariant system the current does not depend on the electron-electron interaction (the latter is characterized by a standard dimensionless parameter r(S)) and hence is not sensitive to the microscopic structure of the electron correlated state. This changes, however, if a symmetry-breaking external potential is introduced or, in a realistic system, due to the crystal lattice potential (Hamer et al 1987 J. Phys. A: Math. Gen. 20 5677-93). In our model, we calculate the persistent current as a function of r(S) in the presence of a weak Gaussian-shaped 'impurity' potential. We find that while below a threshold value r(S)r(S)(c). This signals the formation of an electron Wigner crystal pinned by the impurity potential. The electron density, homogeneous below r(S)(c), indeed shows a periodic modulation at r(S)>r(S)(c). The modulation amplitude follows a (r(S)-r(S)(c))((1)/(2)) behaviour which is characteristic for a second-order phase transition, as expected in the mean-field-type DFT-OEP approach. Our calculation shows that the macroscopic current, which is a quantity directly accessible in DFT, can serve as an indicator of the formation of a correlated electron state.